The Axxom Case Study state of the art

1. The Axxom Case Studystate of the art Ed Brinksma joint work with Gerd Behrmann Martijn Hendriks Angelika Mader Review Meeting, Brussels, 13 November 2005

2. Contents • case study description • information transfer • modelling • heuristics • extended case study • results • evaluation & current work Review Meeting, Brussels, 13 November 2005

3. Case Study Description • lacquer production scheduling • 3 recipes • for uni/metallic/bronce lacquers • use of resources, processing times,timing • 29 (73, 219) orders: • start time, due date, recipe • extensions: • delay costs, storage costs, setup costs • weekends, nights Review Meeting, Brussels, 13 November 2005

4. Information Transfer Stumbling blocks: • interpretation of terminology • creation of a dictionary • implicit knowledge • late modification of models • biased model description • based on Orion-pi features • non-standard notation Review Meeting, Brussels, 13 November 2005

5. An Axxom Recipe VORDISP.UNI.85 offset 0-4h 13 DISP.UNI.85 offset 6h 15 12 DK.UNI.85 MISCH.UNI.85 13 PRUEFEN1.UNI.85 13 KORREKTUR.UNI.85 98 13 offset 2-4h PRUEFEN2.UNI.85 13 Review Meeting, Brussels, 13 November 2005

6. The recipesin an alternativerepresentation Review Meeting, Brussels, 13 November 2005

7. time<=processing_time resource>0 resource -- time:=0 time==processing_time resource++ A Basic Processing Step • timed automaton with 3 locations: • claiming a resource • processing • releasing a resource • template with parameter for processing_time • combined into recipies and composed with models for resources Review Meeting, Brussels, 13 November 2005

8. Scheduling Synthesis • use real-time model checker (Uppaal) to determine the reachability of states where all orders have been processed in time • schedules can be extracted directly from witness traces to such states • problem: state space explosion • use heuristics to prune search tree Review Meeting, Brussels, 13 November 2005

9. Heuristics We distinguish: • “nice” heuristics do not remove best remaining schedule • “cut-and-pray” heuristics may remove best remaining schedule Review Meeting, Brussels, 13 November 2005

10. Nice Heuristics • non-overtaking orders of the same recipe cannot overtake each other • non-laziness a process that needs an available resource will not waste time if its is not claimed by others (a.k.a. active scheduling) Review Meeting, Brussels, 13 November 2005

11. A Non-Lazy Processing Step time<processing_time resource==0 urgent! resource>0 time:=0 time<=processing_time resource>0 urgent! resource -- time:=0 time==processing_time resource++ Review Meeting, Brussels, 13 November 2005

12. Cut-and-Pray Heuristics • greediness a process that needs an available resource will claim this resource immediately • reducing active orders the number of concurrent orders is restricted (number of critical resources can give an indication) Review Meeting, Brussels, 13 November 2005

13. Experimental Results uses clock optimization & optimized successor calculation Review Meeting, Brussels, 13 November 2005

14. Extending the Case Study • performance and availability factors if a resource has an average availability factor f, its processing time is multiplied by 1/f. • storage, delay and setup costs, working hours penalties for delivering orders too early, or too late; costs for cleaning filling stations; work in shifts, no work over weekends. Review Meeting, Brussels, 13 November 2005

15. Results Availability Factors Review Meeting, Brussels, 13 November 2005

16. Storage, Delay, and Setup Costs • use cost-extended Uppaal CORA • cost optimization problem • delaying earliest starting time heuristic (cut-and-pray) time<=processing_time cost’==late[id]*dcf cost’==late[id]*dcf cost’==late[id]*dcf resource>0 resource -- time:=0 time==processing_time resource++ Review Meeting, Brussels, 13 November 2005

17. Working Hours Taken into account through an extra automaton that calculates the effective processing time “online”. This increases the size of the model considerably Review Meeting, Brussels, 13 November 2005

18. Results Extended Case competitive with Orion-pi results Review Meeting, Brussels, 13 November 2005

19. Evaluation • successful extension of core scheduling problem to 73 and 219 orders all results obtained < 10 s (PC 512MB, 1GHz) • generic patterns for processing steps, resources, and heuristics • first results for inclusion of costs and working hours results competitive with Orion-pi • information transfer was a non-trivial problem Review Meeting, Brussels, 13 November 2005

20. Current Work • scaling up the core problem to O(103) orders • seems feasible with active orders heuristic • relation between long-term feasibility and short-term planning schedules • availability and performance factors are approximative • irrelevance of cost factors and working hours for long planning periods • searching for schedules in reverse time • minimize storage and delay costs Review Meeting, Brussels, 13 November 2005