On the Boundary of Planning and Scheduling: A Study

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On the Boundary of Planning and Scheduling A
Study

• Roman Barták
• Charles University, Prague
• bartak_at_kti.mff.cuni.cz

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Problem area

• complex production environments
• plastic, petrochemical, chemical, pharmaceutical
  industries
• several different resources
• producers, movers, stores
• batch/serial processing with time windows
• transition patterns (set-up times)
• by-products, co-products (re-cycling)
• non-ordered production (for store)
• alternatives
• processing routes, production formulas, raw
  material

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Problem area - example 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
order
processor B1
silo
purchase
processor A
sacks warehouse
processor B2
order
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Constraint Programming (CP)

• Declarative problem solving
• stating constraints about the problem variables
• a set of variables Xx1,,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)

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CP - 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

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Planning and Scheduling - Traditional View

• Planning
• finding a sequence of activities transferring the
  initial world into a required state
• AI CP
• uses schedulers 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
SCHEDULER
Plan a list of activities
Schedule allocated activities
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Planning 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 activitiesto machines over
  time
• sometimes new activities introduced

Marketing plan
Production plan
Schedule
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Separate 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

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Mixing Planning and Scheduling

• A scheduler with planning capabilities
• generating activities during scheduling

PRODUCTION SCHEDULER
MARKETING PLANNING
Schedule - what activities are necessary to
satisfy the marketing plan - how the activities
are allocated to the resources over time
ACTIVITY GENERATOR
Marketing Plan what should be produced (custom
orders plus expected stock)
Activity
Values for parameters
ACTIVITY ALLOCATOR
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Conceptual models

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

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Constraint 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

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Time-line model

• a discrete time line with time slices
• description of situation at each time point/slice
• planning 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

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Order-centric model

• a 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)

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How to 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)

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Resource-centric model

• a 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

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Comparison of models
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Whats 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