Dynamic Constraint Models for Complex Production Environments * 07/16/96 Dynamic Constraint Models for Complex Production Environments Roman Barták Charles University, Prague bartak@kti.mff.cuni.cz *

Talk Schedule Problem area Mixing Planning & Scheduling Conceptual Models discrete & event based time static vs. dynamic representation overview & comparison of models mixing models Future research

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

Problem area (cont’d) 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 purchase silo processor A processor B2 sacks warehouse order

Planning and Scheduling finding a sequence of activities transferring the initial world into a required state high-level view of the factory low resolution longer time period what and how to produce? AI & CP Scheduling allocating the activities to available resources over time respecting the constraints low-level view of the factory high resolution shorter time period how to produce in detail? OR & CP

Mixing Planning and Scheduling Problems too tighten plans (impossible to schedule) too free plans (less profitable schedule) backtrack from the scheduler to the planner what if appearance of the activity depends on the allocation of other activities? transition patterns (set-ups), alternatives, non-ordered production Solution a scheduler with planning capabilities generating activities during scheduling

Conceptual models High-level declarative model of the problem data structures (composition of variables) composition of constraints resource constraints (compatibility, capacity) transitions between activities (set-ups) supplier/consumer dependencies Expressiveness What could be modelled? (problem area) What is easy/hard to express? (constraints) Efficiency constraint propagation

Conceptual models (cont’d) View of time discrete (time slices with the same duration) event-based (activities) Representation

Time-line model discretising the time line into time slices activities change at the edge between successive time slices duration = the greatest common divisor of activities’ duration description of situation at each time point/slice Example: the store - the stored quantity for each item good for both planning and scheduling activities for given time point/slice are chosen during scheduling a matrix representation (description x time) static / dynamic / semi-dynamic contents of the cells easy capture of initial & future situations 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 Time slice

Order-centric model a chain of activities per order assigning resources to activities description of the activity start, end (duration), resource representation production chain = a list of (virtual) activities time resources storing extruding polymerizing slots … candidate activities

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)

Resource-centric model Activity based 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 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 No order Order1

Comparison of models

Mixing the models Minimising drawbacks while preserving advantages of different models different task = different model the time-line model for planning the order-centric model for scheduling different resource = different model producer & mover - activities (resource-centric) store - time-line

What’s next? constraint model implementation expressiveness a complete specification of the constraints implementation propagation (early detection of inconsistencies) labelling (incremental) heuristics (choice of alternatives) expressiveness secondary resources traceability agent based scheduling