futurefarm deliverable 6 - au...

Project no. 212117 Project acronym: FUTUREFARM Project title: Integration of Farm Management Information Systems to support real‐time

management decisions and compliance of management standards Instrument: Collaborative project Thematic Priority: THEME 2 FOOD, AGRICULTURE AND FISHERIES, AND BIOTECHNOLOGY

Deliverable 6.3: Preliminary report on optimized fleet management to reduce

energy consumption and costs

Due date of deliverable: 31/12/2009 Actual submission date: 15/12/2009

Start date of project: 1st January 2008 Duration: 36 months

Work package 3: “Analysis Influences of robotics and biofuels on economic and energetic efficiencies of farm production” Organization name of lead contractor for this deliverable: WUR Authors: Vougioukas, S. (AUTH), Bochtis, D. (AU), Sørensen, C. (AU), Oksanen, T. (TKK), Guzman, H. (UA).

Project No. 212177 FutureFarm D.3.3

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REPORT INTRODUCTION ....................................................................................................................................... - 4 -

1 FLEET MANAGEMENT: LITERATURE REVIEW .............................................................................................. - 5 -

1.1 INTRODUCTION TO AGRICULTURAL FLEET MANAGEMENT .................................................................................... - 5 - 1.2 PROBLEM DESCRIPTION ................................................................................................................................. - 7 - 1.3 PROBLEM DEFINITION ................................................................................................................................... - 9 - 1.4 OFF‐LINE FLEET OPERATIONS PLANNING ......................................................................................................... - 11 -

1.4.1 Scheduling of fleet operations ........................................................................................ - 12 - 1.4.2 Harvesting in forestry ..................................................................................................... - 13 - 1.4.3 Harvesting in agriculture ................................................................................................. - 14 -

1.5 FIELD TRAFFIC PLANNING ............................................................................................................................. - 15 - 1.5.1 Independent machines ................................................................................................... - 15 - 1.5.2 Cooperating machines .................................................................................................... - 19 -

1.6 ON‐LINE FLEET MANAGEMENT ...................................................................................................................... - 20 - 1.6.1 Dynamic scheduling of fleet operations ......................................................................... - 21 - 1.6.2 Field traffic planning ....................................................................................................... - 24 - 1.6.3 Field traffic control .......................................................................................................... - 26 -

1.7 SUMMARY AND CONCLUSIONS ..................................................................................................................... - 29 - 1.8 REFERENCES ............................................................................................................................................... - 30 -

2 FLEET MANAGEMENT: ASSESSMENT OF POTENTIAL SAVINGS ................................................................ - 36 -

2.1 INTRODUCTION .......................................................................................................................................... - 36 - 2.2 IDENTICAL MACHINES ................................................................................................................................. - 37 -

2.2.1 Methods .......................................................................................................................... - 37 - 2.2.2 Simulation Results ........................................................................................................... - 42 -

2.3 FLEET OF COOPERATING MACHINES .............................................................................................................. - 59 - 2.3.1 Methods .......................................................................................................................... - 59 - 2.3.2 Results ............................................................................................................................. - 62 -

2.4 CONCLUSIONS ............................................................................................................................................ - 65 - 2 . 5 R E F E R E N C E S ................................................................................................................................ - 67 -

3 FLEET MANAGEMENT: DATA AND INFORMATION REQUIREMENTS ........................................................ - 75 -

3.1 DATA AND INFORMATION FLOWS .................................................................................................................. - 75 - 3 . 2 D A T A A N D I N F O R M A T I O N R E Q U I R E M E N T S .................................................................. - 78 - 3 . 3 C O M M U N I C A T I O N S I N F R A S T R U C T U R E ............................................................................ - 79 -

3.3.1 Dispatcher‐to‐vehicle ...................................................................................................... - 79 - 3.3.2 Vehicle‐to‐vehicle ........................................................................................................... - 80 -

3 . 4 C O N C L U S I O N S ................................................................................................................................ - 83 -

4 APPENDICES................................................................................................................................................ - 84 -

Project co‐funded by the European Commission within the Seven Framework Programme (2007‐2013)

Dissemination Level

PU Public X

PP Restricted to other programme participants (including the Commission Services)

RE Restricted to a group specified by the consortium (including the Commission Services)

CO Confidential, only for members of the consortium (including the Commission Services)


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APPENDIX A: TERMINOLOGY ..................................................................................................................................... - 84 - APPENDIX B: REPRESENTATIVE SCHEDULING PROBLEMS ................................................................................................ - 87 -

4.1.1 Project scheduling ........................................................................................................... - 87 - 4.1.2 Job shop scheduling ........................................................................................................ - 88 - 4.1.3 Vehicle routing ................................................................................................................ - 89 - 4.1.4 Solution techniques ........................................................................................................ - 90 -

REPORT INTRODUCTION

Deliverable 6.3 is a report titled “Preliminary report on optimized fleet management to reduce energy consumption and costs “. Its objectives are: a) to investigate the potential savings in energy consumption and production cost by optimising single and multiple machine (fleet) machine usage at the farm level b) to investigate the required data, information flow and information management for optimised farm mechanization management comprising single machines or fleets of conventional, or autonomous machines. The report is divided into three sections. Section 1: This section presents a scientific literature review to assess what the research community has shown to be possible for planning and managing the operation of teams of conventional and semi‐autonomous machines. Then, it presents the currently available commercial technology for planning and managing the operation of agricultural machine fleets. It proceeds by identifying the limitations of currently available commercial research‐prototype systems. Finally it offers recommendations for bridging the gaps between what is commercially available, and what constitutes state of the art in research, and develops a roadmap for what needs to be developed further. Section 2: This section presents an assessment of the energy and cost savings that could be achieved when farming operations (e.g., fertilising, grain harvesting) are performed by many machines (fleet) operated in an optimal way, as opposed to the standard operation of current agricultural practice. The assessment will be based on available state of the art algorithms which model, optimise and simulate the execution of agricultural operations at the farm level. Section 3: This report investigates the required data, information flow and information management for optimised farm mechanization management comprising single machines or fleets of (autonomous) machines. It compares the currently available data flow with the required one, identifies the limitations of current technology and suggests directions for future technological development.


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1 Fleet Management: Literature Review

Vougioukas2 S G; Bochtis1 D D; Sørensen1 C G; Oksanen3 T; Guzman4 J L.; van Henten5 E.

1Aristotle University of Thessaloniki, Faculty of Agriculture, Department of Agriculture Engineering, Greece.

2 University of Aarhus, Faculty of Agricultural Sciences, Department of Agricultural Engineering, Blichers Allé 20, P.O box 50, 8830 Tjele, Denmark.

3 Helsinki University of Technology, Department of Automation and Systems Technology, P.O. Box 5500, 02015 TKK, Finland.

4 University of Almería, Department of Languages and Computation, Ctra. Sacramento s/n, 04120, Almería, Spain.

5 Wageningen University and Research Centre, Bornsesteeg 59, 6708 PD Wageningen, The Netherlands,

1.1 Introduction to agricultural fleet management

By 2050, global population is projected to be 50% larger than at present and global grain demand is projected to double (Alexandratos, 1999). The U.S. Department of Energy (DOE) aims to displace 30% of the 2004 gasoline use (60 billion gal/yr) with biofuels by 2030 as outlined in the Energy Independence and Security Act of 2007, which will require 700 million tons of biomass to be sustainably delivered to biorefineries annually. In European Union, the biofuel directive set as a target to blend 10% of bio‐based fuels with conventional gasoline and diesel for road transport by 2020, although the goal is under reconsideration due to environmental and social concerns. The necessary biomass for energy will come mainly from energy crops as well as agricultural residues. Pressures like the ones mentioned above have been major thrusts for the intensification of agricultural production and can explain the demand for agricultural machines of increasing size, capacity and cost. Furthermore, the introduction of sensors, actuators, software, on‐board networking and auto‐steering technology is gradually transforming conventional agricultural vehicles into supervised semi‐autonomous machines which can traverse field lines, turn at headlands and control implements automatically. Given the large amounts of capital invested in such high‐efficiency agricultural machinery and the computing and communication platforms they carry, it is both imperative and technologically feasible to plan and coordinate the execution of field operations by fleets of modern agricultural machines in an optimal manner. Such planning has the potential to lower operational cost by reducing fuel consumption and the number of required machines and operators, to reduce emissions and to increase machine utilisation. In parallel, research shows that an alternative mechanisation model which relies on smaller and more intelligent multi‐robot systems rather than on a few large machines (Blackmore et al., 2005; Pedersen et al., 2006; Blackmore et al., 2007) may bring significant benefits. Examples include micro‐spraying for significant reduction of applied chemicals, automated documentation for traceability, elimination of soil compaction, independence of production from labour shortage, effective scouting for disease, etc.


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It is likely that both mechanisation models will coexist in the not so distant future. Such a development would increase the demand for advanced automated fleet management which will act as mission planner for teams of autonomous robots. In an agricultural context, a Fleet Management System (FMS) is regarded as a practical tool for managing a fleet of vehicles to improve resource allocation, scheduling, routing and monitoring of vehicles involved in agricultural operations (Auernhammer, 2001). Existing commercial FMS for agriculture (e.g., PROGIS LoGIStic™, Claas Telematics™, Trimble’s Agricultural Manager™, John Deere JDLink™) focus on telematics, i.e., real‐time monitoring of vehicle operational parameters during in‐field operation and transport, data collection and documentation for accounting, statistics, and communication with the drivers. Optimal routing via the road network is not present in the majority of systems and automated dispatching and optimal dynamic scheduling tools are not widely available. This is in sharp contrast with commercial fleet management and dispatch systems in other industries, like trucking, courier and transport services, construction and mining where automated scheduling, dispatching and routing is the norm. A major goal of the first section of this report is to provide a systematic analysis of the theoretical problems involved with fleet management, to review solutions to these problems as those have been developed for agricultural operations, and to provide links to approaches in other areas, such as transportation science, automation and robotics. An important consideration in fleet management for agriculture is that operations are being performed at different levels. These levels require management at different spatial and temporal resolution. This is illustrated in Figure 1 for the case of biomass harvesting.

Figure 1 The total supply chain of integrated field operations (Sørensen and Bochtis, 2009).


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For the purposes of analysis, fleet management will be expressed as a sequential decision making process, i.e., a systems control problem. This framework does not offer tools for solving the problem, but it provides the insight to analyse the various levels of field operations and examine their relations, coupling and different requirements. Special attention will be given to the management of machine teams at the farm level (in‐field operations), for two basic reasons. First, fleet scheduling and routing is an established field and assessments of cost, time and energy savings have been performed for them. This does not appear to be the case for in‐field operations. Second, in‐field operations are strongly coupled with higher‐level fleet management, i.e., decisions taken in one affect the other. Therefore, greater savings in energy, time and overall cost may be achievable by optimising fleet operations at the farm level as well as the fleet scheduling and routing level. The application domain of this report is on management of teams of semi‐autonomous vehicles, i.e., vehicles which can operate autonomously in the field for parts of an operation (e.g., row auto‐guidance, headland turning) but require a human operator to execute parts of the operation and to supervise the entire operation. Such machines constitute state of the art, when it comes to single machine operations. Multi‐vehicle cooperation and coordination is not currently available commercially but it has been demonstrated experimentally (Johnson et al., 2009) using off‐the shelf technology and lies within current technological capabilities.

1.2 Problem description

Let us consider the following general scenario. We are given a set of separate fields and for each field a sequence of agricultural field operations which are associated with it. A minimum time lag is given for any given operation, which implies that the operation cannot start before a specified time has elapsed after the finish of one of its predecessor operations (e.g., necessary set‐up times for various types of machines). Similarly, a maximum time lag exists for any given operation which implies that the operation must be started, at the latest, a certain amount of time after the finish of one of its predecessor. The presence of a combination of both minimum and maximum time lags for a given pair of operations result in a time window during which an operation has to be started in relation to the finish of a preceding operation. If all operations are known at start time, a time window may be given for the execution of all operations in all fields; otherwise, new operations may arrive at any time. Except for the agricultural operations, there is an “idle” operation in which a machine is idle, a “setup” operation in which a machine is being setup for an agricultural operation, and a “transfer” operation in which a machine is moving or is being transferred from one field to another. Also, a fleet of (semi‐)autonomous machines of different types is available (e.g. corn harvesters, tractors) and for each type, a fixed set of individual machines is always available, with different operational characteristics. An operation may require only one type of machine (e.g., tractor in plowing), or several types of cooperating machines (e.g., harvester and unloading truck in grain harvesting). For an operation, one or more machines of the same type can be used at the same time (e.g., three corn harvesters in the same field). A machine can only perform one operation at a time but it may also be or become temporarily unavailable at any time (due to refuelling, maintenance, etc). Finally, a number of workers are available. Each worker can set up and operate specific types of machines and the setup and operation of a machine may require certain numbers of workers.


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If we were to take a snapshot at any time instant within the specified time window of all machines’ activities we would see that each machine would be either idle, travelling towards a target field, being setup in a field for operation, or operating in a field. Consider a simple example with three farms with one field each, two operations per field (swathing ~ operation 1, harvesting ~ operation 2), with

operation 1 preceding operation 2, and six machines, three of type 1 ( 1 2 31 1 1, ,M M M ) and three of type 2

( 1 2 32 2 3, ,M M M ) respectively. Initially al machines are located in farm 1. The following figure shows an

example of the operation of each machine over time.

Figure 2 Examples of machine fleet operation over time (Basnet, et al., 2006)

For example, at time instant tk=2 two machines ( 11M , 2

1M ) are being setup for swathing in field 1, one

machine ( 31M ) is moving towards farm 3 and the machines of type 2 are idle, since harvesting must be

performed after swathing. At time instant tk=8 two machines ( 11M , 2

1M ) are swathing in farm 1 and

machine 31M is being setup in farm 3. Obviously there are many different combinations of machine

assignments and sequences that could accomplish the overall task. The performance of each combination with respect to a desired criterion will vary. Now, consider a combination in which three harvesters were assigned to operate in a field concurrently and assume that two carts are available in that field for unloading the harvesters’ grain tanks. During the agricultural field operation (i.e., inside the “OP 1” boxes of Figure 2) the traffic of the harvesters and trucks must be carefully coordinated (e.g., Figure 3) so that important efficiency parameters such as the idle times of the harvesters, the total dead distance and the fuel are minimised.

Figure 3 Cordinated traffic pattern for harvesting operation (Bochtis et al., 2007b)


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Clearly, the time, fuel, and cost requirements of an agricultural field operation such as harvesting are not fixed, or even completely known in advance. They depend – possibly non linearly ‐ on factors, such as: number and operational characteristics of assigned machines, field geometry, a machine’s field visiting order which changes the entry and exit points of the machine in a field, the traffic of the machines and the work demand, which can be affected by soil resistance, yield spatial distribution and moisture, etc. Therefore, the assignment of operations to machines over time is strongly coupled with the way each operation is executed; hence the entire problem should be solved together, if global optimality is desired, even under the assumption that all information relevant to the operations is known in advance. Finally, conditions may change during the execution of operations by the machine fleet. For example: a machine may break or a new one may become available; a new field may need to be cultivated; a field’s yield may be much higher than the predicted; the weather may change suddenly and consequently short completion time may become more important that low fuel cost. Therefore, in practice the assignment of operations and the coordination of their execution should be dynamic and not static.

1.3 Problem definition

Fleet management can be expressed as sequential decision making/control problem. The goal is not to utilise control techniques to solve the problem, but to state it in a general form, analyse the levels of field operations and examine their relations, and show how existing approaches correspond to simplified versions of the general problem and assess the possibilities for possible future improvements.

Definition: Fleet Management System In the context of this work, a fleet management system (FMS) is a sequential decision making system (control system). Given sets of operations, machines, constraints, and some utility function, an FMS at every time instant:

a) Assigns a specific operation to each machine b) Coordinates the execution of each operation by the coalition of machines assigned to it.

The above definition regards a fleet management system as a dispatcher which schedules machine assignments to fields and also routes inter‐field transfers, and as a coordinator which orchestrates the in‐field operations. Hence, the FMS operates at two distinct levels. For the purposes of this study, any other machine‐related issues such as maintenance are not included in fleet management. Task (a) constitutes a resource scheduling and routing problem. At any time instant tk, each machine must be assigned to a certain operation. Operations may include field operations, set‐up operations, inter‐field transportation, etc. An assignment can be thought of as a vector containing ones and zeros,


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where zero (at an appropriate location within the vector) means that a machine is not assigned to execute an operation, and one means that it is. Each assignment contributes an instantaneous assignment cost. For example, the cost could be the distance travelled, or the fuel required for moving the assigned machine from its current position and operation towards the location of its assigned operation within the time interval [tk tk+1]. Note that in the general case, at any time instant a machine may suspend its execution in the current operation ‐ before finishing it ‐ and be reassigned to a different operation. This mode of operation is called pre‐emptive operation. Task (b) is a control problem. In general the state of each machine may have continuous and discrete components (e.g., speed, implement up/down). Therefore, the FMS must provide at each time instant tk suitable continuous and discrete control commands (e.g., speed=2.2 m/s, implement=up), which execute the assigned collective operation for each machine in each coalition. The continuous control commands are related to the control of a machine’s motion, whereas the discrete controls involve typically various implements. The execution of a field operation by a coalition is associated with: an instantaneous execution cost, which stems from the actual operation/motion of the coalition

members in the assigned field (e.g., distance, or fuel needed to move within the interval [tk tk+1]).

an instantaneous execution utility, which expresses the benefit from executing the operation (e.g., quantity of harvested grain, field area covered) within the interval [tk tk+1].

The overall goal of an FMS is to plan and orchestrate the execution of all operations so that the cost minus the utility of the fleet during the entire operation is minimised; equivalently, the utility minus all cost is maximised. This has to be done while satisfying any imposed constraints. In the agricultural context these constraints may be related to weather, crop physiology, soil conditions, workforce availability, market demand, etc. According to the principle of optimality, an optimal policy has the property that whatever the initial state and initial decision are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision (Bellman, 1957). The optimal solution to the fleet management problem can be expressed as dynamic programming problem: compute at each time instant tk, a control vector FMk which depends on the current state of the fleet and contains solutions to problems (a) and (b) which optimise the cost‐to‐go:

arg min , 0,1,...,

END

k k k kn k

FM AssignmentCost ExecutionCost ExecutionUtility k T (1)

The above formulation describes a fleet management problem in which any cost, utility term or problem parameter may change at any time. It is based on a time‐indexed formulation (Dyer and Wolsey, 1990) which discretizes the planning horizon of the problem into time periods. A time‐indexed formulation has very large size because decision variables are defined at each time instant. As a result, for instances with many operations or operations with large processing times, the memory requirements and the solution times will be huge. An agricultural FMS operates at two levels: in‐field traffic coordination requires real‐time control of the fleet and therefore very fine time discretization, in the order of fractions of a second; scheduling and routing is a slower decision process and a time


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discretization of several minutes might suffice. Expressing both operations in a single formula implies that a common fine time discretization must be used. Clearly the formulation is not intended to be used for solving the fleet management problem, especially in an agricultural context in which the planning horizon may be several weeks. However, it is ideal for expressing the problem as a general sequential decision making problem and using existing analysis to identify and classify different versions of the problem (Bertsekas, 1976). Let us consider the fleet management problem under the assumption that all necessary information for solving equation (1) is available from the beginning and that nothing changes after the solution has been constructed. The assumption of available information includes the following cases:

1. all involved quantities are deterministic and known a‐priori. The problem is deterministic and the solution can be found off‐line, by a‐priori optimisation of equation (1). The solution will be an open‐loop policy.

2. some quantities are random (stochastic) with known probability distributions. The problem is stochastic and can be solved either off‐line, resulting in an open‐loop policy which will be most likely suboptimal, or on‐line using an optimal closed‐loop policy.

3. some quantities change during operation or are unknown before the beginning of the operations and reveal themselves during the operation of the fleet. For example, the number of fields may be unknown because many new orders arrive for cultivating fields. The problem is dynamic and can only be solved on‐line using appropriate policies, which depend on current state.

1.4 Off‐line fleet operations planning

Existing approaches to off‐line fleet operations planning, i.e., the deterministic problem will be reviewed first. Task (a) is essentially a static resource scheduling and routing problem, i.e., allocating specific units from a limited resource pool to alternative spatially remote possible uses over time. If only the number of resource units assigned to each operation were to be computed, the problem would be a resource capacity scheduling problem. The machines and human personnel constitute the “resources” and the field operations correspond to “uses” which demand utilisation of the resources. Numerous variations of this problem have been studied in manufacturing, project management, computing and networking, human resources management, logistics, robotics and many other application fields (see Appendix B: Representative scheduling problems). Under the assumption of determinism, task (b) is equivalent to a motion planning problem for one or multiple machines working in the field. This problem has been studied extensively in the robotics and automation literature. In the context of agricultural fleet management motion planning is not relevant for inter‐field motion because over the rural or public road network the machines are either carried, or they simply follow the road. On the other hand, motion planning in the field (aka traffic planning) involves area coverage, since entire areas need to be cultivated or harvested and also multiple machine coordination when many machines operate in the same field. The next two sections will


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present the existing approaches to the problems of agricultural fleet operations scheduling and in‐field motion planning within the agriculture‐related literature.

1.4.1 Scheduling of fleet operations

The problem of agricultural fleet operations planning is related to other scheduling and routing problems like the vehicle routing problem (VRP), the job‐shop scheduling problem (JSSP), the project scheduling problems (PSP) etc. However, there exists one major difference which is the operations’ execution costs. In deterministic scheduling problems the execution costs are known in advance, and are typically fixed. For example, in JSSP the operation cost relates directly to the time a processing machine is busy servicing a job. In VRP the execution cost corresponds to the time spent at each customer‐node. The execution cost of performing an agricultural field operation, depends on factors, such as: number and operational characteristics of assigned machines, field geometry, work demand (e.g., soil resistance, yield, or pest infection spatial distribution), and traffic of the vehicles. The last, vehicle traffic is a direct result of the motion plan generated by the FMS itself. Therefore, tasks (a) and (b) are strongly coupled and ideally must be solved together, if global optimality is desired, even under the assumption that all information relevant to the operations is known in advance. Various versions of deterministic scheduling of machines and crew resources for operations in dispersed locations have been addressed in the areas of agricultural and forest science; all of them deal with harvesting. Due to the long growing period of trees, harvest planning in forestry is done at three levels: strategic, tactical and operational. The operative phase focuses on scheduling harvest crews on a monthly or weekly basis, truck scheduling and choosing bucking instructions. This phase is the one closest to agricultural harvest planning because it spans periods of weeks to months, whereas the first two levels are concerned with long term financial and forest growing planning. In general, forest harvesting involves decisions pertaining to:

a) when harvest units (forest parts, or stands) are harvested b) who harvests them (machine and crew) c) what log‐types are made (bucking / cutting patterns of stems into merchantable tree‐logs) d) which customers are supplied

Problems (a), (b) are closely related to resource scheduling for multi‐field harvesting in agriculture. Problem (d) is also similar to transferring cropped product to silos, bio. Problem (c) is related to traffic planning for agricultural harvesting, in the sense that the stem‐cutting (bucking) strategy affects the required time and cost of the operation, just like traffic patterns affect time and cost for harvesting. Additionally, in forestry the bucking strategy affects strongly the yield (merchantable tree‐logs) whereas in agriculture traffic does not influence the field’s yield. Also, the introduction of green‐up adjacency constraints (not cutting nearby forest areas) complicates the harvest scheduling problem for forestry.


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1.4.2 Harvesting in forestry

The problem of allocating stands and cutting patterns to logging crews for a single time period (no scheduling) was addressed by Murphy (1998). Solutions which maximised total profit were computed using tabu search. Brumelle, et al., (1998) solved a forest harvest scheduling problem with green‐up constraints. These are adjacency constraints which aim to eliminate large clear cut areas and dictate for example that the trees in a block must reach a certain mean height before any adjacent block can be harvested. The introduction of these adjacency constraints complicates the harvest scheduling problem, as it becomes combinatorial in nature. Before the emergence of such constraints linear programming had been applied to solve timber harvesting problems for over 25 years (Johnson and Scheurman, 1977). The problem of planning harvest sequences or schedules for harvest crews for a period of 4–6 weeks was addressed by Karlsson et al., (2003). The harvesting of areas was planned in order to meet industrial demand. The total cost included harvesting, transportation, and storage. One considerable cost was due to the quality reduction of logs stored at harvest areas. Areas are of varying size and the composition of assortments in each area was different. Each harvest team had different skills, a different home base, and different production capacity. There was also a cost related to road opening (restoring, snow removal). A mixed integer programming model was developed for the problem with 0/1 variables representing schedules. A commercial MIP solver and a heuristic solution approach were used and compared. Mitchell (2004) modelled and solved various versions of operational harvest scheduling which included: assigning forest harvesting crews to locations within a forest in the short‐term (4‐8 weeks); instructing crews to harvest specific log‐types and allocating these log‐types to customers; maximising profitability while meeting customer demand. The problem was modelled as a Mixed Integer Linear Program (MILP) and was solved using techniques developed in previous work on aircraft crew scheduling optimisation (Ryan 1992). These techniques include constraint branching and column generation. Pre‐emptive scheduling was made possible by introducing the concept of relaxed integer solutions. A traditional integer solution requires harvesting crews to move between harvesting locations at the end of a week (time period). However, a relaxed integer solution allows crews to move at any time during a week and provides improved solutions. Moura and Scaraficci (2008) treated the forest planning problem stemming from the daily operation of some large pulp and paper companies. The problem consists in planning and scheduling harvest and transportation activities for each day in a planning horizon of around one year, while satisfying a sizable and complex set of constraints related to the structure of the harvest areas, structure and productivity of the harvest teams, transportation conditions during the rainy seasons, and some properties of the harvested logs. The cost function was a weighted sum of terms which penalised: the volume of logs not delivered on time; the distances of wood quality index and the average density of the logs from the desired values; the kilometres covered by the teams; the number of periods before or after the appropriate time waiting window the logs were delivered. A hybrid approach was proposed which focused on the GRASP (greedy randomized adaptive search procedure) metaheuristic


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and on linear models. Other techniques such as construction based on memory, path‐relinking, and recombination methods were used to enhance the basic GRASP procedure.

1.4.3 Harvesting in agriculture

Fokkens and Puylaert (1981) developed a linear programming planning model for the management of harvest operations at the large scale grain farm. Their objective was to minimise the total cost for harvesting, which included: cost of field losses (crops are ripe and cannot be harvested at that moment so the grain falls or germinates), cost of resource capacities for the harvesting period, and cost of moving resources from one parcel of land to another and for transferring grain to silo elevators for drying. The decision variables included: the number of combine‐harvesters, tractors and grain transport‐wagons allocated to parcels, the transfers of machines between parcels and from parcels to silos. Their model uses numerous parameters such as number of threshing hours per hectare per crop, expected yield per hectare of a crop, the size of each parcel, the available resource capacities, the delays and costs due to machine transfer between parcels. The solution resulted in optimal capacity scheduling of the resources, i.e., how many machines of each type process each parcel. The problem of assignment specific machines to parcels was not addressed. The implicit assumption was that the machines of each type (harvesters, tractors, transport wagons) had identical capacities. Furthermore, only a single type of field operation, i.e., scheduling was addressed. In the work of Bin Deris and Ohta (1990) scheduling for rice production in numerous farms was scheduled in two phases. First, the field operations themselves were scheduled (seedling, planting, field maintenance, harvesting) on a yearly basis. The criterion was minimisation of required machines and dynamic programming was used. In a second stage, given the sequence of operations and machine types with different operational characteristics, the weekly assignment of machine capacity and required transfer was expressed as a linear programming transportation problem. The objective function was the cost of operation in the field plus transfer. Higgins et al., (2004) developed a modelling framework identifying the key drivers and links in the complex system of sugar cane harvesting and transport operations in Australia. It was argued that optimising the entire system as a single entity is too complex and that although overall optimality may be achieved, conflicts between whole‐of‐system objectives and those of individual system components in the sugar industry negate this advantage. Each harvester was assumed to be located at a particular farm. A capacitated clustering problem was formed to solve the problem of allocating farms to harvesters. The objective was to form a set of harvesting groups so that the sum of distances from the assigned harvester to the centre of the harvesting group is minimised. This problem was solved by combined simulated annealing and tabu search. Sugar cane is transported by truck from the fields to railway sidings and then to processing plants via railway. For this reason, transport planning was done by adopting capacity planning models from railway applications, instead of using scheduling methodologies. Foulds and Wilson (2005) focus on harvesting of renewable resources such as rape seed and hay on a single farm, in the presence of machine and labour resource constraints and minimum and maximum time lags between successive operations. The duration of each operation is dependent upon the combination of constrained resources allocated to it. Also, equipment and worker capacity allocation is


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restricted. Further, minimum or maximum time lags on the start and completion of operations are imposed. The problem was expressed as 0‐1 integer programming (IP) and two heuristics are compared against the exact optimal solution found by the commercial integer programming code XPRESS‐MP. Basnet et al., (2006) extended this approach to scheduling of operations that are carried out by contractors who harvest crops at numerous farms. Since harvesting at more than one farm is addressed, inter‐farm travel times are also taken into account. The problem was expressed as an integer programming (IP) problem containing mostly 0‐1 variables. An example problem involving three farms, two types of operations in each farm (swathing, harvesting) and three machines/crews for each operation was solved. A greedy heuristic and the Tabu search heuristic were used and compared against the exact solution to solve it. If more than ten farms and four operations were involved, the IP software failed to converge within the pre‐specified cut‐off time of three hours. The model is sophisticated, yet it is constrained to a single type of operation (harvesting) and performs capacity scheduling and not scheduling of individual units (assignment).

1.5 Field traffic planning

Planning field traffic in agricultural fields involves in general:

a) Agricultural field area coverage: the entire field area must be cultivated or harvested by machines with a given working width

b) Subfield and swath traversal planning: the optimal subfield and swath traversal sequences must be generated so that dead distances are minimised

b) Headland turning: vehicles need to manoeuvre at the field boundary in a way that minimises dead distances and guarantees no collisions

When many machines operate in the same field there are two classes of operations which have different characteristics. In one class the machines are independent of each other, i.e., they do not share any resources. In such cases, machine coordination planning is not necessary because the machines can simply work on different swaths or parts of the field. The other class of operations is cooperative field operations which are executed by one or more primary unit/s performing the main work task and one or more service unit/s supporting it/them. For example, in a harvesting operation a self‐propelled harvester may be supported by transport wagons used for out‐of‐the field removal of harvested grain. Similarly, in fertilising operations a tractor carrying a sprayer is supported by transport vehicles carrying the fertiliser for the refilling of the application unit. Such operations require careful planning of the coordination in order to achieve high efficiency.

1.5.1 Independent machines

The complete area coverage problem (visiting all points in free space) for known and unknown environment, has been researched extensively in the robotics literature. It has been shown to be related to the covering salesman problem and proven to be NP‐hard. (Arkin et al., 2000). Specifically, the covering salesman problem is a variant of the travelling salesman problem where, instead of visiting each city, an agent must visit a neighbourhood of each city that minimizes the travel length for


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the agent. A review of approaches can be found in Choset (2001). Most approaches either implicitly or explicitly use a cellular decomposition which breaks down the coverage area into simpler cells such that coverage in each cell is “simple”. Then a graph is created with nodes representing cells and coverage is cast as a search problem. Most approaches assume an omni‐directional robot; very few examine the case of a vehicle with non holonomic constraints, as is the case in agricultural applications. In the agricultural literature, due to the nature of the crops and the machines, swaths instead of cells have been used by many researchers to provide field coverage. The working width of the machine is very important because it sets the width of the swath which will be used for field coverage. In order to reduce complexity, most researchers have split the field coverage problem into the following steps:

a) Field subdivision Fields of complex geometry cannot be traversed with a single orientation; the efficiency would be too low because of excessive turning. Therefore, a field of arbitrary geometrical complexity may need to be split into simpler subfields or regions. b) Selection of margins and driving direction The optimal orientation of the driving direction (swaths/rows) and the appropriate field margins must be computed for each subfield, in order to achieve maximum efficiency and feasibility of manoeuvres. We refer to these two steps as “spatial planning for field coverage”. c) Swath based field coverage The problem is static in the sense that the inputs and outputs of this procedure are geometrical entities, or primitives. However, the procedure must take into account the characteristics of the machine(s) (working width, turning radius).

1.5.1.1 Agricultural field area coverage Agricultural field coverage has been addressed by numerous researchers. In the work of Taïx et al. (2006) a convex polygonal field with at most one vertex of concavity is split into a work area and a turning area. The driving direction is given as input (not computed) and the work area is covered by parallel non‐overlapping swaths. Non convex fields and fields with large obstacles are subdivided along the boundary segments defined by the concave vertices, and are treated separately. Oksanen (2007) used exact trapezoidal decomposition to split non‐convex fields into simpler trapezoids which later merged into as large as possible blocks. Split‐and‐merge was performed along driving directions which varied iteratively in order to come up with the optimal combination of field subdivisions and corresponding driving directions. The optimisation criterion was a weighted sum of the efficiency, area and total driving distance. Examples of such field planning with fixed working width are given in Figure 4.


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Figure 4 Examples of splitting fields and computing motion directions (Oksanen 2007)

Jin and Tang (2006) subdivide a polygonal field with obstacles recursively (two, four, eight subfields, etc). For each subfield they compute its optimal driving direction by minimising the total dead distance at the headlands. In the work of de Bruin et al., (2009) optimal swath directions for simple polygonal fields are computed by exhaustive incremental search, based on the minimisation of cost involved with un‐cropped areas, turning at headlands and subsidies received for field margins. Sörensen et al. (2004) presented a planning method using a range of solution methods attached to the Chinese Postman Problem (Greistorfer, 1995) for finding the optimal coverage path for a designated field operation. Ryerson and Zhang (2007) conducted a feasibility study to determine the applicability of a genetic algorithm for path planning of agricultural vehicles. Although, this methodology did not result in completely optimized paths, the approach achieved 90% coverage of the field. Oksanen and Visala (2007) presented two different algorithms to solve the coverage path planning problem for agricultural machines. The first merge and search algorithm, based on trapezoidal split, used to split a complex shaped field plot, including obstacles, to smaller parts. The second algorithm utilizes a bottom‐to‐top approach and solves the problem recursively for real‐time usage. This second approach does not split the coverage problem into static covering with parallel swaths and swath sequence computation. It is inspired by model predictive control and generates a coverage pattern based on swaths of various lengths by simulating a machine which is driving and at the same time is optimising its efficiency along a future horizon. This approach can generate more complex coverage patterns, like circular, and can handle non convex, non rectangular fields. Further, the machine’s capacity constraints have been included and the swath sequence is computed simultaneously. A recent approach (Ali et al., 2009) is inspired by cellular decomposition and represents the field as a polygonal area. An obstacle in the field is represented by a polygon within the field that encloses the obstacle. After representing the field and the obstacles, the remaining area is converted into a grid of equally spaced vertices, where each vertex represents the centre point of a cell. The result is a grid graph of a field. Each cell approximates the area covered by the combine harvester when standing still. The crop yield from a cell is determined on the basis of the estimated density of the crop. formulates the field coverage problem as an integer linear programming vehicle routing problem with additional turn penalty constraints. This is further converted into a minimum‐cost network flow problem for solution efficiency. The result of solving the problem with the proposed modelling approaches is a set


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of itineraries ('tours'), covering the entire field. Each 'tour' is characterized by the combine harvester's start and end points and the positions where the combine harvester needs to be unloaded. The planning models minimize non‐productivity (i.e. the time when a combine harvester travels in a field without harvesting). The advantage of such a method is that non parallel swaths may e used to cover the field (e.g. spiral pattern). However, turning is addressed simply as a cost and it is assumed that the machine’s turn radius enables it to turn from one cell to its adjacent. Further, although cell primitives (instead of swaths) provide flexibility they increase dramatically the number of variables and the required solution time (10 hrs for 5 hectares). The most common criteria used for field coverage planning are minimum length of travel and number of headland turns. However, it has been shown recently (Stombaugh et al., 2009) that other criteria like minimizing the overlap in automatic section control result in coverage patterns which differ drastically from the patterns which maximize field efficiency. Hence, field coverage which optimises multiple objectives is still an open area of research. Furthermore, all coverage algorithms use a swath of fixed width, implicitly assuming that the field will be covered by one machine, or many machines with the same operating width. If this assumption is relaxed the problem becomes much more complicated.

1.5.1.2 Subfield and swath traversal sequence generation Given that the subfields and driving direction orientations are fixed, this planning problem concerns the computation of the visiting sequence of the subfields to be covered, and also the traversal sequence of the rows in each subfield. The solution to this problem depends on characteristics of the vehicles and on the work demands of the operation. Especially important are the machine’s working width and turning radius. Also, capacity constraints which may be imposed by the type of operation and machine can affect these sequences. For operations where the machine must apply or gather material in the field (e.g., harvesting, fertilising) the machine’s storage capacity affects the maximum number of swaths that the machine can travel until its capacity is met; the same applies to fuel. For operations which do not involve material transfer (e.g., ploughing), or when the quantities involved are smaller than the machine’s tank or storage space, the machine’s limited storage capacity does not affect the solution. In the work of Taïx et al. (2006) the endpoints of the parallel swaths of a polygonal convex field constitute nodes in a graph. The optimal coverage path (swath sequence) of a single machine is determined by computing a Hamiltonian path of this graph. Non convex fields and fields with large obstacles are subdivided and treated separately, whereas small obstacles are treated heuristically, using an avoidance curve. For one machine without capacity constraints a solution has been presented by Bochtis and Vougioukas (2008). According to the proposed method field coverage is expressed as the traversal of a weighted graph and the problem of finding optimal traversal sequences is shown to be equivalent to the Vehicle Routing Problem (VRP) of finding shortest tours in the graph. In this work the problem of computing the right sequence for visiting subfields has been solved simultaneously with the one of finding the best swath sequence, by creating a large graph containing all the swaths of all subfields. The inter‐field distances are approximated by Euclidean distances. The same approach has been


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extended (Bochtis 2008) for many vehicles with capacity constraints (e.g., fuel tank, fertiliser tank, etc) which must visit stationary stations at fixed locations out of the field.

1.5.1.3 Headland turning If autonomous machines were to operate in a farm, general coordinated motion planning would be required for motions out of the field, e.g., when moving from a parking location to the field or from the field to a silo, etc. This problem is not addressed in this review; it lies in the area of general coordinated motion planning and has been studied extensively in the robotics literature. The fact that the machines operate independently of each other in the field means that they do not share resources other than the physical area they work in. Hence, their corresponding paths can be planned independently. Furthermore, in fields cultivated according to parallel‐swath patterns the paths of the vehicles are predetermined and do not intersect, with the possible exception of headland areas where machines turn in order to move from their current swath to their next. Therefore, the major tasks of motion planning for headland turning are: a) plan independent geometrical paths for turning, and b) compute appropriate velocity profiles for these paths so that collision avoidance is achieved, when two or more paths intersect. Problem (b) is a coordinated trajectory planning problem and has been solved by various researchers in the robotics literature (LaValle and Hutchinson, 1998; Simeon, et al., 2002). The problem of automatically computing optimal headland turning paths has received some attention in the literature. One approach (Bochtis, 2008) is to compute a set of turning path primitives off‐line (e.g., fish‐tail turn, u‐turn, etc) which include parameters such as turning radius and swath distance. Then, the turning manoeuvre can be generated on‐the‐fly after the parameters have been set. Optimal control formulations (Torisu, 1997; Oksanen and Visala, 2004) have also been used to compute optimal paths of single tractors and tractor‐trailers in free space, with a focus on headland‐turning. One problem with such approaches is that the optimisation constraints are highly non‐linear and non‐convex. Therefore, the computed solution depends strongly on the initial feasible motion estimate which, in the general case, is not available. A two‐stage motion planning algorithm was developed by Vougioukas et al. (2005) which can be used to compute low cost paths (e.g., shortest path, maximum clearance etc) in free space and also in the presence of obstacles. In the first stage, the algorithm utilizes randomized motion planning to explore the space of possible motions and computes a feasible suboptimal trajectory. In the second stage, the optimisation of the stage‐1 motion is formulated within the optimal control framework. The drawback of this approach is that because it is generic and not tailored to headland turning, it is computationally expensive.

1.5.2 Cooperating machines

Cooperative agricultural field operations are typically executed by one or more primary unit/s performing the main work task and one or more service unit/s supporting it/them. For example, in a harvesting operation a self‐propelled harvester may be supported by transport wagons used for out‐of‐the field removal of harvested grain. Clearly, the PU’s interact directly with the SUs; however they also interact with each other indirectly, because they may share the services of the same SU. For example, a


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harvester may have to wait for a transport wagon to finish loading from another harvester before using it for unloading its own cargo. Since the operation of PUs and SUs is strongly coupled, field traffic planning requires consideration of both categories of vehicles. It should be reminded that such planning assumes that the work demand is known perfectly (e.g., yield distribution) and that each machine’s operation is also perfectly predictable (fuel consumption, fertiliser application rate, etc). Traffic planning for cooperating machines must address issues of timing and how timing is affected by operational constraints like capacity. The general problem of motion planning for multiple cooperating machines has been addressed in the robotics literature for applications involving industrial manipulators, unmanned aerial vehicles, and teams of ground robots. The main focus of existing literature is on coordinated collision avoidance and on formation planning for teams of robots. However, the requirements and special structure of agricultural applications does not allow the adoption of existing approaches. More specifically, motion‐planning for teams of robots which transfer material from one to another and have limited storage and fuel capacities have not been addressed in the general robotics literature. The problem of in‐field traffic planning for cooperating machines has not received much attention in the literature. The same applies to static area coverage for cooperating machines (excluding timing) for which it is not clear how much it differs from doing so for independent machines. To a large extent, field coverage with primitives is a geometric problem, which is influenced though by the operational characteristics of the machines. If swath primitives were to be used, the solution requires dividing the field into subfields, selecting the margins and driving direction in each subfield and covering the field with swath primitives. It is conceivable though that the need to accommodate cart circulation or unloading points in a headland may affect the required margin of the field or even the choice of driving direction. One recent approach (Bochtis et al., 2007b) addresses harvesting and simplifies the problem by decoupling it into planning for PUs and SUs separately. The traffic planning problem for the independent, capacity‐limited PUs is considered already solved (section 1.5.1). The swaths and headlands of the field are represented as nodes in a graph and the motion of the SUs is formulated as a graph search optimisation problem. The cost is the time needed for a cart to move from its current position to the PU needing service plus the PU’s idle time waiting for service. The graph search is very fast and it is proposed that this scheme be used in real time for dynamic traffic planning of the cooperating vehicles.

1.6 On‐line fleet management

Fleet management problem is an inherently dynamic problem, because part of the input required to solve it is revealed only during fleet operation and information relevant to its solution changes during operation. For example, very often the number of fields to be cultivated is not known exactly in advance and new requests arrive during operations. Also, a machine may break down, or the time required for moving between fields or cultivating a certain field may turn out bigger than the time used for computing the off‐line operations schedule.


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Off‐line (static) scheduling algorithms require knowledge of all problem parameters and accurate predictions of the durations of in‐field operations and inter‐field transfers in order to compute good schedules. Their computational complexity is very high and it may take tens of minutes, or even hours to come up with very good schedules. Similar comments can be made about off‐line traffic planning for operations in the field, although running times may be significantly lower, depending on the approach. Once each machine has received its scheduling and field traffic plan, the operation can start. During cultivation it is very likely that the traffic plan will need to be recomputed due to unexpected events or conditions in the field. For example, differences between the real crop yield distribution and its off‐line prediction may render the planned grain unloading places and times obsolete, causing the a‐priori traffic plan of the loading carts to become useless. The ideal solution would be to re‐solve on‐line the entire scheduling and traffic planning problem centrally every time some parameter changes. This is – and most likely will remain – impossible because of the problem’s computational complexity. The standard approach is to decouple the scheduling from the traffic planning problem and effectively pretend that scheduling does not “care” about the details of in‐field traffic, as long as the durations of in‐field operations are known for any machine assignment that it makes. This means that the new in‐field traffic plan could be computed locally and that only the updated estimated cultivation time must be communicated to the central dispatcher. Next, the problems of dynamic scheduling and dynamic field traffic planning will be treated separately.

1.6.1 Dynamic scheduling of fleet operations

In scheduling, when some quantities are random (stochastic) with known probability distributions the problem is called stochastic and it can be solved either off‐line, resulting in an open‐loop policy which will be most likely suboptimal, or on‐line using an optimal closed‐loop policy. Another possibility is that the problem is dynamic, i.e., part of the input required to solve it is revealed concurrently with the determination of the route or information relevant to its solution changes during operation. Given this, it is impossible for an optimal schedule be produced in advance. One such example is scheduling without a priori knowledge of the total number and start‐times of the tasks. Dertouzos and Mok (1989) showed that without a priori knowledge of task start‐time, it is impossible to guarantee optimal scheduling. In dynamic scheduling, at best, what can be produced is a policy, specifying what action should be taken as a function of the state of the system. This means than no open loop solution exists to equation (1) and a closed loop policy must be adopted. To summarize, both stochastic and dynamic problems require the use of on‐line decision making policies in order to achieve optimal performance. Agricultural fleet management in the real world is inherently a dynamic problem. The operating time needed for field cultivation is typically long and it is generally unknown in advance. If an accurate yield distribution estimate is available, then it could be approximated based on machine performance data from past years from the same field, or form the literature. However, such data for teams of cooperating machines are not readily available. Weather conditions and soil conditions also affect these time. Also, the inter‐field transport time depends on traffic, road and weather conditions and cannot be known accurately in advance. Unexpected events, like machine failures, operator illness, may happen at any time. Also, new orders for cultivating and harvesting fields may arise, or be cancelled; however the rate is much smaller than in other fleet management applications, like courier services, repair‐crew dispatching, delivery services, taxi services, etc.


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The standard approach to solving stochastic and dynamic scheduling and routing problems is to compute in a first stage, off‐line a nominal, or tentative solution, and to update the routing and scheduling by applying corrective actions on‐line, according to some chosen policies (Gendreau, 1996). When a problem is very dynamic, i.e., there is no a‐priori knowledge of the number of jobs, jobs require little processing time but new jobs arrive at high rates, then no a‐priori solution can be computed and operations rely on policies. Examples of such problems can be found in computer networking applications such as queuing and routing packets and bandwidth allocation. Agricultural applications however do not share such characteristics. In general, jobs arrive with low rates, they require long processing times and there is a good estimate of their total number in advance. The stochastic and dynamic versions of the fleet management problem have not received attention in the agricultural and forestry related literature. One approach is to re‐solve regularly on‐line the static scheduling problem using any new or updated information available at the moment. This could be practical only in the case where the time required for solving the static problem is relatively small with respect to the reaction time of the scheduler. Foulds and Wilson (2005) report: “The model could be comfortably solved for instances of size 35 workers, 10 types of machine and up to three duplicates of each machine, which is a realistic practical size of problem. Problems solved in fewer than 5s of CPU time using XPRESS‐MP. For a larger problem of the type solved the size is approaching 30,000 constraints and 1400 binary variables. A problem of this size is close to our local limitations on size for the software XPRESS‐MP, so the difficulty with problems of larger size is not CPU time but the actual size of the IP matrix. However, the rapidity of solution with fewer than 100 branch and bound nodes being required is extremely encouraging and indicates that practical problems can be solved relatively easily”. Also, Basnet et al., (2007) report the following table for six machines and increasing number of farms and operations:

Figure 5 Execution times of exact (IP) and heuristic (Tabu) solutions for problems of various sizes

Clearly, even for small problems exact solutions are impractical to compute with currently available computer systems of reasonable cost. For small to medium size problems, heuristic solutions have been reported to give reasonably good results in less than a minute of run time. Hence, it seems that


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re‐solving the static problem regularly on‐line may be a practical approach to dealing with the dynamic and stochastic nature of small size real‐world problems. Of course, if a contractor has to service hundreds of fields it is possible that even heuristic approaches cannot solve such problems in acceptable time. The dynamic vehicle routing problem (DVRP) problem is the one that is closest to dynamic agricultural fleet management. It has been analysed extensively on the literature and various policies have been proposed and studied. Bertsimas and Van Ryzin (1991) have proposed and analysed several policies for a simpler version of dynamic VRP, the dynamic travelling repairman problem. The policies are also used in DVRP: First Come First Served (FCFS).

The demands are served in the order in which they are received by the dispatcher. Stochastic Queue Median (FCFS‐SQM).

The FCFS‐SQM policy is a modification of the FCFS policy. According to the FCFS‐SQM policy the server travels directly from the median of the service region to the location of the demand. After the service has been completed, the server returns to the median and waits for the next demand.

Nearest Neighbor (NN). After completing service at one location the server travels to the nearest neighbouring demand.

Traveling Salesman Problem (TSP). The demands are batched into sets of size n. Each time a new set of demands has been collected, a Traveling Salesman Problem is solved. The demands are served according to the optimal TSP tour. If more than one set exists at the same time, the sets are served in an FCFS manner.

The DVRP that has recently received most attention is the one in which new customer requests arrive and/or the travel times between destinations are variable. This is typical of urban environments, where traffic congestion depends on the time of day. Representative approaches mainly from the operations research literature are presented next. In Montemanni et al., (2005) the DVRP with new customer requests orders was solved using ant colony optimisation. Their approach is based on the idea of dividing the working day into time slices with equal length and to postpone the processing of each new order arrived during a time slice to the end of it. During each time slice, a problem very similar to a static VRP, but with vehicles with heterogeneous capacities and starting locations, is created, and optimization is carried out. In each of these problems, the aim is to minimize the total travel time while serving all the known orders. The concept of time slice has been introduced to set a bound on the time dedicated to each static problem. In the work of Potvin et al., (2006) a dynamic vehicle routing and scheduling problem with time windows was described where both real‐time customer requests and dynamic travel times were considered. Different reactive dispatching strategies were defined based on a minimum‐cost insertion heuristic of new customers and forecasts of travel times.


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Bernard et al., (2008) propose a framework in which a static vehicle routing problem is solved before the start of the daily operation. Dynamic changes of the routing are made whenever new information is obtained throughout the day. Heuristic solution methods are proposed for both the static and dynamic problems. The heuristic for the static problem emphasizes effectiveness. It includes the development of an initial feasible solution using the idea of ‘‘seed selection’’, as well as the refinement of the solution via local search techniques and a genetic algorithm. The heuristic for the dynamic problem emphasizes efficiency and it tries to transfer customer nodes to another position or route for the same vehicle, or another vehicle’s route. Updated routes are constrained to short computational time limits, in the order of half a minute.

1.6.2 Field traffic planning

Planning motions trajectories for teams of robotic vehicles is in general a complex and time consuming problem. In centralised approaches all the robots are grouped together as a single composite robot (Latombe, 1991). Thereafter, the problem reduces to a single‐robot motion planning problem. The issue with this approach is that usually the resulting composite robot has many degrees of freedom (DOF) which is undesirable given that the time complexity of general path planning methods grows exponentially with number of DOF. In decoupled approaches, planning is done in two essentially decoupled phases. In the first phase, for each robot, a path is computed which is collision‐free with respect to the obstacles in the environment excluding the other robots. Collisions between the robots are resolved in the second phase by velocity tuning, i.e., velocities for robots along their paths, computed in the first phase, are selected in such a way that the robots avoid collisions with each other along their respective paths. In essence, velocity tuning involves assigning time along the paths planned in the first stage so that inter‐robot collisions are avoided (Kant and Zucker, 1986). Decoupled planning can be performed in a distributed manner, locally by each robot, whereas centralised planning leads naturally to a single computer implementation which uses global knowledge. Centralised planning performs exhaustive computing to come‐up with optimal solutions, whereas in decoupled implementations suboptimal plans are the norm. Usually centralised planning cannot be performed in real‐time, i.e., in the time scale that the machine controllers operate (e.g. milliseconds). In real‐world conditions a motion plan for all robots will be valid only for a limited time, because external disturbances, sensing and control errors will soon render the plan useless. There are various approaches to planning vehicle paths and trajectories under uncertainty. One approach is to compute a nominal path off‐line (before the operation starts) based on existing a priori knowledge and to rely on control techniques to compensate for small disturbances or unexpected deviations during the actual operation. A second approach is to re‐plan on‐line when disturbances or unexpected events during the operation render the original plan useless, or suboptimal, or when new information arrives which may improve the existing plan. Of course, this approach implies that there is a way of recognising that the existing plan is no longer valid, or optimal which is not trivial, and that the time required for re‐planning is not prohibitive for on‐line execution. Another approach is to express uncertain quantities as probabilistic variables which have a probability distribution and perform off‐line stochastic planning; combinations of these approaches can be used too.


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Another approach for on‐line traffic planning is to compute centrally a high‐level task plan which assigns tasks to each robot taking into account the required coordination of the robot team. Each robot can then plan its own path and trajectory in real‐time. This approach splits the computing load among a central task‐planner and the members of the team and can achieve real‐time performance while incorporating global knowledge in the plan. This approach has been used by Johnson et al. (2009), to coordinate a team of peat moss harvesting robots in an open field. In their work each tractor had a high‐level controller that was capable of performing its own behaviours such as path planning, mission execution, and obstacle avoidance. However, the coordination of these tractors was handled by a centralized component known as the mission director. The mission director’s primary purpose was to provide the system with a mechanism for multi‐robot coordination by acting as a gateway between all of the pertinent vehicle telemetry and the human team leader. Additionally, it provided a central repository for shared data and configuration information, as well as a mission generator (task allocation). It was the responsibility of the mission director to allocate tasks to the individual robots as well as maintain overall coordination between robots. These missions were a sequence of parameterized commands for performing one of four simple tasks: drive to a given field, harvest a given field, drive to a given pile, or dump at a given pile. Various rules were used by the mission director to ensure that missions were safe (collision free) and deadlock‐free. Each robot used the task description to generate its own plan using a combination of visibility graph planning and grid search based on an optimal A* algorithm. A similar approach was implicitly adopted by Bochtis (2008) for on‐line traffic re‐planning for many independent machines cultivating a field in parallel swaths. The machines had identical working widths and different capacity constraints (e.g., fuel tank, fertiliser tank) and had to visit stationary stations at fixed locations out of the field. The main task of field coverage was structured and therefore it was expressed as the traversal of a weighted graph, where each swath represents a node. The visiting sequence of a set of swaths was essentially the task that a robot had to execute. The problem of finding optimal traversal sequences is equivalent to a multiple Travelling Salesman Problem (m‐TSP). Using heuristic search the solution time for solving the static problem was reported to be in the order of seconds and it was proposed that the method be used for on‐line re‐planning. The issues headland turn path planning and trajectory generation were not addressed in this work. In Bochtis et al., (2007b) static planning for cooperating machines harvesting a field in parallel swaths was performed by planning for PUs and SUs separately. The traffic planning problem for the independent, capacity‐limited PUs was considered already solved (section 1.5.1). The swaths and headlands of the field were represented as nodes in a graph and the motion of the SUs was formulated as a graph search optimisation problem. The cost was the time needed for a cart to move from its current position to the PU needing service plus the PU’s idle time waiting for service. The graph search was very fast and it was proposed that this scheme be used in real time for dynamic traffic re‐planning of the cooperating vehicles.


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1.6.3 Field traffic control

In the robotics literature work has mainly focused on formation control, i.e., how can a group of robots be controlled in a coordinated way to get into and maintain a formation with a certain shape, such as a wedge, a circle or a chain. The focus is on large or very large teams of robots, with applications in surveillance, search, and mobile sensor networks. There are two major approaches: centralised and decentralised control. In centralized pattern formation methods, a computational unit oversees the whole group and plans the motion of the group members accordingly. The motion of each robot is then transmitted to the robot via a communication channel. Egerstedt et al., (2001) propose a coordination strategy for moving a group of robots in a desired formation over a given path. Path planning is separated from the path tracking task. It is done in a centralized way and the tracking of virtual reference points are handled separately. The path for a virtual leader is computed as a reference point for the robots to follow. They applied the method to coordinate the movement of simulated robots in a triangular formation while avoiding an obstacle. Belta and Kumar (2004) propose a centralized trajectory computation scheme that uses kinetic energy shaping. Instead of using a constant kinetic energy metric, they employ a smoothly changing the kinetic energy metric. The method generates smooth trajectories for a set of mobile robots. The proximity between the robots can be controlled via a parameter. However the method does not take obstacle avoidance into consideration and that is not scalable. Centralized formation control relies on a central unit that oversees the whole group and assumes the existence of a fast and reliable communication channel between the central unit and the individual robots. Such assumptions make the centralized strategy more costly, less robust to failures, and less scalable to the control of large number of robots. An alternative is to use decentralized formation strategies. In distributed behaviour‐based approach (Balch and Arkin, 1998; Carpin and Parker, 2002; Fredslund et al., 2002; Lawton et al., 2003) each robot has basic motor schemas. Each schema generates a vector representing the desired behaviour response to sensory input. Possible motor schemas include collision avoidance, obstacle avoidance, goal seeking, and formation keeping. The control action of each robot is a vector weighted average of the control of all behaviours. Behaviour based approaches have been combined with potential fields for guidance and obstacle avoidance (Reif and Wang, 1999; Savvas et al., 2003). Another approach uses leader‐follower patterns (Desai, et al., 2001; Das et al., 2002; Vidal et al., 2004) and assumes that only local sensor‐based information is available for each robot. The leader specifies its own trajectory and the followers track the leader’s trajectory under desired spatial constraints which describe the formation. Model predictive control (Wesselowski, 2003), receding horizon control (Dunbar and Murray, 2006) and sliding mode control (Sanchez, Fierro, 2003) have also been proposed for tracking leader‐follower schemes. Formation control has been stated as a tracking problem and Liapunov theory has been used to achieve coordinated tracking and collision avoidance for groups of robots with non‐holonomic dynamics (Mastellone et al., 2008). Bio‐inspired approaches are based on swarming and flocking behaviours observed in nature (Reynolds, 1987; Jadbabaie, 2002; Tanner et al., 2005) and rely on rules based on local sensing to achieve overall formation.

1.6.3.1 Independent machines

Most agricultural operations are structured (e.g., parallel swaths) and therefore general formation control methods are not directly applicable. When machines operate independently of each other in


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the field they do not share resources other than the physical area they work in. Also, the large majority of fields are cultivated according to the parallel‐swath pattern. In this pattern the paths of the vehicles are parallel and do not intersect, with the exception of headland areas where machines turn in order to move from their current swath to their next. Therefore, the major task of traffic control is to coordinate the motion of machines during headland turning. This is naturally performed in a distributed manner, i.e., each vehicle runs its own trajectory tracking algorithm. Two distinct cases arise:

a) The trajectories of the vehicles or any moving obstacles intersect momentarily at a single point; therefore collision between machines can be prevented by adjusting their respective velocity profiles without changing their paths.

b) Unexpected obstacles may exist on the robot’s path, or the vehicles have parts of paths which coincide; therefore path alterations are required to avoid collisions.

In both cases it is important that each vehicle has a good estimate of the trajectories of all unexpected obstacles and other nearby vehicles. The work of Kyriakopoulos and Saridis (1992) addresses case (a) for a single robot among moving obstacles. A detailed dynamic model of a robotic vehicle is used, which takes into account skidding and imposes bounds on the velocity and control. During operation the velocity is changed along the nominal path based on estimated robot velocities so that the robot can avoid dynamic obstacles crossing its path. It is assumed that the obstacles will never obstruct the robot permanently. An extension of this approach (Papageorgiou and Steinkogler, 1994) allows deviation from a nominal path (cases a, b). It uses dynamic programming to control a moving vehicle in real‐time using measurements from a changing environment. The optimal control solution is continuously updated, applying the rolling horizon method. Measurements of the number, the dimensions, the current positions, and the speeds of the obstacles are used along with extrapolation of the obstacle’s movements to cover the time horizon. These approaches were not developed with multiple robots in mind therefore the issues of precedence have not been addressed. For example, if the trajectories of two moving robots intersect, each one will think of the other as obstacle and adjust its velocity or steering accordingly. It is conceivable that both robots decelerate or accelerate together in order to avoid each other causing oscillations or even deadlock. This problem has been addressed by Fujimori et al., (2000) by assigning priorities to robots and assuming that the position of each robot is made known to all others by some means of communication. Each robot can be in one of three modes: navigation, cooperative collision avoidance, or final. The danger of collision is estimated by extrapolating other robot’s speeds and computing possible collision points. Robots arriving first at a collision point are given higher priority. If the collision danger is high the cooperative collision mode is entered in which the velocity and direction of a robot are computed via appropriate first‐order differential equations. It is proved that under certain conditions collision avoidance can be achieved. These conditions however can be violated when more than two robots have intersecting trajectories. The work of Vougioukas and Sigrimis (2007) is a further extension which covers both cases (a) and (b). A distributed control scheme for coordination and collaborative collision avoidance was proposed. Each vehicle is equipped with its own nonlinear model predictive tracking controller which optimises


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tracking performance along a fixed future horizon. Each controller provides accurate tracking when possible, but also avoids collisions with nearby vehicles by altering the path velocity profile or the path’s geometry. To do this, it assumes that the motion trajectories of all other nearby vehicles are known via some broadcast mechanism. Implicitly, it is assumed that the trajectories of all unexpected obstacles are also known within the future horizon, something which in practice is not trivial. Robot priorities are not addressed. Precedence could be imposed by introducing an “importance” weight‐factor for each robot. The stability properties of such a scheme were not investigated.

1.6.3.2 Cooperating machines

The increasing need for financially competitive and environmentally sustainable agricultural production, combined with a decreasing workforce in the entire agricultural section are the major thrusts towards incorporating information technologies, automation and robotics in the production process. The introduction of auto‐steering has turned conventional agricultural vehicles into supervised autonomous machines which can traverse field swaths autonomously. Autonomous headland turning has already been achieved and will reach very soon commercial level. Also, a lot of effort has been made towards automating agricultural operations like spraying, harvesting, etc. The incorporation of supervised autonomous machines in many real‐world agricultural production processes will require the cooperation and coordination of more than one machine. For example, robotic vegetable harvesting in a greenhouse would require the cooperation of specialised autonomous harvesting robots with robotic carriers which will move the harvested produce towards a collecting point for further processing. In many cases one machine is performing the main work and one or more machines support its operation. An example is grain harvesting with on‐the‐go unloading where a combine harvester must be followed by an unloading truck. Other examples include seeding, fertilising and spraying where the machine performing the work has a tank with limited capacity and therefore must be reloaded regularly, possibly by a reloading vehicle. In the work of Hao et al., (2004) the problem of operating a tractor−cart combina on in conjunc on with a small−grain combine harvester, was inves gated. The harvester and tractor combina on were treated as a formation of autonomous robots that need to maintain a specified geometric relationship. The combine path dictated the path of the trailer to ensure a collision−free path that would allow grain transfer. The path of the trailer, in turn, dictated the required path of the tractor to ensure that the trailer is in the optimal location at the correct time. The idea of differential flatness was used to plan and optimize local collision‐free trajectories for the machines and a special trajectory controller for non holonomic vehicles was used. The approach was generalised to multiple tractor‐trailers following one harvester which basically acts as the leader of the formation and simulation results were given along with experimental results for scaled‐down versions of the real machines. Noguchi et al. (2004) have proposed a general master‐slave architecture for two robots performing farm operations. The master commands the slaves to either follow a path parallel to it ‐ at a fixed distance from it ‐ or go to a certain point along any path, as long as it does not collide with the master. Sliding mode control was used for accurate path tracking and collision avoidance was achieved by a risk function based on the master‐slave distance, which was included in the velocity and steering laws of the slave.


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In (Vougioukas, 2009) a control framework was proposed for cooperative control of teams of tractor‐robots operating in the same field. The framework supports master‐slave and peer‐to‐peer modes of operation. It is based on a distributed control approach, where each robot is equipped with its own nonlinear model predictive tracking controller. Each controller minimises the tracking error along a finite horizon and thus provides accurate tracking. When necessary, it also avoids collisions with nearby vehicles by altering the path velocity profile or the path’s geometry. To do this, it uses information about the motion trajectories of all other vehicles which may interfere with its own projected motion. The communication requirements of this approach along with the computational complexity of model predictive control limit the application of this framework to small robot teams consisting of a few vehicles.

1.7 Summary and Conclusions

From a theoretical point of view, fleet management for agriculture is a two‐level problem: a) dynamic vehicle scheduling and inter‐field routing, and b) in‐field traffic planning and coordination. The two problems are characterised by different spatial and temporal scales, yet they are coupled, although all existing literature treats them separately to reduce problem complexity. In the agricultural and forestry literature, the existing work on scheduling and routing concerns deterministic off‐line plans. In real applications the data used for planning contains a lot of uncertainty, errors, and sometimes is simply not available. No work has been done for incorporating uncertainty, either through stochastic scheduling with off‐line and on‐line policies, or robust off‐line scheduling. Clearly, some of the policies developed for dynamic vehicle routing could be transferred and tested in the agricultural domain. In‐field traffic and coordination planning requires the collaborative coverage of the entire field by cultivating/harvesting units and their service by secondary vehicles. The planning problem has been split by most researchers into static field coverage based on swaths, generation of swath traversal sequences for each machine and motion planning for headland turns. Field coverage for independent machines has been studied, but issues like multi‐objective coverage, non flat fields, and swaths of different widths have not been addressed. For cooperating machines field coverage and dynamic motion planning have also not received enough attention. A basic conclusion of this report is that in addition to vehicle scheduling and routing, fleet management for agricultural operations should integrate somehow the planning and real‐time coordination of in‐field operations. The framework of sequential decision making used in this report could be used for computing solutions to (very?) small instances of the combined problem. Such solutions may provide insights as to how strong the coupling is between the two problems; they could also be used as globally optimal solutions against which other heuristics‐based solutions could be compared. From a practical point of view, real‐time agricultural fleet monitoring is already a commercially available technology and automated scheduling, dispatching and routing tools already exist in other commercial sectors like trucking, construction, delivery and courier services, etc. It is likely that incorporation of such tools in agricultural production has not materialised yet because there was no


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economic justification for it. Additionally, agriculture is notoriously slow in adopting information and communications technologies (NASS, 2009).

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2 Fleet Management: Assessment of Potential Savings

Bochtis1 D D; Vougioukas2 S G; Sørensen1 C G; Hammed1 I A; Oksanen3 T 1 University of Aarhus, Faculty of Agricultural Sciences, Department of Agricultural Engineering, Blichers Allé 20, P.O box 50, 8830 Tjele, Denmark

2Aristotle University of Thessaloniki, Faculty of Agriculture, Department of Agriculture Engineering, Greece

3 Helsinki University of Technology, Department of Automation and Systems Technology, P.O. Box 5500, 02015 TKK, Finland

This section presents an assessment of the energy, time and cost savings that could be achieved when farming operations are performed by many machines (fleet), operated in an optimal way, as opposed to the standard operation of current agricultural practice. The operations examined take place at the farm level, i.e., in one or neighbouring fields. This is equivalent to computing the minimum possible execution cost of these operations. This is very important to know, since the execution cost is needed by the agricultural fleet operations scheduling to compute the optimal resource allocation over time. The assessment will be based on available state of the art algorithms which model, optimise and simulate the execution of farming operations. In the first part of this section, the savings will be assessed for field coverage operations in which numerous machines cover parts of the field independently, i.e., they do not share any resources. In the second part, the savings will be estimated for farming operations in which numerous machines must cooperate in order to perform the task. In practice, almost all field operations involve the motion of one or several machines. The machine(s) must cover the entire field area while performing the assigned task. The field pattern that the machines use could be parallel swaths, circular, etc. (Hunt, 2001). In this report we restrict ourselves to parallel‐swath field patterns.

2.1 Introduction

The maximisation of agricultural machine productivity is an important element in the continued efforts of planning and controlling resource inputs in both arable and high value crops farming. A preliminary step in the direction of achieving increasing operational efficiency is a renewed focus on the usage of advanced systems both in terms of technology and management measures. In the longer perspective, research shows that a paradigm shift from large machines to smaller and more intelligent multi‐robot systems, which can establish and nurse, for example, plants at an individual level is expected (Blackmore et al., 2005; Fountas et al., 2007). Such a development will increase the demand for advanced management tools, like fleet management tools, for scheduling, monitoring and on‐line coordination of multiple vehicles to improve operational efficiency and effectiveness (Auernhammer, 2001; Sørensen and Nielsen, 2005). The objective of this report is to assess the on potential savings in terms of operational time as well as non‐working travelled distance (that is equaled with fuel consumption) as a result of the implementation of optimisation measures for operations carried out by a teams of agricultural mobile


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units (non‐autonomous or autonomous). These operations include the optimization of the configurations of teams of co‐operative machines (e.g., combines and transport units, fertilizers and supply units) as well as of identical machines (e.g., multiple forage harvesters). The first case regards agricultural field operations involving a number of interconnected tasks executed by cooperating heterogeneous agricultural machines. For example, this is the case for operations that take place within the biomass supply chain such as harvesting, material handling, removal of biomass from the field, and subsequent rural and public road transportation. Multiple machinery operations of similar planning complexity as harvesting (‘‘output material flow’’) are operations such as spraying and fertilising (‘‘input material flow’’). These operations also involve multi‐machinery systems that potentially include one or a number of self‐propelled or tractor‐pulled application units and one or more transport units (Bochtis and Sørensen, 2009a; 2009b). In addition to the agricultural operations that naturally incorporate the fleet machinery concept, the growth of the range of available self‐propelled machines including fertilizer spreaders, plant protection sprayers, mowers, etc., motivates the adoption of ‘‘team work’’ for the execution of the corresponding agricultural operations. This adoption has the advantages of a collective behaviour and allows scheduled work to be carried out on time. On the other hand, if large teams of smaller autonomous machines are to replace smaller groups of heavier machines in the future, ‘‘fleet management’’ will also play a key role in maximizing the overall efficiency (Sørensen and Bochtis, 2009).

2.2 Identical Machines

2.2.1 Methods

Mission planning for operations involving the coverage planning for an area has been studied extensively in the robotics literature. The research has been prompted by applications such as cleaning, mapping unknown environments, and mine detection. See Choset (2001) for an extensive presentation of developed algorithms). However, the pursued approaches cannot be adopted for the coverage problem in the case of agricultural operations due to the special features and agronomic constraints inherent in these operations. In agricultural operations, a number of additional constraints must be taken into account such as soil compaction, operating while following contour lines, and the fact that a typical agricultural machine usually cannot operate while manoeuvring. Another important factor influencing the planning is the fieldwork pattern followed in previous treatments or by other machinery types. Consequently, area coverage planning for field operations is mostly determined by agronomic structures and constraints. Here, the area coverage planning problem for field operations is considered as a hierarchy of sub‐problems:

1. Field area decomposition. Decomposition of the coverage region into sub‐fields and generation

of the corresponding headlands.

2. Determination of the driving direction in each sub‐field.

3. Field tracks generation. It determines how the set of parallel field tracks is generated given sub‐

fields.


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4. Route planning over the geometrical representation derived from the above sub‐problems. The

resulting route refers to the sub‐fields body coverage, that is, the generation of a path that

covers each sub‐region ensuring that the mobile unit covers the field main body (between

headlands and access paths) in an optimum way, according to an optimisation criterion (i.e.

minimisation of the non‐working travelled distance or non‐productive time), without overlaps

or missed areas and avoiding all obstacles.

5. Sub‐fields sequence. It determines the sequence that the mobile unit visits the sub‐fields given

the access paths between them.

Steps 1, 2, and 3, regard the representation of the field as a geometrical entity while steps 4 and 5 regard the the route planning by adhering to this representation.

2.2.1.1 Field geometrical representation

Recently, a number of algorithms for the representation of the field as a geometrical entity have been resented. Figure 6 presents examples of developed methods. The most important of them are briefly described in the following. Oksanen (2007) presented a two‐stage method for the field coverage planning problem. In the first stage, a field is split into blocks that are easy to cover with tracks. In this algorithm, a greedy selection is used. First, the best block is found and removed from the region and the same algorithm is repeated until the whole field is split. In the search of the best block at each step, the best driving direction is the searching criteria. In the case of several possible driving directions, so called trapezoidal decomposition is applied in order to split the region into smallest possible pieces, trapezoids. After trapezoidal decomposition, trapezoids which can be merged are merged into blocks. The condition for merging includes equal parallel lines and certain requirements for headland angles. After trapezoidal decomposition and merging, the block with most efficient track coverage is selected as the block which is removed from the region. The algorithm can handle also obstacles in field. Details of the algorithm can be found in Oksanen (2007), and Oksanen and Visala (2009). Two examples are presented in Figure 6a. At the left side, a simple field is presented containing seven blocks and on the right there is a more complex field with an obstacle, resulting in 30 blocks. In both cases the, the results are logical. Hameed et al., (2009) presented two algorithmic approaches for the geometrical representation of a field as an entity that can be used for the route planning of an agricultural mobile unit.

Single‐block representation algorithm for both convex and non‐convex fields: This algorithms works in

two stages: in the first stage, it generates a predetermined number of parallel headland passes

peripheral to the field boundary to be used as the headland area. In the second stage, the algorithm

selects the longest edge of the field, or the side of the field resulted from a set of sequential edges

within a predefined threshold angle difference, and that will cover the whole field as a single‐block area

(Figure 6b).


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Multiple‐blocks representation algorithm: The first stage of this algorithm is the same as that of the

previous one. In the second stage, a non‐convex field is divided into convex sub‐fields by recursively

checking for intersections between the track being generated and field boundaries Figure 6c).

In de Bruin et al., (2009), the optimal direction for parallel straight tracks is generated automatically based on criterions like the minimisation of the cost of loss of net income for un‐cropped area, the cost of an additional track, cost of turning, and subsidy received for field margins. The resulted fieldwork patterns were oriented along the longest direction of the fields. The inclusion of obstacles within the field requires further study. Hofstee et al., (2009) presented a tool for determining the optimum path for field operations. It gives optimal solution for single convex fields. When fields consist of more than one subfield, the current optimal solutions are not necessarily the optimal solution.

(a)

(b) (c)

Figure 6 – Examples for algorithmic subfields and tracks generation: a) Oksanen (2007), and b) and c) Hameed et al. 2009

Here, the method of Hammed et al., (2009) was used for the geometrical representation of the field where the generation of optimal routers for teams of agricultural machines in the examined simulated scenarios will take place.


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2.2.1.2 Optimal route planning method

The implemented route planning method is based on an algorithmic approach aimed at computing traversal sequences for parallel field tracks (tracks), for one or for numerous fields, covered by one machine or by a fleet of them (Bochtis, 2008; Bochtis and Vougioukas, 2008). This algorithmic approach improves the field efficiency of the agricultural machines, by minimizing the total (in‐field and out‐field) non working travelled distance. Field coverage is expressed as the traversal of a weighted graph and the problem of finding optimal traversal sequences is equivalent to finding shortest tours in the graph. The traversal of the graph is subject to the constraint that the tour has to be of minimum total cost while each node has to be visited exactly once and any sub‐tours should be excluded from a feasible solution. For the solution of the optimization problem, a heuristic graph search algorithm was constructed. The algorithm operates in two stages:

1. The randomization phase, where by choosing the best amongst traditional headland fieldwork patterns,

e.g. alternation patterns, continuous patterns, an initial solution is built, and

2. The improvement phase, where various improvement heuristics are performed based on the use of local

search techniques e.g. Or‐opt operation, 2‐opt operations and swap operations (Papadimitriou and

Steiglitz, 1998)

Details of the method can be found in Bochtis (2008). An implementation of the algorithm on conventional machines can be found in Bochtis and Vougioukas (2008) while its implementation in the mission planning on an autonomous tractor can be found in Bochtis et al. (2009). Figure 2 illustrates a solution from the algorithm implementation in the mission planning of the autonomous tractor Hako tractor (a description of the tractor can be found in Griepentrog and Blackmore, (2007)).

Figure 7 ‐ Agricultural coverage operations in a rectangular field based on optimal and on traditional planning (adopted from Bochtis et al., 2009)

2.2.1.3 Integration of algorithms

For the complete implementation of the above described route planning method, the integration of the route planning algorithm with a geometry generation algorithm has to take place. The


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implementation of the integration of the algorithms is presented through a simple example (Bochtis and Oksanen, 2009). The example regards a real field located in Southern Finland (Figure 8a). The area of the field is approximately 1 ha, the working width of machine (for example hitch mounted seed drill) is 2.5 m, and the minimum turning radius is 6m.

(a)

(b)

(c)

(d)

Figure 8 – (a) An example field and the split algorithm result, (b) the resulted nodes representing the endings of the field

tracks, (c) the problems topology and (d), the permitted transitions between sub‐sets.

The split algorithm results in five blocks, shown in Figure 8b. The area of the largest block is 0.73 ha, the second largest is 0.17 ha and the third largest 0.084 ha. The rest of the blocks are under 0.001 ha. The result makes sense as the largest block covers most of the field and it results in long straight driving lines which provide good efficiency for operation. The main body of the particular field consists of the three largest blocks with number of tracks |T1|=22, |T2|=8, and |T3|=9, respectively. Consequently, the main body corresponding graph is composed by three sub‐sets e.g., S Si, i{1,2,3} where the number of the nodes included in each subset is given by: |Si|=2|Ti|, i1,2,3} (Figure 8c). Concerning the operation at the headland area, this area usually consists of two or three tracks (each one equals to the effective operating width of a machine) and the order in which the machines operate at the headlands is determined by the type of the operation (for example, in harvesting operations headland area is harvested first while in the seeding operations headland area is seeded last). As it is easily understood from the blocks layout, some connections between tracks can be permitted or not, depending on the machine’s current moving direction. Let us consider for example, Block 1 and Block 2. If two nodes correspond to the upper endings of two tracks, the connection between them is permitted. In contrast, if two nodes correspond to the lower endings of two tracks, the connection is


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permitted only if the tracks are elements of the same subset. These restrictions are automatically taken into account by the algorithm assigning an infinite cost to the undesirable connections. The topology of the permitted connections for the particular field is depicted in Figure 8d, where green arrows depict the permitted transitions between the field blocks and white and grey areas, within the sub‐sets, designate the two opposite headlands of each field block. From the implementation of the optimization algorithm, the optimal track sequence for the given field was:

BLOCK1 BLOCK 2 BLOCK 1

*

BLOCK 3 BLOCK 1 BLO

3 8 2 7 1 6 13 18 12 17 11 16 5 10 15 20 27 23 19 ...

34 39 33 38 32 37 31 36 35 21 26 30 25 29 24 28

BLOCK 1CK 2

22 14 9 4

From the track sequence, it is obvious that the resulted optimal field‐work pattern is not akin to any traditional pattern. Furthermore, this optimal planning is diversified from any traditional planning in the way the machine visits the field blocks. According to the ‘traditional sense’ in field operation execution, the driver starts working in a block and moves to the next one only after the completion of the work in the first one. In the proposed planning, as it is depicted in Figure 9, after operating in track 20 which belongs to Block 1, the machine is moving to Block 2 where it operates in two tracks (27 and 23). Next, it returns to Block 1 where whilst operating on track 19 it is moving to Block 3.

Figure 9 ‐ Part of the resulted optimal planning.

2.2.1.4 Traditional planning The fieldwork pattern that was simulated for the case of the traditional planning was the straight alternation pattern. In the case of a single‐field operation, the field area was divided in a number of parts equal to the number of units. The applied rule stated that the total effective distance (and not the number of the tracks) should be (about) the equal.

2.2.2 Simulation Results

In the following, the comparison between the traditional and optimised planning of field operations carried out by one, two, three, and four identical units is presented. All relative time factors (i.e., blockages, preparing time, and operator’s mistakes) have been excluded from the operational time.


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The comparison is based on the travelled distance which is divided into effective and non‐working distance (turnings, and out‐of‐field travelled distance). The time elements (effective, non‐effective) result from the corresponding travelled distances using average speeds. The average speeds that use used throughout the simulations were operating speed: 2 m/s (7.2 km/h as a mean typical driving speed for the most of the field operations, ASAE (2009)), out‐of‐field travelling: 1.8 m/s, maneuvering in smooth headland turnings: 1.5 m/s, and maneuvering in steep headland turning: 1.2 m/s. In a field operation, headlands are created by the sequential passes that the agricultural machine has to perform peripheral to the field before or after (depending on the operation) the operation in the main field. Thus, the headland width results from the multiplication of the effective operating width of the machine with the number of the peripheral passes. For the simulated operations three headland passes were considered. The operation regarding headland area generation was common for both traditional and optimal planning:

1 unit: sequential passing on three headland tracks starting from the entry point of the field.

2 units: the first two passes are carried out simultaneously by the units moving in parallel and the third pass is allocated to the unit with the shorter operational time. It has to be noted that the operational time that result from the allocated route to each machine is not equal for all units, and that is because there is a lower limit on the distance ”entities” that is the track lengths which cannot be divided.

3 units: all passes carried out simultaneously by the tree units moving in parallel.

4 units: the passes are allocated to the (3) units with the shortest allocated operational time. In order to cover the range from large size units to medium and small size units, four machinery cases in terms of operating width and maneuverability (minimum turning radius) were considered (namely: case A, B, C, and D) (Table 1). Table 1 – The four machinery cases were used in the simulated scenarios

Size operating width (m) min turning radius (m)

Case A small size unit 1.5 3.5 Case B small/medium size unit 3 3,5 Case C large/medium size unit 3 5 Case B large size unit 6 5

As test fields, four fields located at Research Centre Foulum (Denmark: [N 56o 29´ 21.55, E 009o 34´ 59.40]), were used (Figure 10). The geometrical representation of the field was based on shape‐files including all the necessary information pertaining to the field as a geographic feature. The shape‐file was provided by the GIS database of the Danish Ministry of Food, Agriculture and Fisheries. The area of each field is given in


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Figure 10 ‐ The farm and the four fields Table 2 – The area of the four fields

Filed Field area (m2) Aprox. Field area (ha)

A 60577 6,01

B 56497 5,65

C 57033 5,70

D 37580 3,76

total 211689 21,17

In the following figures, the total operational time for each field separately as well for the whole farm (four fields), for the above mentioned machinery cases, are presented.


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(a)

(b) Figure 11 ‐ Operational time for a) optimized and b) traditional planning in field A for one and teams of 2, 3, and 4 identical units, for the 3 scenario cases


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(a)

(b) Figure 12. Operational time for a) optimized and b) traditional planning in field B for one and teams of 2, 3, and 4 identical units, for the 3 scenario cases


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(a)

(b) Figure 13. Operational time for a) optimized and b) traditional planning in field C for one and teams of 2, 3, and 4 identical units, for the 3 scenario cases


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(a)

(b) Figure 14. Operational time for a) optimized and b) traditional planning in field D for one and teams of 2, 3, and 4 identical units, for the 3 scenario cases


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(a)

(b) Figure 15 ‐ Operational time for a) optimized and b) traditional planning in four fields for one and teams of 2, 3, and 4 identical units, for the 3 scenario cases


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Table 3 – Savings from using optimal planning in field A

operating width (m) turning radius (m) number of units nonworking distance operational time

1 60,48 9,76

2 58,24 8,95

3 55,33 9,24

4 52,25 7,45

1 54,23 8,41

2 50,73 6,68

3 43,89 7,54

4 40,01 4,65

1 57,94 11,98

2 55,37 10,40

3 50,64 10,91

4 48,93 10,11

1 57,30 10,51

2 47,53 6,15

3 41,07 8,63

4 37,15 7,21

savings (%)

case A

case B

case C

case D

1,5

3,0

6,0

3,5

5,0

Table 4 ‐ Savings from using optimal planning in field B


1 60,11 10,72

2 58,69 9,91

3 53,64 9,89

4 52,09 7,82

1 56,94 9,53

2 58,37 8,90

3 59,75 9,924 61,27 9,90

1 51,94 12,20

2 43,15 9,28

3 34,36 9,24

4 25,47 4,91

1 56,11 10,79

2 45,50 6,13

3 39,55 8,53

4 28,75 3,40

savings (%)

case A 1,5

3,5

case B

3,0

case C

5,0

case D 6,0


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Table 5 ‐ Savings from using optimal planning in field C


1 60,72 9,13

2 58,87 8,33

3 57,21 8,84

4 53,43 7,16

1 60,85 8,44

2 63,30 7,81

3 64,91 9,10

4 66,15 9,52

1 58,45 11,17

2 59,09 10,22

3 52,48 10,33

4 48,51 7,76

1 58,16 9,76

2 48,98 5,72

3 41,49 7,96

4 35,26 4,40

savings (%)

case A 1,5

3,5

case B

3,0

case C

5,0

case D 6,0

Table 6 ‐ Savings from using optimal planning in field D


1 59,58 14,20

2 57,81 12,98

3 53,38 13,02

4 50,62 10,12

1 56,39 12,57

2 57,81 11,48

3 59,35 12,88

4 60,90 12,97

1 57,24 17,01

2 54,66 14,73

3 49,44 14,91

4 46,33 10,36

1 54,97 14,19

2 44,45 7,68

3 33,68 10,07

4 27,47 3,26

savings (%)

case A 1,5

3,5

case B

3,0

case C

5,0

case D 6,0


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Table 7 ‐ Savings from using optimal planning in the four fields


1 31,60 9,42

2 30,34 8,43

3 35,04 8,50

4 36,32 7,45

1 38,00 8,24

2 6,43 6,43

3 33,78 6,89

4 31,17 6,01

1 34,73 10,20

2 36,79 8,72

3 28,35 9,34

4 26,24 8,26

1 41,35 7,13

2 39,83 6,64

3 32,36 5,92

4 28,28 4,12

savings (%)

case A 1,5

3,5

case B

3,0

case C

5,0

case D 6,0

Table 8 – Range of the savings operational time from the adoption of optimal fieldwork patterns in single‐field operations

number of units min savings (%) max savings (%)

Mean savings (%) median (%)

1 8.41 17.01 11.27 10.75

2 5.72 14.73 9.08 8.92

3 7.54 14.91 10.06 9.57

4 3.26 12.97 7.56 7.61

Table 9 ‐ Range of the savings in non/working travelled distance from the adoption of optimal fieldwork patterns in single‐field operations


mean savings (%)

median (%)

1 51,94 60,85 57,59 57,62

2 43,15 63,30 53,91 56,59

3 33,68 64,91 49,39 51,56

4 25,47 66,15 45,91 48,72


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Table 10 ‐ Range of the savings in operation time from the adoption of optimal fieldwork patterns in multiple‐fields operations


mean savings (%)

median (%)

1 8,24 10,20 9,09 8,96

2 6,43 8,72 7,76 7,94

3 6,89 9,34 8,24 8,37

4 6,01 8,26 7,04 6,94

Table 11 ‐ Range of the savings in non/working travelled distance from the adoption of optimal fieldwork patterns in multiple‐fields operations


mean savings (%)

median (%)

1 26,24 36,79 30,62 29,73

2 28,35 41,35 34,81 34,73

3 26,24 39,83 34,29 36,79

4 28,35 41,35 34,02 32,36

2.2.2.1 Machinery Capacity

In the above simulated results, as it concerns the non‐effective time, the factors that have been taken into account are turning time

Turning time on headlands during operating at the main field

Turning time during operating at headlands

Travel time to and from the field from and to the farm For the machine capacity the following factors also have to be taken into account:

Machine preparation time in the field both before and after operations (not including daily servicing, preparation for towing, and lubrication, time spent in the field to replace or renew parts that have become inoperative)

Machine adjustment time

Maintenance time (i.e. refueling)

Operator’s personal time For the implementation of average of the above factors, a time delay of 1.65 min/ha (100 s/ha) was added to the operational time and a super‐addition of 5% dedicated to personal breaks (Sørensen, 2003; Sørensen and Nielsen, 2005) Since the study regards the operational time, it was not taken into consideration the machine preparation time at the farmstead, and also the time for removal from and preparation for storage, and shop work.


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Table 12 – Effective capacity based on field A

increase increase increase increase

units trad. opt. (ha/h) trad. opt. (ha/h) trad. opt. (ha/h) trad. opt. (ha/h)

1 0.89 0.98 0.09 1.73 1.88 0.15 1.64 1.85 0.21 3.01 3.33 0.32

2 1.69 1.84 0.16 3.14 3.34 0.20 2.99 3.30 0.31 5.13 5.41 0.28

3 2.42 2.65 0.23 4.34 4.64 0.31 4.14 4.58 0.44 6.77 7.27 0.50

4 3.02 3.24 0.22 5.15 5.36 0.21 4.95 5.42 0.47 7.60 8.06 0.45

Case A Case B Case C Case D

capacity (ha/h) capacity (ha/h) capacity (ha/h) capacity (ha/h)

Table 13 ‐ Effective capacity based on field B



1 0.77 0.86 0.09 1.49 1.64 0.15 1.40 1.58 0.19 2.67 2.97 0.30

2 1.47 1.62 0.15 2.71 2.95 0.24 2.56 2.80 0.24 4.56 4.81 0.26

3 2.11 2.33 0.22 3.77 4.13 0.37 3.58 3.90 0.32 6.05 6.51 0.46

4 2.64 2.84 0.21 4.49 4.91 0.42 4.28 4.48 0.19 6.80 6.99 0.19



Table 14 ‐ Effective capacity based on field C



1 0.86 0.94 0.08 1.66 1.80 0.14 1.58 1.77 0.19 2.97 3.26 0.29

2 1.62 1.76 0.14 3.00 3.23 0.23 2.87 3.16 0.30 4.99 5.25 0.26

3 2.33 2.54 0.21 4.14 4.51 0.36 3.98 4.38 0.40 6.57 7.02 0.45

4 2.89 3.10 0.20 4.90 5.34 0.44 4.72 5.06 0.34 7.31 7.57 0.26



Table 15 ‐ Effective capacity based on field D



1 0.77 0.89 0.12 1.49 1.69 0.20 1.37 1.64 0.27 2.60 2.99 0.39

2 1.45 1.66 0.21 2.70 3.01 0.32 2.50 2.90 0.40 4.42 4.74 0.32

3 2.09 2.38 0.29 3.73 4.22 0.48 3.49 4.03 0.54 5.84 6.38 0.53

4 2.60 2.87 0.27 4.42 4.98 0.56 4.16 4.57 0.42 6.53 6.71 0.18



Table 16 ‐ Effective capacity based on whole farm



1 0.84 0.93 0.09 1.61 1.75 0.14 1.53 1.70 0.17 2.82 3.02 0.20

2 1.55 1.68 0.14 3.00 3.19 0.19 2.86 3.11 0.25 4.98 5.28 0.30

3 2.28 2.48 0.20 4.01 4.27 0.26 3.85 4.20 0.35 6.26 6.58 0.32

4 2.60 2.80 0.19 4.49 4.74 0.25 4.31 4.65 0.34 6.94 7.18 0.24




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Figure 16 – Effective capacity (ha/h); comparison between traditional (trad.) and optimal (opt.) planning in field A

Figure 17 ‐ Effective capacity (ha/h); comparison between traditional (trad.) and optimal (opt.) planning in the four fields


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Figure 18 – Increase of the effective capacity (ha/h) for the implementation of optimal planning Table 17 ‐ Range of the increase in effective capacity from the adoption of optimal fieldwork patterns (single fields)

number of units mn incr. (%) max incr. (%) mean incr. (%) median (%)

1 8.69 19.53 12.09 11.38

2 5.15 15.82 9.19 9.12

3 6.90 15.49 9.83 9.27

4 2.71 12.76 7.12 7.24

Table 18 ‐ Range of the increase in effective capacity from the adoption of optimal fieldwork patterns (multiple‐fields)

number of units mn incr. (%) max incr. (%) mean incr. (%) median (%)

1 7.01 10.80 9.12 9.32

2 6.03 15.82 7.43 7.47

3 5.10 15.49 7.32 7.56

4 3.41 10.03 6.03 6.46


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2.2.2.2 Fuel savings For the prediction of the fuel consumption during the above operations and the corresponding savings from using optimal planning, the measure of specific volumetric fuel consumption (SVFC) was used. SVFC is given in units of /( )l kW h . SVFC is generally not affected by the engine size and can be used to

compare energy efficiencies of tractors having different sizes and under different operating conditions. SVFC for diesel engines typically range from 0.244 to 0.57 /( )l kW h (Grisso et al., 2004). For the

calculations the equation given at Agricultural Machinery Management Data, D497.4 (ASAE Standards, 2002b) was used:

2.64 3.91 0.203 738 173l

X XkW h

where, X is the ratio of equivalent PTO power required by an operation to that maximum available from the PTO. It has to be mentioned that the above equation models fuel consumptions 15% higher than typical Nebraska Tractor Test Laboratory (Grisso et al., 2004) performance to reflect loss of efficiency under field conditions. Also, the equation is estimate of specific volumetric fuel consumption, (SVFC) along the full throttle or governor response curve. It does not provide estimates of the fuel consumption during reduced engine speed settings that are often recommended for partial load applications (Grisso and Pitman, 2001). For the prediction of the fuel consumption the considered units in terms of power were the following: Table 19 – The four machinery cases were used in the simulated scenarios

Size Power (kW)

Case A small size unit 25Case B small/medium size unit 50 Case C large/medium size unit 75 Case B large size unit 100

In order to evaluate an “average” field operation, X was set to 75% while operating. During turnings X was set 0% (PTO off). It has to be noted that all of the savings derived from the minimisation of the turning and transport distances and thus fuel consumption during effective operation is the same for both optimal and traditional planned operations. This means that in the case of field operations that carried out also while turning, the expected savings should be even more. The results of the implementation of the above method on the examined cases are given in Fig. 19 and 20.


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Figure 19 ‐ Fuel consumptions for field A

Figure 20 – Fuel savings in ( /l ha ) from the implementation of optimal planning (presentment results regard field A)


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2.3 Fleet of Cooperating Machines

This part examines the potential savings derived from optimal management of a fleet of cooperating agricultural machinery units. The case of large‐scale grain harvesting was examined, since it constitutes the most important operation where in‐field cooperation between heterogeneous units (i.e. combines and transport carts) takes place.

2.3.1 Methods

2.3.1.1 Simulation Model for the optimal execution

During grain harvesting, the exact times when a harvester’s grain tank will become full and the corresponding locations where it must unload the grain can only be estimated with considerably large uncertainty because of the variability of the yield. Hence, the efficient scheduling for the unloading carts that serve a fleet of harvesters constitutes a stochastic optimization problem. There are two general methods developed to deal with stochastic optimisation problems; the a priori methods (Bertsimas et al., 1990) and the real‐time optimisation methods (Papastavrou, 1996). The first one is based on a priori probabilistic information on future expected events. For the harvesting case, for example, the a priori information comprise of knowledge of the statistics of the yield spatial distribution in the field. Such statistics are difficult, if not impossible to obtain. Furthermore, the uncertainty related to the time and location of a “full‐grain‐tank” event increases the uncertainty of the next similar event, and so on. Due to the dependence between sequential “events”, the a priori scheduling method is of limited use for planning the operational execution of agricultural field operations. On the other hand, real‐time optimisation methods include the repetitive solution of a new static optimisation problem at a fixed sampling rate based on the latest updated information. For field operations related to un‐known demands, real‐time optimisation methods are more suitable due to the limited number of primary units (i.e. combines) which does not result in planning problems of high complexity making re‐planning possible in almost real time (Bochtis and Sorensen, 2009). The method used for optimal operation planning is based on an algorithmic approach for on‐line coordination of combines and transport carts during harvesting operation presented by Bochtis et al., (2007). The method regards a real time optimization where static optimization problems are solved continuously, at a fixed sampling rate, based on the latest updated information. At a determined sampling interval, state vectors for each mobile unit participating in the operation (i.e. harvesters, transport carts) are received from the dispatching centre. State vectors contain the location of each unit (x, y co‐ordinates) including the load that they are carrying and their state (if they are in an unloading procedure or not). From the evaluation of the vehicles’ state vectors, the probabilistic parameters are updated. These parameters are the average yield, the average operating speed of the harvesters, the average speed manoeuvring at the headlands, the average in‐field and out‐field travelling speeds of the carts. Using these parameters, a simulator predicts the possible locations as well as the remaining time for the next filling of each harvester’s grain tank. For the generation of optimal in‐field paths to be followed by the service units, a path planning approach presented by Bochtis et al., (2009) was used. The approach is based on an abstraction of a field as a 2‐dimentional grid in which obstacle, free, initial and goal regions are defined. From the


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action spaces of the grid states, the nodes of a discrete transition graph are created and by using a breadth‐first graph search algorithm the optimal path is generated. The paths that connect the current location of each transport cart with each other location (facility units, i.e. silos, and harvesters) have to be determined each time a re‐planning occurs. Based on the provided information, a weighted graph is created. The static capacitated routing problem is solved using dynamic programming and its solution results in the assignment of harvesters to the carts, the sequence of their service and the routes which the carts have to follow, according to the optimization criterion of minimisation of the total travelled length of the paths followed by the carts and the penalty factor for the cases where a harvester stops its operation while waiting for the transport cart. For the simulation of the above described planning tool, a simulation program developed by Bochtis and Vougioukas (2007) has been implemented. The architecture of the program is described in Figure 21. The input data that are provided to the simulator are the following:

Field: These data concern the area and the geometry of the field and also the locations where the silos

or the transport trucks are placed as well as their capacities and their cycle time.

Machinery: In the case of harvesting, this input concerns the number of the harvesters, the number of

the grain carts, and the operational features of these machines/vehicles. These features include their

kinematics (minimum turning radius, operating speed, speed during turnings, etc.), the capacities of

their tanks, the operating width of each harvester, the unloading rate of each harvester and each cart.

Traffic mode: There are available two options for the field traffic of the grain carts concerning the kind

of paths that they are commanded to follow. According to the first mode, the carts are restricted to

manoeuvring only on the field’s boundaries and thus they must enter the track where they will meet the

harvester and moving in the same direction as the harvester. According to the second option, the carts

can move freely inside the harvested area. This means that the carts are allowed to perform loop turns

in the field’s interior if there is adequate space.

Field work pattern: The area coverage plan of the operation. It concerns the allocation of the field tracks

to the harvesters, and the permutation of the allocated tracks that each harvester must follow.

Initial system state: These data concern the initial locations of the harvesters and the carts and their

initial load (if there is). Also, initial values are given to the probabilistic parameters of the system. These

parameters are the average yield, the average operating speed of the harvesters, the average in‐field

and out‐field travelling speeds of the carts.

The important feature of this simulation tool is that the yield is not known at the beginning of the operation. On the contrary, it is provided to the simulator as the simulation proceeds, just like in the actual operation where the yield after the current point is unknown. By doing so, the dynamic nature of the harvesting operation is being taken into account and the simulation’s results are more realistic.


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Figure 21 ‐ The architecture of the simulator for the optimal machinery co‐operation

2.3.1.2 Simulation Model for the traditional execution

For the evaluation of the system’s performance when operations are carried out based on the traditional operation planning, a simulation model presented by Sørensen (1999) was used, supplemented with modules for specific operations (Sørensen, 2003; Sørensen et al., 2003). The simulation model has been designed with the purpose of analysing and supporting the managing of the physical farm resources (time, labour, technical equipment, installations, etc.) associated with production activities in the field – see Figure 12. The simulation model has been built by using detailed work studies producing basic performance data (time required, machine performance, etc.), enabling the evaluation of operational performance to be adjusted to farm‐specific conditions. The total time for specific machines or collaborating machines is divided into time elements. These time elements include operation time (effective field time, turning time, unloading, etc.), ancillary time (adjustments, repair time, disturbances due to crop or soil, relaxation allowance, etc.), waiting time and preparation time. The simulation model is used in two ways: (1) in a diagnostic way to determine the “current state” of the field operations, or (2) in a prognostic way to predict the state of the field operations system given operational variables including machinery size, transport distance, dosage, etc. The latter data application involves the use of work models (labour requirement/machine capacity as a function of machinery size, dosage, etc.) using the data for work elements as building blocks for such models (e.g., Auernhammer, 1976; Nielsen and Sørensen, 1993; Achten, 1997, Sørensen & Nielsen, 2005)). The work models are then aggregated to different levels, such as machine level, crop level, and farm level..


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Figure 22 ‐ Procedural outline for analyzing and modelling operational resources

2.3.2 Results

The simulation examples were based on recorded yield data from the harvesting of a winter wheat field of approximately 5.5 ha (Figure 23). The average yield was 7.69 tn/ha.

Figure 23 - The yield map of the field used for the case studies; the black polygonal line indicates the part of the field where the simulation took place. The effective operating width of the harvesters was set to 5 m. The average yield‐dependent speed of the harvesters was set to 1.4 m/s, while the load‐dependent traveling speed of the carts was set to 2 m/s for in‐field transportation and 2.4 m/s for out‐of‐field transportation. The unloading rate for the harvesters (to the cart) was set to 75 l/s and for the cart (to the silo) 105 l/s.


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Table 20 – Simulation results for the optimal operation execution Number of harvesters

Harvester’ Grain tank Capacities (t)

Number of Carts

Cart Capacities (t)

Idle time (s)

Total Delay(s)

Operational time (s)

Harvester 1

Harvester 2

Harvester 3

Capacity (ha/h)

2 6 2 12 219 543 543 6170 2.81

18 261 36 261 5888 2.93

3 4

3

12 0 96 87 96 4702 3.59

16 0 96 0 96 4702 3.59

6 18 0 0 0 0 4606 3.66

Table 21 – Simulation results for the traditional operation execution Number of harvesters

Harvester’ Grain tank Capacities (t)

Number of Carts

Cart Capacities (t)

Idle time (s)

Total Delay(s)

Operational time (s)

Harvester 1

Harvester 2

Harvester 3

Capacity (ha/h)

2 6 2 12 745 890 890 6517 2.67

18 365 619 619 6246 2.78

3 4

3

12 327 512 715 715 5321 3.21

16 0 245 435 435 5041 3.38

6 18 0 230 265 265 4871 3.48

Table 22 – Savings for the implementation of optimal planning

Number of Carts

Cart Capacities (t)

Total delay reduction (%)

Operational time reduction (%)

Capacity increase (ha/h)

Capacity increase (%)

2 12 38.99 5.32 0.14 5.17

18 57.84 5.73 0.15 5.57

3

12 86.57 11.63 0.38 11.80

16 77.93 6.72 0.22 6.46

18 100.00 5.44 0.18 5.15


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Figure 24 – Effective capacity (ha/h) for the cases of optimal and traditional planning

Figure 25 – Increase of effective capacity from the implementation of optimal planning


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2.4 Conclusions

Multiple identical units:

The adoption of optimal fieldwork patterns for field coverage operations reduced the operational time

in the case of single‐fields in the range of 3.26% to 17.01% (

Table 8), and the non‐working travelled distance in the range of 25.47% to 66.25% (

Table 9), while the increase in the effective capacity (ha/h) (of the teams) was in the range of 2.71% to

19.53% (Table 17). The reduction in the case of multiple‐fields was 6.01% to 10.20% and of 26.24% to

41.85% for the operational time and the non‐working distance, respectively (

Table 10, and Table 11), while the increase in the effective capacity was in the range of 3.41% to 15.82%

(Table 18).

There is a non‐linear correlation between the number of units and the total operational time and

consequently to the effective capacity of system. In the case of the capacity, in a same extent, this is due

to the presence of the fixed non‐productive time (such as preparations, and adjustments). Nevertheless,

increasing the team size did not result in a corresponding reduction of the operational time. This fact is

mainly caused by the presence of the individual operation at the headland area that imposes the notion

of the prioritized tasks. In such cases of planning, route planning is not enough for the optimisation of

the whole operation. Optimised task allocation and a general mission planning problem should provide

the optimal planning of multiple‐units operations. Furthermore, the increased motion coordination

problems as a result of the increased traffic are expected to increase even more the divergence from a

linear type of correlation between number of units and operational time.

In the case of a single field operation, the differences between the executions using optimal and

traditional planning was seen in terms of the turning distances and the distances for travelling from the

last track to the exit point and form the entry point to the first track. In the case of multiple‐fields

operations, the inter‐fields travelled distance also is minimised in the case of optimal planning.

Fuel consumption


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The reduction in the fuel consumption during optimal planned operations was in the range of 1.82 /l ha

to 4.75 /l ha for different combinations of machinery power, maneuverability and working width. It

has to be noted that all of the savings derived from the minimisation of the turning and transport

distances. This means that in the case of field operations that carried out also while turning, the

expected savings will be even more.

Fuel consumption in the case of traditional planning for a 100 kW unit operating with working width of

6m, for the presented fields, was predicted to be 16.76 /l ha , while the total fuel consumption for a

team of 4 units of 25 kW power was 12.18 /l ha . The total operation times for these two case were

predicted to be 6291 s and 5818 s, respectively, resulting to a effective capacities 3.24 ha/h and 3.01

ha/h, respectively.

Cleary, the case of 4 small units operating following optimal planning is significant more effective of a

large unit operating according to the current traditional planning in terms of fuel consumption, effective

capacity and consequently in timeliness cost, and soil compaction effects. Nevertheless, fixed,

ownership costs, labour costs and reliability have also to be considered.

Cooperating units

The use of optimised panning in the case of the multiple‐harvesting operations resulted in savings in

operational time and increase in the effective capacity of the whole system. The reduction in the

operational time was mainly a result of the reduction of the in‐field travelled distance. The out‐of‐field

travelled distance remains the same since the same number of trips required for the removal of the

total harvested yield in both cases of traditional and optimal planned operations. This fact that provides

additional benefits in terms of reduced soil compaction, given that transport carts usually carry material

quantities that are multiple times greater than the tank capacities of the harvesters.

When the number of the cooperating units increases the savings in operation time also increase. In

terms of the implementation of larger teams of agricultural machinery units, effective planning tools are

needed.

Optimal planning can even reduce the required machine capacity (and consequently, the machinery

size) that necessary in order to obtain a total operational time as predicted by the modelling of the

traditional operations execution. For example, according to the traditional execution for the case of 3

harvesters with a 6 t grain tank supported by 3 carts with a 18 t grain tank, the total operational time

equals 4,871 s (Table 21). In the case of optimal planning of the operation carried out by 3 harvesters of

4 t grain tanks supported by carts of 12 t grain tanks, the total time is almost the same (even reduced

about 3 min ‐ 4,702 s) (Table 20).


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Issues for further consideration:

Enhanced task allocation (headlands, especially in the case of a number of subfields where more than

one headlands need to be covered before or after the operation)

Development of algorithms capable of generating optimal routes for multiple‐ non‐identical

(homogenous in terms of the operation) units. This make sense since usually the available teams, i.e. of

a contractor, consists of different units in terms of operating width, maneuverability, capacity, power,

etc.

Docking issues (Hao et al., 2004)

Traffic coordination issues (Vougioukas et al., 2006)

General:

Low computational time requirements of the planning algorithms (for the route planning of coverage

operations and the on‐line coordination of cooperating machines), makes it feasible to perform the re‐

planning of the operation in almost real‐time. This is a very important aspect in the case of a unit failure,

since new routes and tasks can be planned, sequenced and allocated to the rest of the team very fast,

resulting in an increased reliability of the multiple‐unit system compared to the single‐unit systems, as

long as there is overlap between the capabilities of the units.

2 . 5 R E F E R E N C E S

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Auernhammer H (1976). Eine integrierte Methode zur Arbejtszeitanalyse. KTBL‐Schrift 203. Kuratorium für Technik und Bauwesen in der Landwirtschaft e. V. 61 Darmstadt‐Kranichstein, Germany. 261 pages

Auernhammer H (2001). Precision farming‐the environmental challenge. Computers and Electronics in Agriculture, 30(1–3), 31–43.

Blackmore B S; Stout W; Wang M; Runov B (2005). Robotic agriculture–the future of agricultural mechanisation? In: Fifth European Conference on Precision Agriculture (Stafford J V ed), pp. 621–628 Wageningen Academic Publishers, The Netherlands.


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Bochtis D D; Vougioukas S G (2007). Agricultural Machine Allocation based on Simulation. In Proceedings of the 2nd IFAC International Conference on Modeling and Design of Control Systems in Agriculture, 147‐152. Osijek, Croatia.

Bochtis D (2008). Planning and Control of a Fleet of Agricultural Machines for Optimal Management of Field Operations. Ph.D. Thesis. AUTh, Faculty of Agriculture, Department of Agricultural Engineering, Greece.

Bochtis D D; Vougioukas S G (2008). Minimising the non‐working distance travelled by machines operating in a headland field pattern. Biosystems Engineering, 101 (1), 1–12.

Bochtis D D; Vougioukas S G; Griepentrog H W (2009). A Mission Planner for an Autonomous Tractor. Transactions of ASABE, 52(5).

Bochtis D D; Sørensen C G (2009a).The Vehicle Routing Problem in Field Logistics Part I. Biosystems Engineering, 104(4), 447‐457.

Bochtis D D; Sørensen C G (2009b). The Vehicle Routing Problem in Field Logistics Part II. Biosystems Engineering. Article in press, available on‐line, doi: 10.1016/j.biosystemseng.2009.10.006.

Bochtis D D; Oksanen T (2009). Combined coverage path planning for field operations. In Proc. Joint International Agricultural Conference, JIAC 2009, Precision Agriculture 09, Edts: Van Henten E J; Goense D; Lokhorst C, Wageningen, Netherlands pp 521‐527.

Bochtis D D; Sørensen C G; Vougioukas S G. Path Planning for in‐Field Navigation‐Aiding of Service Units. Computers and Electronics in Agriculture, under review, submitted 03‐Nov‐2009.

Choset H (2001). Coverage for robotics ‐ A survey of recent results. Annals of Mathematics and Artificial Intelligence, 31: 113‐126.

Fountas S; Blackmore B S; Vougioukas S; Tang L; Sørensen C G; Jørgensen R (2007). Decomposition of agricultural tasks into robotic behaviours. CIGR E‐Journal, IX. October.

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Griepentrog H W; Blackmore B S (2007). Autonomous Crop Establishment and Control System. In Proc. Land‐Technik AgEng 2007 ‐ Engineering Solutions for Energy and Food Production, Hanover, Germany, VDI‐Verlag, Duesseldorf, Germany, 175‐181.

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Oksanen T (2007). Path planning algorithms for agricultural field machines. PhD Thesis, Helsinki

University of Technology Automation, Technology Laboratory, Finland.

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Papadimitriou C H; Steiglitz K (1998). Combinatorial Optimization. Mineola, New York: Dover Publications, Inc.

Papastavrou J D (1996). A Stochatic and Dynamic Routing Policy using Branchin Processes with State Dependent Immigration. European Journal of Operational Research, 95(1), 167‐177.

Sørensen, C.A.G. (1999) A Bayesian Network Based Decision Support System for the Management of Field Operations. Case: Harvesting Operations, PhD Thesis, Technical University of Denmark.

Sørensen, C.G., Jacobsen, B.H., & Sommer, S.G., 2003. An Assessment Tool applied to Manure Management Systems using Innovative Technologies. Biosystems Engineering 86(3), 315‐325.

Sørensen, C.G., 2003. Workability and machinery sizing for combine harvesting. The CIGR Journal of AE Scientific Research and Development, Vol 5. ISSN 1682‐1130.

Sørensen C G; Nielsen V (2005). Operational Analyses and Model Comparison of Machinery Systems for Reduced Tillage. Biosystems Engineering, 92(2): 143‐155.

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Vougioukas, S., Blackmore, S., Nielsen, J., Fountas, S., 2006. A two‐stage optimal motion planner for autonomous agricultural vehicles. Precision Agriculture 7:361–377.


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Figure 26 ‐ Field A operations. Left to right: teams of 2,3 and 4 units, up to down: cases A, B, C, and D.


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Figure 27 ‐ Field A operations. Left to right: teams of 2, 3 and 4 units, up to down: cases A, B, C, and D


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Figure 28 ‐ Field C operations. Left to right: teams of 2, 3 and 4 units, up to down: cases A, B, C, and D


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Figure 29 ‐ Field D operations. Left to right: teams of 2, 3 and 4 units, up to down: cases A, B, C, and D


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Figure 30 – Multiple‐field optimal operations for case D. Up to down: cases A, B, C, and D


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3 Fleet Management: Data and Information Requirements

Vougioukas2 S G; Bochtis1 D D; Sørensen1 C G; Oksanen3 T; Guzman4 J L.; van Henten5 E. 1Aristotle University of Thessaloniki, Faculty of Agriculture, Department of Agriculture Engineering, Greece.

2 University of Aarhus, Faculty of Agricultural Sciences, Department of Agricultural Engineering, Blichers Allé 20, P.O box 50, 8830 Tjele, Denmark.

3 Helsinki University of Technology, Department of Automation and Systems Technology, P.O. Box 5500, 02015 TKK, Finland.

4 University of Almería, Department of Languages and Computation, Ctra. Sacramento s/n, 04120, Almería, Spain.

5 Wageningen University and Research Centre, Bornsesteeg 59, 6708 PD Wageningen, The Netherlands,

This section of the report analyses the data and information requirements and flows of a fleet management system for agricultural operations. The term “data” refers to numbers or strings that can be stored in a database, communicated over some network and that can be used by some algorithm in order to come up with optimal or very good solutions to the scheduling and in‐field operation problems. The term “information” refers to any input can be used by humans to alter or guide the solution computed automatically by the system. One way to achieve this is by adjusting the cost function or the constraint set of the problem. For example, the current locations of all combine harvesters of a certain type in a fleet constitute data. The fact that the operators’ union has declared a strike for the next day constitutes information that must be entered into the system so that re‐scheduling is done. The flows of data and information describe the paths that can be used to travel from sources to destinations, and back and the precedence relations that may exist.

3.1 Data and information flows

Fleet management systems must operate at different levels of abstraction and different time scales if they are to become practical tools for farm machinery management. Off‐line (static) scheduling algorithms require knowledge of all problem parameters and accurate predictions of the durations of in‐field operations and inter‐field transfers in order to compute good schedules. Their computational complexity is very high and it may take tens of minutes, or hours to come up with close‐to‐optimal schedules. The computation depends on the size of the problem (number of fields, operations, types of machines, other constraints). As a general remark, off‐line planning algorithms require global knowledge about the fleet and the field operation requirements and can execute only on powerful computers. Therefore, it makes sense to run them on a central computing system, also called the dispatcher. Similar comments can be made about off‐line traffic planning for operations in the field, i.e., knowledge of all vehicle states and field conditions are required. However, the computational effort may be significantly lower, depending on the approach. For example, field coverage with small rectangular cells (Ali et al., 2009) requires two orders of magnitude longer computation (hrs) than parallel swath‐based coverage (Oksanen, 2007) (min). In a centralised scheme scheduling and traffic planning can be optimised together resulting in better performance. An example of a centralised system is the PROGIS LoGIStic system currently being used by the German sugar beet producers and


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machine contractors. All scheduling is performed on a central dispatching computer which has access to a GIS and database of all data relevant to the harvesting of all fields. In this system no traffic planning is performed, since the machines are conventional and do not utilise auto‐guidance.

Figure 31 Centralised architecture for management of conventional machine fleet for harvesting (PROGIS LoGIStic)

If the simpler approach were used, in‐field traffic planning could be performed locally by the on‐board computer of a designated coordinator machine, or centrally by the dispatcher. The scenario where scheduling is performed centrally and traffic planning is done locally is proposed in the work of Sørensen and Bochtis (2009). One drawback of this scenario is that scheduling and traffic planning are decoupled and there is no way that they could be optimised together, if more computing power were to become available. A centralised scheme would keep such an option open.


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Figure 32 De‐centralized vs. centralized planning distribution (Sørensen and Bochtis, 2009).

Once each machine has received its scheduling and field traffic plan from the central computer, the traffic plan’s coordinated execution in the field requires real‐time control and high‐bandwidth, low‐latency communication among members of the coalition operating in the field. Naturally, these algorithms must execute locally, using the on‐board navigation computers of the machines. It would be technically impossible for a central computer to control the navigation and operations of all machines. During cultivation it is very likely that the traffic plan will need to be recomputed due to unexpected events or conditions in the field. For example, differences between the real crop yield distribution and its off‐line prediction may render the planned grain unloading places and times obsolete, causing the a‐priori traffic plan of the loading carts to become useless. The on‐line computation of a new plan or the modification of the existing one requires information from all machines involved in the cultivation of the particular field and must be computed very fast to avoid idle times. Of course, a new traffic plan may influence the overall performance or feasibility of the original schedule. The ideal solution would be to re‐solve on‐line the entire scheduling and traffic planning problem centrally every time some parameter changes. This is – and most likely will remain – impossible because of the problem’s computational complexity. One approach is to decouple the scheduling from the traffic planning problem so that effectively the dispatcher abstracts the detailed in‐field traffic patterns and treats them as simple numbers expressing the duration of in‐field operations for any given machine assignment. This means that the new in‐field traffic plan could be computed locally and that only the updated estimated cultivation time must be communicated to the central dispatcher. The new plan could also be computed centrally and sent back to the coalition. In terms of speed, the choice will depend on the ratio of central over local CPU power and on the communication delays. In terms of reliability, it would be preferable to perform computation locally to avoid possible dispatcher or communication failures. Both schemes can be implemented in a more coordinated and timely fashion


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if one machine acts as a team coordinator, responsible for communicating with the central dispatcher and for re‐computing plans (Johnson et al., 2009). For example, if a new field traffic plan has been generated by the central computer each machine of a coalition must receive the entire plan, or the part that is relevant to itself. However, before switching to executing the new plan, it should be made sure that all machines have received it. If communication is between every machine and the dispatcher, this will require additional messaging among the members of the team. If a local coordinator exists, it is much easier for this coordinator to distribute the updated plan to all involved parties and verify its reception before signalling its initiation. Of course, if the coordinator fails for some reason, another machine could take its role using some well defined protocol. One very important issue related to data and information flow is the issue of representation. A fleet management system should be able to communicate with on‐board computers of agricultural vehicles of different companies and vice versa, i.e., a vehicle from one company should be able to exchange data with fleet management systems of different companies. As part of fleet management construction efforts, improvements in the on‐machinery communication interfaces and connection to the central managing unit are important. On‐going work in this area include the ISO TC 23/SC 19/WG1 (Agricultural Electronics), which has the purpose of setting up an open interconnected on‐board system, permitting electronic units to communicate, and to define the data exchange with the Farm Management Information System (includes software, decision support system, etc. for farm management).

3 . 2 D a t a a n d i n f o r m a t i o n r e q u i r e m e n t s

First we shall focus on the data required for assigning and scheduling machines to field operations and for planning their in‐field traffic off‐line. This procedure does not require any real‐time data, since it takes place before the beginning of all operations. An indicative list of required data is given below:

1. the set of the fields to be serviced located on a suitable detailed GIS map, from which the field boundary, field and headland areas and any obstacles can be computed accurately, along with additional descriptive data, such as ownership, soil condition, etc.

2. the set of operations in each farm in a suitable representation. For example: for a harvesting operation, the expected yield distribution together with additional descriptive data (crop type, predicted price, earliest and latest harvest dates, field loss function due to non optimal harvest date, etc)

3. the sequence in which the operations must be performed in each farm 4. the distance from one farm to another farm. This can be estimated by searching the road

network available in the GIS. 5. the time to transport any machines from one farm to another farm estimated by using distance

and expected transport speeds. 6. the price of fuel 7. the set of machines in the fleet. This set gives us the composition of the fleet, and contains for

each machine, its type and suitability for each operation, its availability, operational characteristics, like operating width, turning radius, fuel tank capacity, material capacity (where applicable), fuel consumption, operating costs, etc. The number of machine types, the number of individual machines of each type and similar data can be extracted from this set.


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8. the set of crew members (operators, assistants) and data related to them like hourly costs, availability ability to operate or service different types of machines, etc.

9. the initial locations of all machines 10. the minimum and maximum time lag between operations successive operations at each farm 11. the set up time of machines of a given type and the crew requirements 12. the time needed to carry out each operation at each farm if a certain number of machines of a

specific type are used 13. weather historical and prediction data that can be used to assess soil conditions, predict

unavailable days due to high probability of rain, etc.

3 . 3 C o mm u n i c a t i o n s i n f r a s t r u c t u r e

Within a fleet management system data and information needs to be exchanged between the central dispatching station and the vehicles, and between vehicles. The purposes and requirements of each type of communication are different and will be examined next.

3.3.1 Dispatcher‐to‐vehicle

Communication between a vehicle and the central dispatching unit is typically long distance, with ranges that may exceed hundreds of kilometres. Each vehicle must send periodically, preferably in real‐time its position and operational status to the dispatcher. This is already achieved by commercial fleet management systems using established commercial satellite and cellular telecommunication technologies. In Europe, where the coverage of GSM networks is very high, the need for satellite is lower. In contrast, such communication in USA, Canada, or Australia may need to rely on more expensive satellite links. Combinations of both technologies are also possible (Figure 33). The 2G GSM system supports data communications at the maximum rate of 9.6kbps. Higher data rates are possible when GPRS (<171kbps) and EDGE (<384kbps) are available. New 3G systems support much higher maximum data rates of 144kbps and 384kbps under high mobility and low mobility.


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Figure 33 State of the art fleet management communications architecture (Trimble’s @Road GeoManagerSM iLM® solution)

3.3.2 Vehicle‐to‐vehicle

Once each machine has received its scheduling and possibly its field traffic plan from the central dispatcher, the on‐board tracking controllers of the vehicles in the coalition will have to execute all or part of the traffic plan autonomously in a coordinated manner; hence fast and reliable communication mechanisms will be required. The two main operations which put a heavy burden on communications are cooperative motion control and collaborative collision avoidance. Although algorithms exist which rely solely on local sensing for coordination and collision avoidance it is expected that coordinated motion and collision avoidance in agricultural applications will use the services of the high precision GPS units available on most modern vehicles. This means that at minimum the tracking controllers of each vehicle involved in a formation will have to broadcast or unicast the vehicle’s state (position, velocity, acceleration, fuel and material tank level, etc) to all other vehicles in the formation, or in general nearby vehicles. If more elaborate coordination algorithms are used, such as predictive control, then the future states within a short time horizon must be sent. The key characteristics for evaluating wireless technologies for vehicular network communication are: performance, coverage area, reliability, security, and mobility. Performance is assessed from measured bandwidth and latency. High‐bandwidth and low latency are necessary to maintain fast and timely data exchange suitable for real‐time coordination. Coverage area is evaluated from the measured distance needed between base stations, the number of devices required to support the infrastructure, and whether the technology has the ability to switch/hand‐off between base stations without loss of coverage. Coverage area is an important characteristic for in‐field coordination because fields can be quite large, in the order of hundreds or thousands of meters. Reliability is characterized by the average number of dropped packets, average number of disconnects, and whether the technology is affected by environmental factors such as line of sight, weather, etc. Reliability is very important because the network will be used for coordinated motion and collaborative collision avoidance. If a connection is not reliable, packets are being dropped; the speed of the network connection will decrease. This would adversely affect the performance of the operation. Mobility is the speed of the mobile access point at which the technology can connect and remain connected without packet loss or service interruption. Naturally, a wireless vehicular environment will need to be mobile. The network must sustain connection at vehicular speeds which in agricultural applications are not very high. Since digital tracking controllers operate with a sampling period of a few milliseconds, coordinated motion and collaborative collision avoidance will require high‐bandwidth, low‐latency, high reliability, relatively long range and relatively high mobility networking technologies among members of the coalition operating in the field. In the next paragraphs existing candidate wireless technologies will be presented and compared. These technologies are: DSRC (IEEE 802.11p), WiMAX (IEEE 802.16) and 3G (ITU). A future emerging standard, MBWA (IEEE 802.20) is also presented. Dedicated Short‐Range Communication (DSRC) is a short to medium range communication technology operating in the 5.9 GHz range, which was developed especially for vehicle‐to‐vehicle (V2V) network applications. DSRC systems in Europe, Japan and U.S. are not at the present moment compatible. In


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the US DSRC will be based upon a group of IEEE standards, namely IEEE 802.11p and 1609 family, and will use seven 10 MHz‐wide channels in the 5.85‐5.925 GHz bandwidth. IEEE 802.11p is an extension to 802.11 Wireless LAN medium access layer (MAC) and physical layer (PHY) specification in order to add wireless access in the vehicular environment (WAVE). WAVE mode of operation foresees data exchange between vehicular devices in rapidly changing communication environments, where mobile stations may move up to 200 Km/h, have a nominal transmission range of 300m (up to 1000m), and default data rate of 6Mbps (up to 27Mbps). DSRC has two modes of operations: (1) Ad hoc mode characterized by distributed multi‐hop networking (vehicle‐vehicle), (2) Infrastructure mode characterized by a centralised mobile single hop network (vehicle‐gateway). Depending on the deployment scenarios, gateways can be connected to one another or to the Internet, and they can be equipped with computing and storage devices. The communication between the V2V devices is performed through a pre‐assigned communication channel when nearby vehicles are within range. It takes approximately 20 ms to handshake. Then each vehicle would allocate a channel, out of 10 possible channels, and communication would take place through that dedicated channel. The minimum time for data exchange between two vehicles is in milliseconds. This time includes data transmission and broadcasting latency and would vary depending on the load on the communications channels. A recent study has shown that the delay performance of a DSRC warning message falls well within the 100 msec delay requirement for safety applications (Tang and Yip, 2010). On the other hand the average throughput lied between 50% and 60%, which is considered modest performance from a safety point of view since more than 40% of vehicles, on the average, within the sender’s broadcast range will not receive the warning messages. WiMAX is the latest wireless technology to be approved by the IEEE 802.16 working group. It is a standard for point‐to‐multipoint wireless networking. The IEEE 802.16e version is an extension of the IEEE 802.16 standard that was drafted specifically to deal with mobility. WiMAX is a point‐to‐multipoint (PMP) technology that operates in the 10 to 66GHz and sub11GHz wavelengths. At higher frequencies, line of sight is a requirement. It can provide service over distances up to 50 Km. The WiMAX‐based solutions are set up and deployed like cellular systems using base stations that service a radius of several kilometers. The most typical WiMAX‐based architecture includes a base station mounted on a building and shall be responsible for communicating on a point to multi‐point basis with subscriber stations located in business offices, homes, and automobiles. Cellular systems have been evolving rapidly to support the ever increasing demands of mobile networking. The 2G GSM system supports data communications at the maximum rate of 9.6kbps. To provide higher rate data communications, GSM‐based systems use GPRS (<171kbps) and EDGE (<384kbps). Now 3G systems support much higher data rate. UMTS/HSDPA provides maximum rates of 144kbps, 384kbps, and 2Mbps under high mobility, low mobility, and stationary environments respectively. The average data rate perceived by users is much lower in practice: <128kbps for GSM/EDGE and <512kbps for 3G technologies. The reported packet latency is 150‐250ms. The behaviour of 3G services in a vehicular environment has evaluated by Qureshi et al. (2006). They reported that 1) the average round trip time (RTT) was consistently high (around 600ms) with high variance (ρ=350ms); 2) there were a small number of short‐lived (<30s) disconnections during their experiments; 3) the download throughput varied, ranging from 100kbps to 420kbps, and the peak upload throughput was less than 140kbps; and 4) they found no correlation between the vehicle’s speed and the achieved throughput, but geographic location is the dominant factor leading to


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variations. The high latency of the GSM packets and the variance in round trip times makes even UMTS/HSDPA technologies it a poor choice for vehicular coordination. Another candidate technology for V2V applications is Mobile broadband wireless access (MBWA) which is a name given to the IEEE 802.20 standard currently under development. The standard is still in its infancy and it is hoping to standardize an efficient packet‐based air interface that is optimized for the transport of IP‐based services. The goal of this standard is to enable worldwide deployment of affordable, ubiquitous, always‐on and interoperable multi‐vendor mobile broadband wireless access networks. The goal is also to support vehicular mobility up to 200 Km/h with spectral efficiency (throughput/bandwidth). It seeks to boost real‐time data transmission rates in wireless MANs (metropolitan area networks) to speeds that rival DSL and cable connections. It is being designed to operating in small chunks of spectrum, meaning that the required channel bandwidth is small. It requires base stations and has an approximate base station range of 15 Km. The following table presents a brief comparison of the wireless technologies.

Max. Bit rate Latency (expected)

Range (up to) Mobility (up to)

DSRC (IEEE 802.11p)

54 Mbps 50 ms 300 m 160 Km/h

WiMax (IEEE 802.16e)

100 Mbps 25‐40 ms 50 Km (LoS) 8Km (NLoS)

120‐150 Km/h

3G 2 Mbps 500 ms 1.5‐8 Km 120 Km/h at 384 Kbps10 Km/h at 2 Mbps

MBWA IEEE (802.20)

16 Mbps 10‐30 ms 15 Km 250 Km/h

Safe navigation support through wireless car‐to‐car and car‐to‐curb communications has become an important priority for car manufacturers as well as transportation authorities and communications standards organizations. While safe navigation has always been the prime motivation behind vehicle‐to‐vehicle (V2V) and vehicle‐to‐infrastructure (V2I) communications, vehicular networks provide a promising platform for a much broader range of large scale, highly mobile applications. Given the automobile’s role as a critical component in peoples’ lives, embedding software‐based intelligence into cars has the potential to drastically improve the user’s quality of life. This, along with significant market demand for more reliability, safety and entertainment value in automobiles, has resulted in significant commercial development and support of vehicular networks and applications. Therefore, the driving force behind V2V technologies is the car manufacturing industry. Given the strict safety requirements from V2V technologies the most promising existing technologies are DSRC and WiMax, provided that a worldwide standard will be achieved. MBWA promises to be superior to both of them, but it has not been implemented yet.


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3 . 4 C o n c l u s i o n s

On‐line fleet management must operate at the inter‐field transportation level performing dispatching, scheduling and routing, and at the in‐filed level providing coordination. The on‐line central computation of solutions of problems at both levels is not practically possible due to the problem’s computational complexity. Therefore computation is expected to be done both centrally and in a distributed fashion. This can be achieved by decoupling the scheduling from the traffic planning problem so that effectively the dispatcher abstracts the detailed in‐field traffic patterns and treats them as simple numbers expressing the duration of in‐field operations for any given machine assignment. This means that the new in‐field traffic plan could be computed locally and that only the updated estimated cultivation time must be communicated to the central dispatcher. Communication between every machine and the dispatcher may require excessive messaging among the members of the team. If a local coordinator exists, it is much easier for this coordinator to distribute the updated plan to all involved parties and verify its reception before signalling its initiation. Of course, if the coordinator fails for some reason, another machine could take its role using some well defined protocol. Within a fleet management system data and information needs to be exchanged between the central dispatching station and the vehicles, and between vehicles. Communication between a vehicle and the central dispatching unit is typically long distance, with ranges that may exceed hundreds of kilometres. Each vehicle must send periodically, preferably in real‐time its position and operational status to the dispatcher. Medium‐size latency, relatively low bandwidth and packet drop are acceptable in this mode of communication because real‐time vehicle monitoring for slow‐moving agricultural vehicles is not a demanding application. This is already achieved by commercial fleet management systems using established commercial satellite and GSM cellular telecommunication technologies. On the other hand, vehicle‐to‐vehicle (V2V) communications for coordinated motion control and collaborative collision avoidance will require high‐bandwidth, low‐latency, high reliability, relatively long range and relatively high mobility networking. The driving force behind V2V technologies is the car manufacturing industry. Given the strict safety requirements from V2V technologies the most promising existing technologies are DSRC and WiMax, provided that a worldwide standard will be achieved. MBWA promises to be superior to both of them, but it has not been implemented yet.


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4 Appendices

Appendix A: Terminology

Agricultural field operations Almost all agricultural field operations require the utilisation of one or several self propelled machines and implements. From a high‐level point of view, all agricultural machines consume energy and perform mass and energy transfer. Based on material exchange between field and machine, agricultural field operations can be categorised in three groups (Bochtis and Vougioukas, 2009):

1. Material input operations: In these operations material is carried by the machine and is distributed in the field area (e.g., seeding, spraying, fertilising).

2. Material output operations: In these operations material which is distributed in the field is collected and carried by the machine (e.g., harvesting, collecting hay bales).

3. Material neutral operations: No material is distributed or collected (e.g., tillage, cultivation, seedbed preparation, mowing)

Coalition of machines A coalition of machines assigned to an operation associated with the a certain field at time t, is any set of available machines which can be used for performing this operation. Control input of machine All manipulated variables which control the operation of a machine are contained in the machine’s time‐dependent control input vector Uij(tk) which may contain a continuous part, and a discrete part. The continuous part may contain real‐number variables such as throttle, wheel turn angle, etc. The discrete part may contain discrete variables such as the commanded machine’s gear (1, 2, 3, ..), lifting an implement (1) or lowering it (0), etc. Control input of fleet The control input of the entire fleet is simply the concatenation of all control input vectors. The fleet control input can be partitioned into a continuous part and a discrete part. Coordination of Machines Cooperation of Machines When more than one machine is used there are two major categories of operations: a) operations where the machines do not share, or compete for any resources, and b) operations for which machines must share, or compete for resources. In the former type of operations the machines work independently whereas in the latter they must coordinate or cooperate in order to execute the task. Coordination in this report is merely the resolution of resource‐sharing conflicts (e.g. avoid occupying


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the same space; aka collisions). Cooperation refers to coordinated motion which also involves the transfer or simultaneous use of resources in order to execute a task. As an example, harvesting requires the cooperation of a harvester and an unloading truck (grain transfer); pulling a log out of the field using two tractors requires simultaneous use of two cooperating machines. Field pattern Guidance pattern The terms field pattern or guidance pattern have been used to refer to the geometric path traveled by a machine inside a field (e.g., circular, parallel lines); motions outside of the field (e.g., headland turning) are typically not included. The same term has also been used to describe the swath sequence of a machine, when it moves in parallel lines. For example, in Hunt (2001) the continuous pattern, the straight alteration and the overlapping alteration are considered field patterns which differ in the sequence that the swaths are traveled. Such a use associates time or sequence information with the word ‘pattern’. In this work the term “field pattern” will be used to refer to the part of the traffic pattern which is strictly inside the field. Thus, the field pattern is a static collection of lines and does not include any time, or sequence information. Path of machine The machine’s path is a continuous geometrical curve and it is defined as the union of all its instantaneous positions. Note that the path is a geometrical entity, whereas the trajectory is a function of time. The term traffic pattern has also been used to refer to a collection of points which are produced by sampling the paths of machines. Position of machine In the context of performing a specific agricultural task T, consider a machine which starts its operation at some time instant t1 and stops operating at a time instant t2. The geo‐referenced position of the

machine at any time instant 1 2 ot t t is given by its coordinates.

Pre‐emptive allocation In pre‐emptive allocation, a machine must complete the execution of the operation it is currently performing before being assigned to another operation. Semi‐autonomous machine A semi‐autonomous machine is one which can operate autonomously for parts of an operation (e.g., row auto‐guidance, headland turning) but requires a human operator to execute parts of the operation and to supervise the entire operation. Hybrid system equations for machine In general, since the state of each machine includes discrete components, its differential state equation which describes the machine’s operation may depend on the discrete state; it is essentially a hybrid system. For example, in a vehicle with four distinct gears, the acceleration depends on the efficiency function of the current gear. State of machine


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All data related to a machine’s current location, operating status, etc is contained in the machine’s time‐dependent state vector which may contain a continuous part, and a discrete part. The continuous part may contain real‐number variables such as UTM Northing, orientation, speed, etc. The discrete part may contain discrete variables such as the machine’s current gear (1, 2, 3, ..) , whether an implement is up (1) or down (0), etc. State of fleet The state of the entire fleet is simply the concatenation of all machine states. Trajectory of machine The motion of the machine during its entire operation in task T is completely described by its continuous trajectory, which is basically its coordinates as a function of time. The trajectory includes the motions outside the field, e.g., during turning. In the agricultural engineering literature the term traffic has also been used to refer to the GPS position and timestamp data associated with the motion of one or more machines. A machine’s traffic constitutes a discrete sampling of its trajectory.


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Appendix B: Representative scheduling problems

The problem of allocating finite resources over time with various constraints arises in many application fields like project management, manufacturing, computing and networking, human resources management, logistics, robotics and many others. Next, three of the more representative problems are presented.

4.1.1 Project scheduling

Following Kolisch and Padman (2001), project scheduling problems (PSP) are made of activities, resources, precedence relations, and performance measures. A project consists of a number of activities, also known as jobs, operations, or tasks. In order to complete the project successfully, each activity has to be processed in one of several modes. Each mode represents a distinct way of performing the activity under consideration. The mode determines the duration of the activity, measured in number of periods, which indicates the time taken to complete the activity, the requirements for resources of various categories as explained later in this section, and possible cash inflows or outflows occurring at the start, during processing, or on completion of the activities. The presence of modes complicates the PSP by requiring assignments of activities to different modes. Often technological reasons imply that some activities have to be finished before others can start. This is handled by depicting the project as a directed graph where an activity is represented by a node and the precedence relation between two activities is represented by a directed arc. Also, minimum and maximum time lags may be given between the finish of an activity and the start of the next one. Resources utilized by the activities are classified according to categories, types, and value. The category classification includes resources that are renewable, nonrenewable, partially renewable and doubly constrained. Each resource type has a value associated with it, representing the available amount. Whenever there is at least one category of constrained resources, we term the resulting PSP a resource‐constrained project scheduling problem (RCPSP). Makespan minimization is probably the most researched and widely applied objective in the project scheduling domain. The makespan is defined as the time span between the start and the end of the project. Since the start of the project is usually assumed to be at t = 0, minimizing the makespan reduces to minimizing the maximum of the finish times of all activities. Other performance measures are the minimization of the (weighted) flow time of the activities or, if due dates are given, the minimization of the (weighted) delays, activity plus resource cost, and others. In the standard PSP the duration or processing of an operation is fixed and known. A generalization of this setting that is still deterministic (and assumes complete information) is obtained by permitting processing times to vary according to how much the planner is willing to pay for it. This control on the processing times can be interpreted as allocation of a nonrenewable resource to the activities, where a larger allocation to an activity (i.e., a higher cost input) reduces its processing time. As the allocation is usually measured in money, these problems are commonly referred to as time‐cost tradeoff problems. In reality the processing time of activities may not be fixed because it is subject to unpredictable changes due to unforeseen events (weather conditions, obstruction of resource usage, delay of


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predecessors of an activity etc). In order to cope with such influences, the processing time of an activity is assumed to be a random variable. This is known as stochastic project scheduling and it leads to the area of stochastic dynamic programming. Because of complexity and stability reasons, scheduling is done by relatively simple policies or strategies (Möhring et al., 1984). The complexity of such problems is open, but there is evidence that is also NP.

4.1.2 Job shop scheduling

The standard deterministic job‐shop‐scheduling problem (JSSP) involves an assignment of a set of jobs to machines in a predefined sequence in order to optimize one or more objectives considering job performances measures of the system. A job shop environment consists of n jobs, m machines and each job has a given machine route in which some machines can be missed and some can repeat. Each job requires a fixed, known processing time on any given machine. The goal is to assign jobs to specific machines according to a schedule which minimises criteria like the makespan (end of last operation), or the average tardiness, etc. The number of all possible solutions of the standard JSSP is in the order of (n!)m and cannot be exhaustively enumerated even for moderate sized problems. Unfortunately, the standard JSSP is known to be NP‐complete when m≥3 (Garey, et al., 1976), which means that no nonenumerative algorithms are known. The deterministic JSSP has been studied extensively because of its importance for manufacturing and numerous approaches have been used to solve it (Jain and Meeran 1999). The standard deterministic JSSP has been extended to problems in which the execution time for a job is increased by a setup time which is dependent on the sequence of previous jobs in the machine. For example, a certain job after completion may impose more cleaning and retooling of the machine than another one, so that the next job is serviced. This problem is equivalent to the multiple Travelling Salesman problem and are even harder to solve than the standard JSSP. Another variation is the Dynamic JSSP (DJSSP) in which the number of jobs is not fixed and new jobs may arrive at any time according to some probability distribution. Furthermore, when job setup times or processing times are not fixed but random, the problem becomes one of Stochastic Job Shop Scheduling (SJSSP). Most of research in production scheduling is concerned with the minimization of a single criterion. JSSP has been recently extended to multi‐objective VRP (Loukil et al., 2005). A multi‐objective optimization problem is one in which two or more objectives or parameters contribute to the overall result. These objectives often affect one another in complex, nonlinear ways. The challenge is to find a set of values for them which yields an optimization of the overall problem at hand. Instead of an optimal solution, a set of solutions is computed which form the Pareto optimal of different objectives. If agricultural machines are thought of as manufacturing machines in a machine shop and field operations as jobs, then the Fleet Management Problem (FMP) looks similar to some variant of the deterministic job‐shop‐scheduling type problem; in particular to the JSSP with sequence dependent setup time. The reason is that in the FMP the assignment cost at time tk depends on the current state of the machines of a candidate assignment and consequently on the previous operations they were involved in. For example, assigning a machine to work in a field A will cost less if the machine is already operating there, rather than if it is currently working in a distant field B. The FMP cannot be expressed trivially as a JSSP because an agricultural field operation can be performed by more than one machine in parallel; this is not the case for JSSP, where a major assumption is that each operation is performed


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by only one machine. The FMP involves machine allocation (coalition formation) in conjunction with scheduling.

4.1.3 Vehicle routing

The classical vehicle routing problem (VRP) determines the minimum cost routes to a set of geographically dispersed customers for a fleet of identical vehicles of a specific capacity starting and terminating at a depot. Each customer must be visited only once by exactly one vehicle. The total demands of all points on one particular route must not exceed the capacity of the vehicle. The problem was introduced by Dantzig and Ramser (1959) and constitutes a difficult combinatorial optimisation problem. A large body of literature has been devoted to it, including a number of extensive reviews (Desrochers et al., 1990; Toth and Vigo, 2002). Following the analysis of Bochtis and Sørensen (2009), the VPR is a generalisation of the travelling salesman problem (TSP), in which one person has to visit a set of dispersed customers with a minimum cost. The TSP can be generalised to the case of multiple TSP (m‐TSP) in which more than one salesman is involved in servicing the customers. This is equivalent tot adding capacity constraints to the classic VRP. Addition of a new set of constraints results in a number of VRP instances. One example is the constraint of maximum length or duration of a route (distance constrained VRP – DCVRP) or that every customer should be served within a given time window (TSP with time windows – TSPTW and VRP with time windows – VRPTW, for the cases of single‐ and multiple‐vehicle problems, respectively). Such cases require vehicle scheduling in addition to routing. Furthermore, in some cases the possibility that customers return some commodities is considered (VRP with pick‐up and delivery ‐ VRPPD), and that all deliveries must be made on each route before any pickups can be made (TSP with Backhaus‐ TSPB and VRP with Backhaus‐VRPB, for the cases of single‐ and multiple‐vehicle problems, respectively). In practise, requests for service can often arrive sequentially in time, with stochastic inter‐arrival times. Moreover, locations and quantities of future demands may be unknown or known only probabilistically, as many routing problems are inherently dynamic (DVRP) and stochastic (SVRP). Stochastic Vehicle Routing Problems (SVRPs) arise whenever some elements of the problem are random (Gendreau et al., 1996). Common examples are stochastic demands and stochastic travel times. Sometimes, the set of customers to be visited is not known with certainty. Stochastic VRPs differ from their deterministic counterpart in several fundamental respects. The concept of a solution is different, several fundamental properties of deterministic VRPs no longer hold in the stochastic case, and solution methodologies are considerably more intricate. Since they combine the characteristics of stochastic and integer programs, SVRPs are often regarded as computationally intractable. Only relatively small instances have been solved to optimality and good heuristics are hard to design and assess. The SVRP can be solved by a‐priori optimisation methods (open loop) which minimise some expected – in a probabilistic sense ‐ cost. On the other hand, the DVRP can only be solved by on‐line policies which depend on the current state of the fleet and the new information arriving. Obviously, given some available information before the route scheduling. no a‐priori solution can be optimal in the cases that a) a new request for service arrives from a new node, b) nothing changes from the available information. A review of stochastic and dynamic VRP’s and various solution methods for can be found in Larsen (2000).


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Figure 34 depicts the relationships between all the previously mentioned VRP variations. More recently, attention has been devoted to more complex variants of the VRP (usually called “rich” VRPs) that are closer to the practical distribution problems than classic VRP models. These complex variants are characterised by such multiple depots, multiple trips, multiple vehicle types, and loading constraints (Bräysy et al., 2002; Cordeau et al., 2006).

Figure 34 Relationships between the basic VRP instances (Bochtis and Sørensen, 2009)

VRP has been recently extended to multi‐objective VRP (Ombuki et al., 2006). A multi‐objective optimization problem is one in which two or more objectives or parameters contribute to the overall result. These objectives often affect one another in complex, nonlinear ways. The challenge is to find a set of values for them which yields an optimization of the overall problem at hand. Instead of an optimal solution, a set of solutions is computed which form the Pareto optimal of both total cost and number of vehicles.

4.1.4 Solution techniques

Moderate and large size resource scheduling problems are too difficult to be solved exactly within a reasonable amount of time and heuristics become the methods of choice. Common heuristics are those based on applying some sort of greediness or applying priority based procedures including, e.g., insertion and dispatching rules. As an extension of these, a large number of local search approaches has been developed to improve given feasible solutions. The main drawback of these approaches, their inability to continue the search upon becoming trapped in a local optimum, leads to consideration of techniques for guiding known heuristics to overcome local optimality. Intelligent search methods like the tabu search constitute meta‐heuristics for solving optimization problems. Other meta‐heuristics include evolutionary algorithms, simulated annealing and ant‐colony optimization. Many state‐of‐the‐art meta‐heuristic developments are too problem‐specific or too knowledge‐intensive to be implemented in cheap, easy‐to‐use computer systems. A recent approach is to use hyper‐heuristics, i.e., use (meta‐) heuristics to choose (meta‐)heuristics to solve the problem. Next, a brief review of solution techniques will be presented for the scheduling problems presented above. There is vast literature available on the solution of PSP problems (Brucker et al., 1999; Kolisch, 2001). Exact procedures offer globally optimal solutions for small problems whereas heuristic procedures may


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solve larger problems without guarantees of optimality. Exact approaches include dynamic programming, zero‐one programming, and implicit enumeration with branch‐and‐bound. Heuristic techniques include single and multi‐pass priority‐rule based scheduling, truncated branch‐and‐bound, and meta‐heuristics include simulated annealing, genetic algorithms, and ant colony optimization. A promising approach is the constraint propagation technique in which model based local reasoning over the constraint set makes problem specific knowledge, which is implicitly contained in the model description, explicitly available. The goal is to accelerate exact algorithms or local search procedures. JSSP is one of the hardest combinatorial optimisation problems. A large number of different solving approaches have been developed over the years. Exact methods use integer programming formulations and enumeration techniques like branch‐and‐bound (Brucker et al., 1994) to find a globally optimal solution. Exact methods can only solve relatively small problems. Many approximate (meta‐)heuristic methods have also been proposed which do not guarantee globally optimal solutions, but can tackle problems of large size. These include the shifting bottleneck procedure (Adams et al., 1988), simulated annealing (van Laarhoven et al., 1992), tabu search (Dell'Amico and Trubian 1993), genetic algorithms (Cheng et al., 1999), ant algorithms (Blum and Sampels, 2005), artificial immune systems (Hart and Ross, 1999) and constraint programming (Dorndorf et al., 2002). VRP constitutes one of the most challenging combinatorial optimisation problems, and a large number of different problem solving approaches have been developed over the years; they can be found in existing overview papers (Laporte, 1992; Bräysy et al., 2002; Cordeau et al., 2002). Exact methods use integer programming formulations and techniques like branch‐and‐bound, branch‐and‐cut, and branch‐and‐cut with pricing to find a globally optimal solution. Exact methods can only solve relatively small problems. Many inexact heuristic methods have also been proposed which do not guarantee globally optimal solutions, but can tackle problems of large size. These include simulated annealing (Osman 1993), tabu search (Gendreau et al., 1994), genetic algorithms, ant algorithms (Bell and McMullen, 2004) and constraint programming (Rousseau and Gendreau, 2002). As it can be seen all problems share similar exact or aproximate solution methods, based on heuristics. Good heuristics are extremely important because they enable the solution of very large problems. Heuristics depend on the aplication domain and require insight; hence they are hard to come up with. An alternative approach is learning appropriate heuristics. For example, Zhang and Dietterich (1995) presented a reinforcement learning approach to scheduling, that learned domain specific heuristics for the scheduling procedure. The state space consisted of possible schedules and actions were possible changes to the schedules. The system learned what changes would quickly create feasible schedules with maximized capacity utilization. The problem domain considered was space shuttle payload processing. Zomaya et al. (1998) presented another algorithm for learning scheduling heuristics. Their algorithm learned dynamic scheduling, i.e., scheduling when there is no a priori knowledge about the tasks. It used a back‐propagation neural network and a history queue that functions like an eligibility trace to learn how to associate a set of job parameters with a set of machines.

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