on the boundary of planning and scheduling: a study

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On the Boundary of Planning and On the Boundary of Planning and Scheduling: A StudyScheduling: A Study

Roman Barták

Charles University, Prague

bartak@kti.mff.cuni.cz

© Roman Barták, 1999

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...Problem areaProblem areacomplex production environments

– plastic, petrochemical, chemical, pharmaceutical industries

several different resources– producers, movers, stores

batch/serial processing with time windowstransition patterns (set-up times)by-products, co-products (re-cycling)non-ordered production (for store)alternatives

– processing routes, production formulas, raw material

© Roman Barták, 1999

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...Problem area - Problem area - example & objectivesexample & objectives

complex production environment

Task– preparing a schedule for a given time period

(not minimising the makespan)– objective

• maximising the profit (minimising the cost)

silo

sackswarehouse

processor B1

processor B2

siloprocessor Apurchase

order

order

© Roman Barták, 1999

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...Constraint Programming (CP)Constraint Programming (CP)

Declarative problem solving

– stating constraints about the problem variables• a set of variables X={x1,…,xn}

• variables’ domains Di (usually finite set of possible values)

• a set of constraints (constraint is a relation among several unknowns)

– finding a solution satisfying all (most) the constraints• systematic search with consistency techniques & constraint

propagation• stochastic and heuristic methods (local search)

© Roman Barták, 1999

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...CP - Advantages & LimitationsCP - Advantages & Limitations

Advantages– declarative modelling

• transparent representation of real-life problems• easy introduction of heuristics

– co-operative solving• integration of solving methods from different areas (OR, AI …)

– semantic foundation• amazingly clean and elegant languages

Weaknesses– NP-hard problems & tractability– unpredictable behaviour– model instability

© Roman Barták, 1999

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...Planning and Scheduling - Planning and Scheduling - Traditional ViewTraditional View

Planning– finding a sequence of

activities transferring the initial world into a required state

– AI & CP

– uses scheduler’s constraints(otherwise too tighten or too relaxed plans)

Scheduling– allocating the activities to

available resources over time respecting the constraints

– OR & CP

– all activities are know in advance

PLANNER SCHEDULERPlan = a list of activities

Schedule = allocated activities

© Roman Barták, 1999

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...Planning and Scheduling in IndustryPlanning and Scheduling in Industry

not strictly distinguished– different discrimination criteria (time horizon & resolution)

marketing planning– what and when should be produced– not planning in AI terminology

production planning– generation of activities– allocation to departments

production scheduling– exact allocation of activities

to machines over time– sometimes new activities introduced

Marketing plan

Production plan

Schedule

© Roman Barták, 1999

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...Separate Planning and SchedulingSeparate Planning and Scheduling

Co-operation between planner and scheduler– too tighten plans (impossible to schedule)– too free plans (less profitable schedule)

backtrack from the scheduler to the planner

Activity generation– what if appearance of the activity depends on the

allocation of other activities?• alternatives• transition patterns (set-ups)• processing of by-products• non-ordered production

© Roman Barták, 1999

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...Mixing Planning and SchedulingMixing Planning and Scheduling

A scheduler with planning capabilities• generating activities during scheduling

MARKETING PLANNING

Marketing Plan = what should be produced (custom orders plus expected stock)

Schedule - what activities are necessary to satisfy the marketing plan

- how the activities are allocated to the resources over time

PRODUCTION SCHEDULER

ACTIVITY GENERATOR

ACTIVITY ALLOCATOR

Activity Values for parameters

© Roman Barták, 1999

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...Conceptual modelsConceptual models

Expressiveness– What could be modelled? (problem area)– What is easy/hard to express? (constraints)

tim e-line m odel

discrete tim e(tim e slices w ith equal duration)

order-centric m odel

per order (task)

resource-centric m odel

per resource

grouping activ ities?

even-based tim e(activities)

view of tim e?

© Roman Barták, 1999

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...Constraint classification in schedulingConstraint classification in scheduling

resource constraints– resource limits in given time point– capacity, compatibility

transition constraints– activity transitions in single resource– set-ups

dependency constraints– dependencies between different resources– supplier-consumer relation

© Roman Barták, 1999

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...Time-line modelTime-line modela discrete time line with time slices

description of situation at each time point/sliceplanning and scheduling - no difference

– a variable for activity in the description of time point/slice

comments– covers all the typical problems in complex production

environments– all the variables are known in advance

• too many variables in large-scale industrial problems

Production (item1) Change-over Production (item 2) Production (item 3)

Storing (item 1)empty Storing (items 1&B)

No production Production (item4) Production (item5)

time

resources

empty

Time slice

© Roman Barták, 1999

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...Order-centric modelOrder-centric modela chain of activities per order (task)

description of the activity– start, end (duration), resource

enhancement– activities in the production chain are generated during scheduling

starting from the order (alternatives, set-ups)– sharing activities between production chains (by-products)

time

resou

rces

storing

extruding

storing

storing

storing

extruding

polymerizingpolymerizing

© Roman Barták, 1999

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...How to model? How to model? (in order-centric model)(in order-centric model)

alternatives– pre-processing (chosen by the planner)– alternative activities in slots

set-ups– set-up slot is either empty or contains the set-up activity

(depending on the allocation of the next activity)

by-products (re-cycling)– sharing activities between the production chains

non-ordered production– pre-processing (non-ordered production is planned in advance -

before the scheduling)

© Roman Barták, 1999

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...Resource-centric modelResource-centric modela sequence of activities per resource“what the resource can process” rather than

“how to satisfy the order”

description of the activity– start, end (duration), quantities, state, suppliers, consumers

representation– a list of virtual activities– transition constraints between successive activities

Production (item1) Change-over Production (item 2) Production (item 3)

Storing (item 1)empty Storing (items 1&B)

No production Production (item4) Production (item5)

time

resources

empty

No order Order1 No order

© Roman Barták, 1999

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...Comparison of modelsComparison of models

Time-line Order-centric Resource-centric

Resourceconstraints

easy complicated easy

Transitions easy complicated easy

Dependencies easy easy complicated

Non-orderedproduction

implicit no (limited) implicit

Cycling implicit limited implicit

Alternatives implicit limited implicit

DRAWBACKS too manyvariables

limitedcapabilities

–

© Roman Barták, 1999

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...What’s next?What’s next?

ad-hoc implementation– dynamic constraints– propagation (early detection of inconsistencies)– labelling (incremental)– heuristics (choice of alternatives)

theoretical foundation– structural constraint satisfaction (A. Nareyek)

parallelism– agent based scheduling