1. Conceptual Models for Combined Planning and Scheduling Roman Barták Charles University, Prague bartak@kti.mff.cuni.cz

2. © Roman Barták, 1999 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

3. © Roman Barták, 1999 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 …

4. © Roman Barták, 1999 Problem area (continue) alternatives –processing formulas various raw material –production routes production for store (non-ordered) maximising profit (minimising cost) complex production environment Silo Sacks warehouse Processor B1 Processor B2 Silo Processor A purchase order

5. © Roman Barták, 1999 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

6. © Roman Barták, 1999 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 => efficiency conceptual model captures –data structures (composition of variables) –composition of constraints What could be modelled? What is easy/hard to express?

7. © Roman Barták, 1999 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 Production (item1)Change-overProduction (item 2)Production (item 3) Storing (item 1)emptyStoring (items 1&B) No productionProduction (item4)Production (item5) time resources empty

8. © Roman Barták, 1999 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 PROPAGATION vs. TOO MANY VARIABLES

9. © Roman Barták, 1999 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 Storing Processing B Storing Processing B Processing A

10. © Roman Barták, 1999 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)

11. © Roman Barták, 1999 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) Production (item1)Change-overProduction (item 2)Production (item 3) Storing (item 1)emptyStoring (items 1&B) No productionProduction (item4)Production (item5) time resources empty No orderOrder1No order

12. © Roman Barták, 1999 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)

13. © Roman Barták, 1999 Comparison of models

14. © Roman Barták, 1999 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

15. © Roman Barták, 1999 What’s 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)