Conceptual Models for Combined Planning and Scheduling

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Conceptual Models forCombined Planning and
Scheduling

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

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Talk Schedule

• Problem area
• Mixed Planning Scheduling
• Conceptual Models
• why are they helpful?
• time-line model
• order-centric model
• resource-centric model
• Comparison
• Future research

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Problem area

• complex production environments
• plastic, petrochemical, pharmaceutical industries
• several different resources
• producers, movers, stores
• batch/serial processing
• time windows
• set-up times, transition patterns
• by-products, co-products
• cycling, re-cycling

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Problem area (continue)

• alternatives
• processing formulas
• various raw material
• production routes
• production for store (non-ordered)
• maximising profit (minimising cost)
• complex production environment

Silo
order
Processor B1
Silo
purchase
Processor A
Sacks warehouse
Processor B2
order
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Mixed Planning and Scheduling

• planning generate activities to satisfy the
  orders
• scheduling allocate the activities to the
  resources over time
• what if appearance of the activity depends on the
  allocation of other activities?
• set-ups transition patterns
• alternatives
• non-ordered production
• MIXED PLANNING SCHEDULING

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Conceptual models

• CP the user states the problem, the computer
  solves it
• we still do not reach this Holy Grail
• choice of a conceptual model gt efficiency
• conceptual model captures
• data structures (composition of variables)
• composition of constraints
• What could be modelled?
• What is easy/hard to express?

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Time-line model

• method of time slices
• duration the greatest common divisor of
  activities duration
• description of situation at each time point
• store - the stored quantity for each item
• producer - the consumed and produced quantities
  the state
• constraints
• the resource constraints - capacity,
  compatibility
• the transition constraints - set-ups
• the supplier/consumer dependencies

resources
Production (item1)
Change-over
Production (item 2)
Production (item 3)
Storing (item 1)
empty
Storing (items 1B)
empty
No production
Production (item4)
Production (item5)
time
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Representation (time-line model)

• a matrix (situation description x time)
• too many unused variables
• initial and future situations
• just set values of variables in given
  time-point(or bind them by the constraint)
• constraints
• can be introduced before the scheduling starts
• GOOD PROPAGATIONvs.TOO MANY VARIABLES

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Order-centric model

• a chain of activities per order
• assigning resources to activities
• description of the activity
• start, end (duration), resource
• constraints
• the supplier/consumer dependencies (easy timing
  only)
• the resource constraints (hard capacity,
  compatibility)
• the transition constraints (extremely hard
  set-ups)

time
resources
Processing A
Processing A
Storing
Storing
Processing B
Processing B
Storing
Storing
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How to model? (in order-centric model)

• alternatives
• pre-processing (a planner chooses the alternative
  in advance - before the scheduling)
• virtual activities (slots filled by the activity)
• set-ups
• virtual activities (slots filled by the activity)
• by-products
• 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 then how
  to satisfy the order
• description of the activity
• start, end (duration), quantities, state,
  suppliers, consumers
• constraints
• the resource constraints (easy capacity,
  compatibility)
• the transition constraints (easy set-ups)
• the supplier/consumer dependencies (hard)

resources
Production (item1)
Change-over
Production (item 2)
Production (item 3)
Storing (item 1)
empty
Storing (items 1B)
empty
No production
Production (item4)
Production (item5)
No order
Order1
No order
time
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Representation (resource-centric model)

• a matrix (or lists of activities)
• activity description x number of activities
• virtual activities
• initial and futures situations
• constraint the variables in given activities
• constraints
• resource/transition constraints are introduced
  before the scheduling starts
• supplier/consumer dependencies
• posted before scheduling (hard more
  propagation?)
• posted during scheduling (easier)

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Comparison of models
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Where to use?

• Order-centric model
• an order-driven production
• a small number of alternatives
• simple resource constraints
• Resource-centric model
• complex resource constraints (transitions etc.)
• a non-ordered production
• alternatives
• Time-line model
• a simple description of the resource
• the model of store

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Whats next?

• constraint model
• a complete specification of the constraints
• (semi)-dynamic representation
• constraints are posted during scheduling
• implementation
• propagation (early detection of inconsistencies)
• labelling (incremental)
• heuristics (choice of alternatives)