on the boundary of planning and scheduling: a study
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On the Boundary of Planning and Scheduling: A Study. Roman Bart ák Charles University, Prague [email protected]. Problem area. complex production environments plastic, petrochemical, chemical, pharmaceutical industries several different resources producers, movers, stores - PowerPoint PPT PresentationTRANSCRIPT
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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
© 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