puigjaner - 1999 - handling the increasing complexity of detailed batch process simulation and...

8/13/2019 Puigjaner - 1999 - Handling the Increasing Complexity of Detailed Batch Process Simulation and Optimisation

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Computers n Chemical Engineering Supplement 1999 S929 S943930Puigjaner and Espufia, 1998; Calderon et al.,1997 .

TIle development of procedures for systematicsolution of the best solvents in a process-widebasis, including environmental risk, plant-siteand life-cycle evaluation Gran et al., 1994,1995, 1996 . The combined treatment of individual plantscheduling, enterprise-wide allocation ofproduction tasks among plants, and the planningunder uncertainty Sanmarti et al., 1995,1996,1997 of the logistics systems linking theseplants, their customers and suppliers Badell etat. 1997,1998 .

The recent research in these topics will bereviewed. Modelling and simulation will pay a keyrole in making those developments occur morerapidly and achieve global process optimization inindustrial practice. Examples from industrial casestudies will be provided which demonstrateencouraging improvements. Future directions will bealso indicated.2. Increasing tbe model complexity of batchoperations

When we look at the technical developments, themarket requirements, the social influences and theeffects of the general economic conditions on theenterprises, we state that the objectives haveundergone a fundamental change, Formerly,efficiency targets or cost-effectiveness ratios, i. e.Productivity mainly were the decisive factors, andexpansion relating to quantities w the basis of theentrepreneurial actims. More recently, inventoryreduction, flexibility and quality improvement havecome as additional factors. At present. the productionhas also to integrate environmental aspects.

So far, enterprise models have been proceedingfrom the approach of reducing the costs ofmanufacturing news products. The production cycleof the product was shortened. we want to masterenvironmental problems in the future, we primarilyhave to take care of the resources material andenergy, i. e. to utilise them to full advantage.However, we are adding complexity to the model andits solution may require infeasible computationaltimes.

Although computing power is being a limitingelement in the development of precise batchquantitative models, the model functionality shoulde the criterion to determine the appropriate trade-offbetween cost of development and benefit obtained. Asuggested hierarchy of models can be found in Rippin1996 ; with information being fed from one stage ofthe hierarchy to another as required.

While modelling environments for continuousprocesses support both simulation and optimisation,environments for batch process modeling arespecialised in two categories Macchietto et at.1986 .Packages that allow the process engineer to create

combined discrete-event differential algebraicmodels for simulation studies: e. g. UNIBATCHCzulek, 1988 , BATCHES Clark et al., 1992 ,gPROMS Barton and Pantelides, 1991 . On the otherside, a number of packages provide simplified modelswithout process dynamics for use in productionscheduling and preliminary design GANTT-KITHalasz et al., 1992 , Batch Master Cherry et al.,1985 , SUPERBATCH Cott and Macchietto, 1989 ,gBSS Shah et al., 1992 and BatchKit Hofmeister,1998 . No system is presently available that canaddress batch design and scheduling with detaileddynamic models.

In the next section we restrict our presentation torecent developments in batch process operationsmodeling that capture additional knowledge in thedetailed representation of batch processing systems.3. ndling the representation of complexrecipes

The realistic and flexible description of complexrecipes has been recently improved using a flexiblemodeling environment Canton et al., 1998a for tilescheduling of batch chemical processes. The processstructure individual tasks, entire subtrains orcomplex structures of manufacturing activities andrelated materials raw, intermediate or final productsis characterised by means of a Processing Networkwhich describes the material balance. Accordingly,the structure of the activities performed within eachprocess is represented by a general Activity Network.Manufacturing activities are considered at threedifferent levels of abstraction: the Process level, theStage level and the Operation level.TIlis hierarchical approach permits theconsideration of material states subject to materialbalance and precedence constraints and temporalstates subject to time constraints at different levels.At the process level, the Process and MaterialsNetwork PMN provides a general description ofproduction structures like synthesis and separationprocesses and materials involved, including

intermediates and recycled materials. n explicitmaterial balance is specified for each of the processesin terms of a stoichiometric-like equation relating rawmaterials, intermediates and final products Fig. 1 .Each process may represent any kind of activitynecessary to transform the input materials into thederived outputs.Between the process level and the detaileddescription of the activities involved at the operationlevel, there is the Stage level At this level isdescribed the block of operations to e executed inthe same equipment. Hence, at the stage level each

process is split into a set of the blocks Fig. 2 . Eachstage implies the following constraints: The sequence of operations involved requires aset of implicit constraints links .


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Fig. 9. Simulation of a pharmaceutical plant: resultsof the simulation .

5. Production scbeduling and optimization.

Fig. 8. Simulation of a pharmaceutical plant: recipedescription at the process level.This is a clear case of a multipurpose facilitywhere materials follow very different paths across theplant. Simulation results are given in Fig. 9 togetherwith storage profiles of intermediate materials. Thehierarchical structure of the recipe is also shown inthe input data window.

::F .i; .1 . 1_

1: :: : - . ~ ; . - : : - . -...- . - _ .

To obtain rigorous solutions to the problem ofoptimum scheduling of multipurpose productionstructures when the number of products andproduction stages increases constitutes a majorchallenge still today (Reklaitis, 1996, . 1998;Grossmann, 1996.Very recently, a novel combinatorial techniquefor short term scheduling of multipurpose batchplants s been proposed (Sanmartf et al. 1998). Ituses schedule-graph representation that offers a highdegree of flexibility and is very efficient in theevaluation of alternative schedules.Master recipes are represented as a directedconjunctive graph, where the nodes represent theproduction tasks and the arcs indicate the precedence

relationships among them (Fig. 10). The arc lengthequals the processing time of the tasks.Once the base schedule has been obtained, thebatch sequence in each unit is represented byadditional conjunctive arcs connecting the tasks that

Fig. 7. The recipe described as a structured set ofoperations. The O representation allows thehandling of complex synthesis problems.Other resources required for each operation(utilities, storage, capacity, manpower, etc.) can bealso considered associated to the respective operationand timing.

4. Plant Simulation.Simulation of plant operation can be performed interms of the EON representation from the followinginformation contained in the process recipe andproduction structure characteristics:

A sequence of production runs or jobs Orpassociated to a process or recipe p. A set of assignments Xujpr associated to eachjob and consistent with the process p tXujpr Sxujp .

A batch size Brp associated to each job and., consistent with the process p B rp m S Brp S rpmj

A set of shifting times Tn tn for all theoperatioos involved.These decisions may be generated automaticallyby using diverse procedures for the detennination ofan initial feasible solution. Hence, simulation may beexecuted by solving the corresponding O todetermine the timing of the operations and otherresources requirements.

5932 Computers and Chemical Engineering Supplement (/999) 5929-5943corresponding TOP, according to the batch size andmaterial Ilowrate..The necessary time overlapping ofsemicontinuous operations with batch units is alsocontemplated in this representation throughappropriate links.

4.1. ApplicationsThe EON representation has been successfullyused in a variety of industrial scenarios (finechemicals, polymers, food and leather industry, etc.)involving complex recipes and high number ofproducts (up to 35000 products) (Puigjaner et al.1996a). In the case of Fig. 8 a pharmaceutical plantproducing a high purity product is shown. Thecomplexity of the product recipe appears at thedifferent set of operations that should be carried outsimultaneously in the same recipe under limitedresources (Canton, et al. 1998b).


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Computers n Chemical Engineering Supplement 1999) S929 5943 5933are carried out in the same unit in the order in whichthey must be executed. Depending on which transferpolicy is used - unlimited intermediate storage illSor Non Intermediate Storage NIS)- and on theoverlapping of consecutive tasks, these additionalarcs present meaningful differences.

Fig. 10. Base graph

unit equipment) after processing until next isavailable.This situation is represented in the schedule graphplot by using zero length arcs. In Fig. 13 is shown the

NIS schedule-graph that minimises makespan for thesame base case of Fig. 10, and in Fig. 14 is thecorresponding Gantt Chart

5 1 UnlimitedIntermediate Storage

Fig. 11. illS schedule that minimises the makespan ofthe se case.

Tonz0

Fig. 14. Gantt Chart corresponding to the NISschedule of the base case.

Fig. 13. The NIS schedules graph that minimises themakespan of the base case.

5 3 Consecutive tasks overlapping

It is worth noting the remarkable differencebetween the resulting schedules obtained in eachcase, which should be taken into account to make arealistic modelling of the scheduling of the process.

In the previous discussion no overlappingbetween consecutive tasks has been. considered. Thismeans, that a task does not start until the preceding inthe recipe has finished. This assumption neglects thetransfer time between units, which is usuallyacceptable because of the small transfer times whencompared with processing times. But, in someinstances transfer times may be significant andsubstantial task overlapping may be potentiated toenhance other production aspects i.e. heatintegration) Corominas et al., 1995; Font et al.,1997). The schedule-graph representation alsoaccommodates to this situation and, what is moreimportant, without adding complexity to the model,simply by modifying the length of somme of the arcs,as it is shown in Fig. 15.

Ht i IH2 I . .ID c r J I J

7 TumO0

Although this is the most usual scenario in thediscrete manufacturing industry, this is not the case inthe chemical process industries CPl). In the illSgraph representation, the sequence in which tasks areexecuted in some unit is contemplated by connectingthese tasks with arcs of length corresponding to theprocessing time of the task. This can be observed inFig. II, where the minimum makespan schedule toproduce the three batches of Fig. 10 is shown. TheGantt Chart for this schedule is given in Fig. 12.

Fig. 12. Gantt chart for the illS schedule of the basecase5 2 Non Intermediate StorageThe NIS transfer policy describes in a morerealistic way the chemical batch plants operation.Here, the intermediate material is hold in the same

5 4 Determination of the optimal schedule based inschedule graph representationThe optimal schedule is found using a Branch andBound strategy B B). Each node in the B B tree

corresponds to a partial schedule. At the root of thetree, only the procedure constraints of each product


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5934 Computers and Chemical Engineering Supplement (1999) S929 S9 13

Fig. 16. Merging nodes to impose tasks simultaneity.When only partial overlapping occurs becausetasks do not start at the same time (Fig. 17), the

corresponding schedule-graph representation iscarried out by split ting the tasks in subtasks, so thatoverlapping occurs at the start of one of the subtasks.

..o .

,JO'0

E:EI

recipe are applied . (i. e. The schedule-graph containsno arcs representing task sequences in the units). Aslower bound the makespan is obtained using thelongest path algorithm based on the schedule-graphrepresentation.The longest path algorithm uses the schedulegraph representation to determine the longest path

from each node to the sink node proceedingbackwards. The path with maximal length gives theschedule makespan and also provides the timing ofthe whole schedule.

,0, ' , rr , ~ ISC oc c

Fig. 17. Partial task overlapping.

G0 , ,,,,

Fig. 18. Heat integration graph for the case of Fig. 17.

Fig. 19. Acyclic and cyclic graphs

6.1. Unfeasible task overlappingTask overlapping may become unfeasible when:a) the tasks belong to the same batch; b) the tasks are

carried outin the same unit. The first case can easilybe avoided, because this information is knownapriori and the corresponding hot-cold streams canbe removed in the preliminary ennumemtion. Thesecond se requires unit task assignment decisionswhen alternate units are considered to perform thesame task. The solution to this problem is equivalentto find feasible schedules.

Feasible schedules can be identified by examiningits associated graph and checking that it is acyclic(Fig. 19). When the arcs connecting the t sks form aloop, the resulting partial schedule is infeasible. InFig.20 is shown that when two tasks that belong tothe same unit sequence are merged into a single node,a loops is always generated.

Fig . 15. Schedule-graph representation of consecutivetasks overlapping.Then, the tasks assigned to the different units aresequenced one by one. Each time a task is sequenced

a branch is generated in the tree and the longest pathalgorithm is applied again. When the tree reaches thebottom, a complete schedule has been obtained andan upper bound of the makespan canbe calculated.Each time that the lower bound of the partialschedule of the node is greater t n the current upperbound, or when the partial schedule is not acyclic (i.e. it is infeasible), the branch that starts in the node ispruned.

This way, highly efficient graph algorithms areincorporated to Branch and Bound optimisationtechniques to solve multipurpose schedule problemsvery effectively. The B B algorithm takes care ofthe combinatorial optimization problem involved ineach scheduling problem, while the graph algorithmsallow a fast computing of the lower bounds thatcontrol the branching strategy (Sanmarti et al.,1998a).6. Heat Integration and scheduleoptimization

In order that two process streams may exchangeheat, they should coincide in time. This necessaryoverlapping imposesand additional constraint to thescheduling problem. The schedule-graphrepresentation can easily incorporate these additionalconstraints by merging the nodes corresponding tothe t sks requiring overlapping into a single node.This situation appears in Fig. 16, where tasks A8 andBI are constrained to start at the same time. Then anew node AlIBI is included now in the sequence oftwo units EI and E2).


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Computers and Chemical Engineering Supplement /999 S929 5943 5935

P3

PI

Fig. 22. Hot-cold streams combination tree

2

PI.P2 and P3 a:eacd...

situation, where some of the stream pairs are activeand the rest are inactive. This can be modelled usinga binary variable that takes value one when the pairsare active and zero otherwise.For example, if there are three possible hot-coldpairs PI , P2 and P3, the possible combinations areindicated in Fig. 22.

.-I R

Fig. 20. Overlapping of two tasks in the same unit.Usually, it will not be possible to get all possibleoverlapping between hot-cold stream pairs. First ofall, because of the assumption that a stream cannot beincluded in more than one selected pair. Secondly,because forcing task overlapping can generatealternate solutions which are not all compatible in thesame schedule. Decision-making optimisation will benecessary Fig. 21).

Fig. 21. Task sequencing determines heat integrationfeasibility.6 2 Heat integration and schedule optimizationThe schedule global optimization makespanminimization) and heat integration energy useminimization) requires and overall objective functionof the type:

For both objective functions, the optimizationprocedure is very similar. It considers two embeddedbranch-and-bound algorithms: one for the heatintegration and the other for the scheduleoptimization. The heat integration B B tree containsall hot-cold stream pair feasible combinations. Eachnode in the tree corresponds to a heat integration

7 Simultaneous energy andwater minimizationModeling the water management in the processindustries has gained considerable attention in theselast years Wang and Smith, 1994; Dhole et al.,1996). The consequences of water management in thebatch processes are of special importance in sectorslike the food industry. The total water demand ofthese industries can be categorised in three groups:process, cleaning and utility water Almato, et al.1996).Process water requirements depend mainly on thecharacteristics of each production process. Equipmentcleaning and set-up are water intensive operations. Inorder to prevent product contamination, these tasksarc often carried out using water streams at differenttemperatures and flowrates. The wastewatergenerated during cleaning t s s may represent a

considerable part of the total waste water originatedin the plant. Finally the water used in the utilitysystems, essentially for cooling and beating, may alsoconstitute a significant fraction of the total waterdemand.

Each node in the tree implies a set of heatintegration constraints. The schedule that minimisesmakespan subject to these constraints is obtained inthis way. no possible schedule satisfying theseconstraints can be generated. the hot-cold paircombination is discarded, as well as all othercombinations generated from this point of the freehe branch is cut).The optimal schedule calculation described beforeis used to find the makespan lower bound. while theenergy use lower bound can be obtained solving theMIP problem formulated above Equations 6) and7, taking into account which hot-cold stream pairsare fixed active or inactive) and which are freeanmartf et al., 1998 b).

6)

5)

7)

z o MS p U

S ~

subject to

Where MS is the masespan, TEU the total energyconsumption and c, p are weight coefficients. Thefine tuning of and P should be done for eachindustrial scenario according to the relativepreponderance of productivity vs. energy in eachcase. In practice, only if there is remaining idle timeafter production objectives are satisfied that adecrease in productivity will be tolerated to enhanceenergy integration.When a minimum productivity of the plant mustbe obtained, the objective function is reduced to find

the minimum energy consumption under theconstraint of keeping the makespan below some timehorizon, that is


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9 6 Computers and Chemical Engineering Supplement 1999)S929 S943Water is used at different temperatures indifferent processes steps and at different times. Intime-dependent process, water requirements andwastewater generationsare closely tied to the specificproductioo sequenceand task schedule Almat6et al.,1997). For this reason, a rust step for the watermanagement modeling is the plant productionplanning and task scheduling. ParalIel to theproduction Gantt Chart, a Stream Chart can bedefined where waterstreams are represented either aswater requirements i. e. operation s inlet waterstream) or as water generations i. e. operation soutlet water stream) in a concentration vs. time plot Fig. 23). Once the Stream Chart is built, waterstreams can be completely characterised by theirflowrate, supply and target temperature, contaminantconcentrationupper boundand operationtime.

5 10 5 20 h

whereas direct mixing can only be used for waterstreams when contamination constraintsare satisfied.The freshwater use, waste water generation and theenergy associated to water depend the assignmentbetween water streams and tanks. Depending on itscontaminatioo level, every water stream generated isstored in a specific tank. A requirement can besupplied by a tank when the contaminantconcentration of this tank is lower than the maximumpermitted by the requirement Operations requiringhigh purity water will possibly be supplied using onlyfreshwater, while some generated streams at highcontaminant levelsmay be directly sent to the end-ofpipe water treatmentsystem.Every time that a streamenters a tank or is supplied by it, the tank level,contaminant concentration and temperature maychange. The general overview for the watermanagementmodel appears in Fig. 25 Almat6et al.,1998).a)

_

252015105 -

5 10 15 20 h

b)\YRI

Fig. 23. ProductionGantt Chart and its correspondingStream Gantt Chart7 1 Water and energy use reduction

Because of the time dependence of the streams,direct reuse of water will ooly be possible if bothstreams operate simultaneously and satisfy thecontaminant concentration and temperatureconstraints. Therefore the water management modelconsiders the use of storage tanks for spent water toincrease the reuse opportunities between operations.These tanks store spent water and supply it for reuseto other sectionsof the plant, which implies a certainpotential for water reuse and energy recovery bymeans of streams direct mixing. Additionally,regeneratioo units for waste water effluents can beused to reduce their contaminationload Fig. 24).Energy recovery in water streams canbeobtainedby means of either heat exchangers or direct streamsmixing. Heat exchange between hot and cold streamscan take place among water and non-water streams,

Fig. 24. Water use reduction opportunities: a) Directwater reuse; b) use of water tanks.

Fig. 25. Watermanagementmodel overall structure.A key issue in the modelingprocedure is the tankstream assignmentproblem. The decision variableXdsis used to describe the fraction of water streamIlowrates assigned to tank Two fictitious tanks areconsidered: one contains the freshwatersource d;O),and the other the wastewater for disposal d=D+l).For a given production plan, the total freshwater


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Plant management and scheduling control,including planning, scheduling and plant wideoptimization;Subplant co-ordination between majorproduction areas, including local scheduleadjustments and recipe modifications;

Switching and supervisory control of processunits, including appropriate handling ofemergencies;

Modeling batch processes may become verycomplex when it comes to the level of detailsrequired to adequately represent real-life operations,and very difficult to standardise if it involves a verywide variety of operations, as happens to be the caseof the batch industries. Also, a major limitation ofpresent solutions is that they do not adequately reflectthe distributed nature of the problem Puigjaner et al.,1994 in terms of organization and production unitsplants, production departments, lines, batch units .As a consequence, internal disturbances occurring atany level of this organitazional context or externalperturbations caused by the market environment maycreate frequent and irrecoverable readjustments inreal-life industrial operations Pekny et al., 1991 . Arealistic answer to this situation inevitably entailsappropriate consideration of the interaction betweenvarious planning levels linked to the batch controlsystem:

8. Real-time optimization models

8The global cost of the water management includesalso the investment and operation cost of the water

reuse network.

Fig. 26. Water reuse network: FW freshwater, DW wastewater disposal, T1water storage tank.The objective function considers the total costsassociated to water use during the production periodconsidered. These costs include the cost associated tofreshwater supply nd conditioning Pq waste watertreatment and disposal P , and the energy consumedfor heating Ph and cooling water streams. Thecosts are related to the volume of water WVj. WV orthe utility consumption U U;

Computers and Chemical Engineering Supplement 1999 S929-5943 S937demand and wastewater generation can be the initial design are necessary to contemplate thedetermined from the tank filling level profiles of the optimal global water reuse network.two fictitious tanks. The assignment procedure allowsthe design of the water reuse network by defining theconnections between tanks and equipment units andidentifying the flowrate at each connection Fig. 26 .

where the investment NV contemplates the cost oftanks and connecting network and the operation OPconsiders the running cost of assignments made.The model is subjected to constraints related to:Assignment, Tank filling level, nk contaminantconcentration, Stream concentration, nk

temperature profile, Stream temperature, and Hot andCold utilities consumption.The resulting model is MINLP. To alleviate thesolution procedure, the model is reformulateddiscretizing the time horizon in time intervals. ninterval is defined between two events. n eventtakes place every time that a water stream starts offinishes to operate. At each time interval, the massand heat balance for each tank and stream involved issolved as a differential equation to find the values oftank levels and concentrations and the temperature of

tanks and streams.Considering that in the batch industries certainproduct campaigns are processed periodically, thewater reuse network should be designed for the mostsignificant production plan. For other plans,assignments should be optimized. Modificatices to

OF] = OF NV OP 9 Individual equipment regulatory and faultdiagnosis actions.All these levels should operate on a real timeprocess information base which must be supportedwith data reconciliation and trend trackingcapabilities Pekny et al., 1991; Puigjaner et al.,1994 .

8.1. Processco-ordination andsupervisory controlTraditionally, process supervisory control workedunder the assumption of that processing times ofelementary subtasks were accurate approximations ofreal executions, whereas time information used byplanning and scheduling actions was frequently anaverage estimation.As a realistic solution to these shortcomings,batch process supervisory control must not only dealwith the co-ordination of plan execution, but alsocapable of promising and analysing the deviations inprocessing time and other data expected in order to:

Avoid undesired bottlenecks in plan executionand management; Readjust schedules to current values under thepermissible limits and task transfer policies;


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5938 Computers and Chemical Engineering Supplement 1999 S929 S943 Provide information to a fault diagnosis systemto be used in recipe modification and adaptationof planned schedules as well Graells et al.,1998 ; Predict equipment malfunction and optimize apreventive maintenance system Sanmartf,1997 .

A process fault detection and diagnosis system forthe complex case of plant-wide control has beenrecently proposed Nougues and Puigjaner, 1996;Ruiz et al., 1998 . It considers an artificial neuralnetwork ANN}-based supplement of a fuzzy systemin a block oriented configuration Fig. 27 . is thesubset of the direct and indirect measurements and/orobservations from the plant, which is selected asinput to the ANN structures.

system, and the information network providing realtime data which involves long term operation,laboratory data, planning and scheduling Nougues etal.,1998 .

Plant

ANN

t

t

MPuzzificationFS F

Fig. 28. Real-timeplatform architectureThis system is being currently implemented at a

laboratory scale fluidized e gasifier plant where theplant performance is optimized in terms of energyand gas quality. Industrial applications include asugar refinery and concentrated juice manufacturingSabadi et al, 1998 .nferen e ngin l ......Set of rules Defuzzification

Fig. 27. ANN-based supplement of a fuzzy system ina block oriented configuration.The system proposed combines the adaptivelearning diagnostic procedure of the ANN and thetransparent deep knowledge representation of astructured form ofknowledge base system ICBES . Ithas been successfully used to handle simultaneousfaults in complex plants with recycle Nougues et al.1998 .

8 2 Real time systems optimizationAn integrated platform has been created thatincorporates optimization and production planningtechniques in conjunction with real time plantmeasurements and control aiming at product quality

enhancement and waste reduction Nougues et al.,1998;Puigjaner et al. 1998 .The system architecture has three layers. The firstis a supervisory control level which incorporatestechniques for diagnosis indicated before Ruiz et al.,1998 . The second is the co-ordination level whichprovides real-time informatioo for decision-makingatupper levels. The third level involves decisions onallocating the available resources under the variousproducts under demand Fig. 28 .The whole system exchanges information in two

ways, by the communications network system, andby the database management system RDBMS . Thecommunications network system incorporates a localcontrol network supported by distributed controlsystem vendors DCS , a control network consistingin a real-time client interface and advance control

9. nterpriseResource Planning odelThe consideration of financial and productionplanning as an entire unbroken process appears to bethe key that closes the loop of the business regulationcycle Badell and Puigjaner, 1998a; Badell and

Puigjaner, 1998b . Present Distributed ArtificialIntelligence tools can simulate the managementcontrol of the entire enterprise combining material,human and financial resources within a flexibleobject-oriented environment.In order to integrate the activities of management,process control and production, a new EnterpriseResource Planning ERP approachhasbeen recentlyproposed Badell et al., 1998 . The system considerstwobasic economic times: the budget assignment andfinanciaVproduction performance including theeconomic execution Fig. 29 .The two-layered model consists in the real timeproduction layer model and the autonomous orderentry layer model which is backed-up with a replicaof the real time schedule and a non-interactivescheduling program managed by a multi-agentsystem. The arriving orders are attached at the endcreating a new virtual plan The autooomous upperlevel system can be accessed through the Web orthrough the business level, which provides a quickfeedback/response to the requested orders. Underblackboard architecture a knowledge-based modelupdated with the daily events supports the rule-based

priority system for the determination of customerpriorities. This two layer architecture allows thevertical integration of the enterprise systems.


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I I I .',.. I I1 1IJ i II . I, '.IIn

.. : _ _._ _ '-

[ ti ' I I t,~ I_ . Ir : l tI

I I II ' M i

. . . . - . .. ,. . - . . . -:: 1Fig. 29. The RP conceptual approach

Theproposed RPsystem demand real time datamanagement (Badell et at 1997) on the state of theprocess, the situation of payments and billings, thefinance, the production accounting, the inventory andthe market The flow control between themanagement functions is guided by the globalplanning objectives.9 Financial scheduling model

Fig. 30. On-line cashflow profile, and minimumlevel, process profit profile and brcakeven line.Whole industry demands for communication

solutions that will bring together process control,scheduling and management systems, this approachgoes further by offering a real link on functionallevels between production, MRP, marketing andfinancial management in ERP systems.

The necessary relationship between productionand financial planning requires a common frameworkfor appropriate decision-making. The ONrepresentation (Canton et al, 1998) has been extendedto consider cash-flow representation. In the ONcontext, additional non-manufacturing processes canbe treated as well. In this case, commercial operationsare simulated using virtual process units.

The safety stock of net cash-flow can becalculated as any other form of inventory, Theminimum cash balance corresponds closely with thereorder point by economical order quantity (EOQ). Afictitious liquidity stream limited by an inviolablerestriction of minimum cash connects and regulatesthe inventory-production-marketing chain. Anenhanced concept of recipe that includes cashflowcan be represented in a Money Gantt Chart thatintegrates the production schedule (Badell andPuigjaner, 1997). The process economics can bedrawn including the net cashflow profile, the level ofminimum stock and the process profit profile with thebreakeven line (Fig. 30).

This new approach to ERP systems avoids the replanning activities of MRP-based systems at thedifferent enterprise hierarchical levels. It turns upsidedown traditional concepts of: first materials, secondproduct ion and then fmancial planning. Here, theprocedure is initiated with money, thensimultaneously production and materials. Moneyrepresentation avoids the blind financial decisionmaking usually present in the current practice. Theconsideration of l iquidity as a strategical variablecreates a partnership relationship between productionand fmance.

10. Supporting software and applicationsAlthough the developments described before bavecommenced essentially as an academic exercise, most

of them are the result of collaborative researchprojects with the industry. Therefore, both prototypesand commercial software is already availablesupporting the models described (MOPP, BOLD,WATERPLUS, MOPP-C, SCHEDUFIN).11. Final considerations

In his exceUent review of the state-of-the-art inbatch processes, Professor Rippin sensed a wideninggap in process simulation and optimization betweenbatch and continuous production systems anddeclared the current situation in batch processes asfilling in the boles . This was in the year 1992 .Now, seven years later, what we contemplate is thebatch problems and solutions situated at the samelevel as in continuous processes, even with a higherdegree of innovation on the batch side. This scenariobas facilitated an integrated and more realistic viewof the chemical manufacturing process as aconglomerate of continuous, semiconlinuous andbatch operations that share common problems thatrequire unified solution proposals. Extendedmodeling frameworks should contemplate continuousand time dependent processes, extensive usc ofdynamic models for real time optimization, improvedERP systems and the use of networkedmanufacturing information systems. These are someof the common challenges we are already facing. We


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Computers and Chemical Engineering Supplement (/999) S929 S94394believe thatdirection. further progress should go in this References

Nomenclature

Acknowledgements

Almato, M., Sanmarti E., Espuiia, A , Puigjaner, L (1996)Reduccion del Consume de Agua en la Industria Quimicade Proceso Discontinue, InnovacionQuimica 23, pp. 7882.Almato, M., Sanmarti, E., Espuiia , A and L Puigjaner(1997) Water and Energy Use Reduction in Food BatchIndustry . AlCirE Annual Meeting Session number 5656g. LosAngeles, California, USA. paper.Almato, M., Sanmarti, E., Espuiia, A , Puigjaner, L (1997)Rationalizing the Water use in the Batch Process Industry.Computers ChemicalEngineering S (5), S971 S976.Almato, M., Sanmarti, E.,Espuiia, A , Puigjaner, L (1998)A Software Tool to Achieve Minimum Water Demands inBatch Process Industries: Food Industry Applications.AlCIrEAnnual Meeting Miami, Florida,Almato, M.,Sanmarti, E..Espufia, A, Puigjaner, L (1999)Economic Optimization of the Water Reuse Network inBatch Process Industries. ESCAPE 9. Budapest, Hungary(accepted).Badell. M., Graells, M., Nougues , J. M., Canton, J.,Delgado, A. and L Puigjaner (1997) Integrated On-lineProduction and Financial PredictiveJReactive SchedulingProvided with Agent-Based Information System . AlCIrEAnnual Meeting Session 205, p 205c, Los Angeles,California, USABadell, M. Graells,M., Santos, G. and L Puigjaner (1997)SchedulingBatch Chemical Process Industries Backed withFinancial Management Tools Proc. InternationalConference on Industrial Engineering and ProductionManagement (Ed. D. Raulier), IEPM 97-FUCAM, Lyon,pp. 362-372.Badell, M. Canton, 1.. Puigjaner, L (1998) SimultaneousFinancial and Production Trade-Off Scheduling in ERMSystems with Profit Management Tools. AlChE AnnualMeeting Paper N241d, Miami, florida.Badell. M., Diez,R..Puigjaner, L. (1998) Scheduling Toolsfor Financial and Production Management at the BussinessLevel. PRESS 99, Budapest, Hungary (accepted).Badell, M., Grau, R., Espufia, A, Puigjaner, L. (1998)ERM Systems with Scheduling Optimisation Tools forBudgeting and Investments Analysis. AlChE AnnualMeeting PaperN239b, Miami, florida.Badell, M. Nougues, JM., Puigjaner, L (1998) IntegratedOn line Production and Financial Scheduling withIntelligent Autonomous Agent Based Information SystemComputers ChemicalEngineering 22 S, pp. S271 S278.Badell, M. Puigjaner, L (1998a) An Enterprise ResourcePlanning System Prototype in the Batch Industry. Proc.Tenth International Working Seminar on ProductionEconomics VoL 3, Kongresszentrum IGLS. Imbruek,Austria pp. 17-27 l998a .Badell. M., Puigjaner, L (1998) A New ConceptualApproach for Enterprise Resource Management Systems,Foundations of Computer ided Process OperationsFOC PO-98). p. P18, Snowbird, Utah.

Balchsizeofjob r following processpMaximum batch size of job r followingprocesspMinimum batch size of job r followingprocesspInversion cost of thewaterreuse networkOperation cost of thewaterreusenetworkBinary variable for the assignment ofprocessp tojob rUnitcostof coldutilityUnitcost of freshwaterUnitcostof hot utilityUnitcostof wastewaterAbsolutetimerelated to node 11Lower boundfor timeofnode11Timeofdestinynodeof linkkTimeof finalnodeof operationmTimeof initialnodeof operationOperation time for operation Waitingtime foroperation Maximum waitingtime foroperation Cold utilityconsumptionHot utilityconsumptionVolumeof freshwaterVolumeofwastewaterfordisposalBinaryvariable for the assignmentof unit uto stagej ofprocessp injob rBinaryparameterallowingtheassignmentofunit u to stagej ofprocessp injob r

rwma rm

JWw

B minrp

rp

Financialsupport from theEuropean Communityis gratefully acknowledged (projects JOE3-Cf950036 and ECSC N 7220-ED-081). This work hasbeen also sponsored by the Generalitatde Catalunya(Projects CERTAP N 10303 and QFN95-4301).This work includesresults of the research carriedoutby the UPC TQG research teamwhosecollaborationis greatlyappreciated.

INV

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Computers and Chemical Engineering Supplement (1999) S929-S943 5941Barton, P. and C.C. Pantelides (1991) The Modeling andSimulation of Combined Discrete Continuous Processes .Proc. PSE 91,Montebello, Canada.Calderon, spufia A., Puigjaner, L (199 ) WasteAnalysis and minimization in Batch and Semibatch reactoroperation through Dynamic simulation and NeuralNetworks, Computers Chemical Engineering, 22 S, pp.S977-S980.Calderon, ZH. Espufia, A., Puigjaner, L. (1999)Minimizing Waste Generation Using Neural NetworksBased Dynamic Simulation. ESCAPE-9, Budapest,Hungary (accepted).Canton, J., Graells, M., Puigjaner, L (1998) Handling ofComplex Recipes in Detailed Batch ProductionScheduling: Aplication to the Pharmaceutical Industry. 13tInternational Congress o f Chemical and ProcessEngineering - CHlSA '98, 6, p.F2.3, Praha, CzechRepublic,Cherry, D.H., Preston, M.L and G.W.H. Frank (1985)Batch Process Schedule Generation - ICl s BatchMASTER. lchemE Symposium Series, N 92, PSE'85, pp.91-100.Clark, S.M. and G.S. Joglekar (1996) General and SpecialPurpose Simulation Software for Batch ProcessEngineering. In: Batch Processing Systems Engineering(G.V. Reklaitis, A.K. Sunol, DW.T. Rippin,O. Hortactsu,eds.). NATO ASI Series No. 143, Springer-Verlag, Berlin,pp. 376-392.Corominas, J., Graells, M., Wilkendorf, Espufia, A.,Puigjaner, L. (1995) Energy Integration of ParallelMultiproduct Batch Processes. Efficiency, Cost ,Optimization, Simulation and Environmental Impact Energy Systems (Eds. Y. A. Goglls, A. Ozturk, G.Tsatsaromisjj , pp. 258-268.Cott, B J. and S. Machietto (1989) An Integrated Approachto Computer-Sided Operation of Batch Chemical Plants.Computers GildChemical Engineering, 13, 1263-1271.Czulek, AJ. (1988) An Experimental Simulator for BatchChemical Processes. Computers and ChemicalEngineering, 12, 253-259.Delgado, A., spufia A., Puigjaner,L. (1996) EvolutionaryOptimization of Nonlinear Time-Dependent Processes byCombining Neural Ne t Models with Genetic Algorithms,jl World Congress Engin eering, San Diego, (A.E.Wechsler American Institute ofCbemical Engineering, Ed),San Diego, California, USA. Vol. L pp. 919-924.Delgado, A., Puigjaner, L Sangeevan, K.,Sole, I. (1996a)Hybrid System: Neural Networks and Genetic AlgorithmsApplied in Nonlinear Regression and Tune SeriesForecasting, CO.\fPSTAT 96, Proceedings inComputationalStatistics (A. Prat,Ed.), Physica-Verlag, pp.217-222.Delgado, A., Puigjaner, L., Serra, M., Wilkendorf, F. andA. Mehlhorn (1997) Neural Networks and GeneticAlgori thms model ing chemical processes . Proc. IIICongresso Brasileiro de Redes Neurais (Eds. : L Caloba eJ. Barreto). Fundacao Biblioteca Nacional, Florian6polis,Brasil, pp. 161166.Delgado, A Graells, M., Font, E. Puigjaner, L (199 )Batch Production Scheduling with Flexible Recipes: Th eSingle Product Case. 13th International Congress Chemical andProcess Engineering - CHISA '98, 6, p.F2.4,Praha, Czech Republic.

Dhole, V.R N. Ramchandani, RA. Tainsh, M. Wasilewski(1996) Make your process water pay for i tsel f. ChemicalEngineering, 103: 100-103 .Espufia, A Puigjaner, L (1996) Integration of DifferentOptimization Criteria for the Desssign of Non-ContinuousChemical Plants, 1996 Spring National Meeting l hESheraton, (American Institute of Chemical Engineers. Ed).Lusiana, EEUU. spufia A., Delgado, A.. Puigjaner, L. (1998) Improvedbatch process performance by evolutionary model ling.Computers in Industry, 36, pp. 271278.Font, E., Puigjaner, L and A. spufia (1997) CombinedEnergy Process Integration and Utility Sys tem Design.AIC/rE Annual Meeting, (The American Institute ofChemical Engineers, Ed), Los Angeles, California, USA.November.Font, E., Espufia, A., Puigjaner, L. (1998) EfficiencyAnalisys o f Utility Systems Alternatives of a realCogeneration Plant. 13 th International Congress Chemical andProcess Engineering - CHlSA '98, VoL 6 p.F2.5, Praha, Czech Republic.Georgakis, C. (1996) Tendency Models for Estimation,Optimization and Control of Batch Processes. In: BatchProcessing Systems Engineering (G.V. Reklaitis, AK.Sunol, D.W.T . Rippin, O. Hortactsu, eds .). NATO ASISeries No. 143, Springer-Verlag, Berlin, pp. 451-494.Graells,M., spufia A., Puigjaner, L (1994) An EfficientIndustry-Oriented Approach for the Scheduling withIntermediate Storage of Mult ipurpose Batch ChemicalPlants. ComputeridedProcess Engineering (F. Perris andJ. D. Perkins , Eds.), Institution of Chern Eng., Rugby,U.K., Vol. 133, pp. 17-24.Graells, M., Cuxart, J., Espufia, A. and L. Puigjaner (1995)Dispatching-Like Strategies Using Intermediate Storage forthe Scheduling o f Batch Chemical Processes. ComputersandChemical Engineering, 19S, pp. 621-626.Graells,M., spufia A., Puigjaner L (1996) EvolutionaryPlanning Ident ificat ion of Best Schedules for Opt imumProduction. Second International Conference on ComputerIntegrated Manufact uring in the Process IndustrieslCIMPRO 96) (J. C. Fransoo, W. G. M. M. Rutten, Eds.),Eindhoven, Holanda, pp. 456-471.Graells, M., Espufia, A., Puigjaner, L (1996) SequencingIntermediate Products: A Practical Solution forMultipurpose Production Scheduling, Computers andChemical Engineering, 20 (5), pp. SI137-S1142.Graells,M., Canton, J., Peschaud, B., Puigjaner, L. (199 )General Approach and Tool for the Scheduling of ComplexProduction Systems, Computers Chemical Engineering,22 S, pp. S3955402.Graells, M., LOberg, E., Delgado, A., Font, E., Puigjaner,L. (1998) Batch Production Schedul ing with FlexibleRecipes: The Single Product Case . Foundations ofComputer ided Process Operations FOCAPO -98), pS13, Snowbird, Utah.Grau, R Espufia, A. and L Puigjaner (1994) Focusing inby-product recovery and waste minimization in batchproduct ion scheduling. Computers ChemicalEngineering, ISS, S271-S275.


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Nougues, JM ., Ruiz, D., Puigjaner, L (1998) ControlStrategies Applied to a Plant with Interacting ControlLoops. Workshop on Chemical Engineering Mathematicsp. 10, Bad Honeff,Germany.Pekny, 1.. Venkatasubramanian. V. and G.V. Reklaitis(1991) Prospects for Computer-Aided Process Operationsin the Process Industries. In: Computer-Oriented ProcessEngineering (L. Puigjaner, A Espufia, eds .), ProcessTechnology Proceedings 10, Elsevier, Amsterdam. pp. 435448.

Chemical Engineering. Katholische Akademie SchwerteKatholische Akademie Schwerte, Ed), Schwerte,

Alemania.

Puigjaner, L. (1993) Modelling Problems Arising inEnergy and Waste Minimization of Batch Proces ses.Second International Workshop on MathematicalModelling in Chemical Engineering Budapest, Hungary,pp.33.Puigjaner L., Espufia, A (1994) Incorporating RecentTechnologies to Batch Chemical Processing Industries. In:Trends in Chemical Engineering Council of ScientificResearch Integration, Trivandrum, 1. pp. 77-91.Puigjaner L., Huercio, A, Espufia A (1994) BatchProduction Control in a Computer Integrated ManufacturingEnvironment, Journal Process Control 4, pp. 281-290.Puigjaner, L Graells, M. Grau, R., Espuiia, A. (1994)Improving the Management of Process Operations in theBatch Manufacturing Industry. TIMS XXXII Anchorage,Alaska, USA, pp. 64.Puigjaner, L. (1996) Information Technology InnovationThrives in Fine Chemicals Industry. Proc. 7 Congreso delMediterraneo de lngenieria Quimica pp. 5, Barcelona.Puigjaner, Espuna, A. (1996) A Disciplined Frameworkfor Expert Scheduling in Batch Process Industries. SecondInternational Conference on Computer IntegratedManufacturing in the Process Industries lCIMPRO '96) (1.C. Fransoo, W. G. M. M. Rutten, Eds.), Eindhoven,Holanda, pp. 444-455.

P u i g j ~ e r L., Espufia, A, Font, E. (1996) Prospects forcombined beat and power integration inbatch/semicontinuous processes. Trends in ChemicalEngineering. 3, pp. 115-128.Puigjaner, L., Espuiia, A, Santos, G. and M . Graellsl996a) Batch Processing in Textile and LeatherIndustries . In: ~ ~ t c h Processing Systems Engineering(Eds.: G. V. Reklaitis, A K. Sunol, D. W. T. Rippin and O.

. a ~ s u Nato AS Series No. 143, Springer-Verlag,Berlin, pp. 808-820.Puigjaner, L., Espufia, A., Santos, G. and M. Graellsl996b) Design of Batch Plants. In: Batch ProcessingSystems Engineering (Eds.: G. V. Reklait is, A K. Sunol, D.W. T. Rippin and O. Hortacsu), NATO ASI Series No. 143Springer-Verlag, Berlin, pp. 86-113. 'Puigjaner , L (1997) Process Integration with CombinedHeat and Power (CHP). Applied Thermal Engineering. (8-10), pp. 1015-1034.Puigjaner, L, Espufia, A., Delgado, A. (1997) RecentAdvances and Perspectives of Neural NetworksApplications in Chemical Engineering Processing , AlChESpring National Meeting p109c, Houston, Texas, USA.

5942 Computers and Chemical Engineering Supplement (1999) S929-S943Grau, R., Graells, M., Corominas, J., Espufta, A., Puigjaner,L (1994) Energy and waste considerations in schedulingand planning of multiproduct batch chemical processes.Processes Systems Engineering-v-i (Ed. E S. Yoon), Seoul,Korea, I, pp. 165-170.Grau, R., spufia, A, Puigjaner, L (1995) EnvironmentalConsiderations in Batch Productions SchedulingComputers and Chemical Engineering 19S, pp. 651-656.Grau, R., Espuna, A, Puigjaner, L (1996) CompletionTimes in Multipurpose Batch Plants Set-Up, Transfer andClean-Up TImes. Computers and Chemical Engineering 20(55), pp. S1143-S114.Grau, R., Graells, M., Corominas, J., Espuiia, A., Puigjaner,L (1996) Global Estrategy for Energy and Waste Analysisin Scheduling and Planning of Multiproduct BatchChemical Processes. Computers & Chemical Engineering20, pp. 1043-1056.Grossmann, I Quesada, I., Raman, R. and V.T. Voudoris(1996) Mixed Integer Optimization Techniques for theDesign and Scheduling of Batch Processes. In: BatchProcessing Systems Engineering (G.V. Reklaitis, AK.Sunol. D.W.T. Rippin, O. Hortactsu, eds.) . NATO ASISeries No. 143, Springer-Verlag, Berlin, pp. 451-494.Halaz,L, Hofmeister, M. and D.W.T. Rippin (1996) GanttKit. An Interactive Scheduling Tool. In: Batch ProcessingSystems Engineering (G.V. Reklaitis, AK. Sunol, D.W.T.Rippin, O. Hortactsu, eds.). NATO ASI Ser ies No. 143,Springer-Verlag, Berlin, pp. 706-749.Hofmeister, H. (1998) BatchKit - A Knowledge integrationenvironment for process. engineering. Computers andChemical Engineering. 22, 109-123.Huercio,A.. Varas, F. J., spufia A. Puigjaner, L. Herranz,1. (1994) Applied Adaptive Dynamical Identification to thePrediction of Chemical Process Evolution. A Case Study.Periodica Politecnica Ser. Chem. Eng.38, 1-2, 81-92.Huercio, A. Espufia, A. Puigjaner, L (1995) React iveScheduling Strategies in Integrated Ba tch ProductionControl, Hungarian Joumal Industrial Chemistry 23pp.233-236.Huercio, A.. spufia A. Puigjaner, L:On- ine ScheduleAdaptation Strategies in Integrated BatchProce.sses :Second International Workshop on ModelingIdentification and Control in Chemical EngineeringSchwerte, Germany, (1995).Macchietto, S. Crooks, C.A. and K. Kuriyanm (1996) AnIntegrated System for Batch Processing. In: BatchProcessing Systems Engineering (G.V. Reklaitis, AK.Sunol, D.W.T. Rippin, O . Hortactsu, eds.). NATO ASISeries No. 143, Springer-Verlag, Berlin, pp. 750-778.Nougues, 1.M.,L. Puigjaner(1996) Neural Nets and RuleBased Expert System, A Combination Approach to FaultDiagnosis in Chemica l Process Industries. Proc. 7Congreso del Mediterraneo de Ingenieria Quimica pp.220, Barcelona.Nougues, J. M., Puigjaner, L (1996) An Object OrientedModel for Information Treatment of ChemicalReactors. 5rhWorld Congress Chemical Engineers (1. Y. Oldshue,Ed.) San Diego, California, USA, Vol. I, pp. 1070-1075.Nougues, 1.M., Pajares, FJ ., Vilasis , X., Puigjaner, L.(1997) Fuzzy Control of Batch Distilla tion Column.International Workshop on Mathematical Modeling in


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Wang, Y.P. R. Smith (1994) Wastewater minimisation.Chem. Eng. Sci. 49, 981-1006.

Wilkendorf, F., Espuiia, A., Puigjaner, L (1998)Minimization of the Annual Cost for Complete UtilitySystems. Chemical Engineering Research Design(A), pp. 239-245.

Wilkendorf, F., Corominas, J., Espuiia, A., Puigjaner, (1997) A General Formulation for the Synthesis ofCombined Heat and Power Systems with Minimum AnnualCost . Computers ChemicalEngineering 21S, pp. 54815486.

Computers and Chemical Engineering Supplement (1999) S929-S943 5943Puigjaner, L. Espufia, A. (1998) Pro spects for Integrated Venkatasubramanian, V. and K. Chan (1989) A NeuralManagement and Control of Total Sites in the Batch Network Methodology for Process Fault Diagnosis. AlCIlEManufacturing Industry. Computers Chemical J. 45. 1993 2 2.Engineering.Tl; pp.87 107.Puigjaner, L.. Espuiia, A. (1998) Prospects for IntegratedManagement and Control of Total Sites in the BatchManufacturing Industry. Computers ChemicalEngineering 22, pp .87 107.Reklaitis , G.V. (1996) Overview of Scheduling andPlanning of Batch Process Operations. In: BatchProcessing Systems Engineering (G.V. Reklaitis, A.K.Sunol, D.W.T. Rippin, O. Hortactsu, eds .). NATO ASISeries No. 143, Springer-Verlag. Berlin, pp. 660-705.Rippin D.W.T. (1993) Batch Processes SystemsEngineering: A Retrospective and Prospective Review.ComputersandChemicalEngineering 17S, SI SI4.Rippin D.W.T. (1996) Current Status and Challenges ofBatch Processing Systems Engineering. In: BatchProcessing Systems Engineering (G.V. Reklaitis, A.K.Sunol, D.W.T. Rippin, O. Hortactsu, eds .). NATO ASISeries No. 143. Springer-Verlag, Berlin, pp. 1-19.Ruiz, D., Nougues JM. Puigjaner, L (1999) On-lineProcess Fault Detection and Diagnosis in Plants withRecycle. ESCAPE-9 Budapest, Hungary (accepted).Sanmarti, E.,Espuiia, A. and L Puigjaner (1995) Effects ofEquipment Failure Uncertainty in Batch ProductionScheduling. Computers and Chemical Engineering. 19S,pp. 565-570.Sanmarti, E., Espufia, A., Puigjaner, L ProductionPlanning of Multipwpose Batch Chemical Plant UnderDemand Uncertainty , Inagural Workshop theInternationalInstitutefor GeneralSystemsStudies (Dep, ofMathematics Slippery Rock University, Ed), SlipperyRock, EEUU (1995)Sanmarti, E.,Huercio, A., spufia, A.. Puigjaner, L. (1996)A Combined Scheduling/Reactive Scheduling Strategy toMinimize the Effect of Process Operation Uncertainty inBatch Plants. Computers and Chemical Engineering 20(SS), pp. SI263-S1268.Sanmarti, E.. Espuiia, A., Puigjaner, L. (1997) BatchProduction and Preventive Maintenance Scheduling UnderEquipment Failure Uncertainty. Computers and ChemicalEngineering. 21 (10), pp. 1157-1168.Sanmarti, E., Friedler, F., Puigjaner, L (1998)Combinatorial technique for short term scheduling ofmultipurpose batch plants based on schedule-graphrepresentation, Computers Chemical Engineering 22 S,pp. S977-S980.Sanmarti, E., Friedler, F., Puigjaner, L (1998) HeatIntegration in Chemical Multipurpose Batch Plants UsingSchedule-Graph Representation. I3 h InternationalCongress Chemical and Process Engineering ClllSA '98, 6, p.F2.I Praha, Czech Republic.Santos, G., Puigjaner, L (1997) A General Formulation forthe Optimal Design of Multipurpose Noncontinuous Plants.BulgarianChemicalCommunications 29 (10), pp.48-64.Shah, N., Pantelides, C.C. and R.W.H. Sargent (1992) AGeneral Algorithm fort Short-Term Scheduling of BatchOperations - II Computational Issues . Computers andChemicalEngineering 17, 229-244.

puigjaner - 1999 - handling the increasing complexity of detailed batch process simulation and...

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