Dynamic Constraint Models for Complex Production Environments

1. Dynamic Constraint Models forComplex Production Environments Roman Barták Charles University, Prague bartak@kti.mff.cuni.cz

2. 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

3. 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

4. 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

5. Planning 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 Planning and Scheduling

6. 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

7. 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

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

9. Time-line model resources Production (item1) Change-over Production (item 2) Production (item 3) empty Storing (item 1) Storing (items 1&B) empty Time slice No production Production (item4) Production (item5) time • 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

10. Order-centric model time resources polymerizing polymerizing storing storing extruding extruding storing storing • 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 slots … candidate activities

11. 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)

12. Resource-centric model resources Production (item1) Change-over Production (item 2) Production (item 3) empty Storing (item 1) Storing (items 1&B) empty No production Production (item4) Production (item5) No order Order1 No order time • 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

13. Comparison of models

14. 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

15. What’s next? • constraint model • 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