Constraint Based Scheduling and Optimization: From Research to Application

1. Constraint Based Scheduling and Optimization: From Research to Application Brian Drabble Computational Intelligence Research Laboratory www.cirl.uoregon.edu drabble@cirl.uoregon.edu & On Time Systems, Inc www.otsys.com Univ. Nebraska

2. Overview • Constraint based scheduling • Algorithms • LDS and Schedule Pack • Squeaky Wheel Optimization • Applications • Aircraft assembly • Ship construction • Future Directions • Summary Univ. Nebraska

3. Constraint Based Scheduling • Problem characteristics • Search based techniques Univ. Nebraska

4. Problem Characteristics • Task details: • resource requirements • deadlines/release times • value Univ. Nebraska 3

5. Problem Characteristics • Task details • Resource characteristics: • type • capacity • availability • speed, etc. Univ. Nebraska 4

6. Problem Characteristics • Task details • Resource characteristics • Precedences: • necessary orderings between tasks Univ. Nebraska 5

7. Problem Characteristics • Constraints: • setup costs • exclusions • reserve capacity • union rules/business rules • Task details • Resource characteristics • Precedences Univ. Nebraska 6

8. Problem Characteristics • Constraints • Optimization criteria: • makespan, lateness, cost, throughput • Task details • Resource characteristics • Precedences Univ. Nebraska 7

9. Optimization Techniques • Operations Research (OR) • LP/IP solvers • seem to be near the limits of their potential • Artificial Intelligence (AI) • search-based solvers • performance increasing dramatically • surpassing OR techniques for many problems Univ. Nebraska 8

10. Search-based Techniques • Systematic • explore all possibilities • Depth-First Search • Limited Discrepancy Search • Nonsystematic • explore only “promising” possibilities • WalkSAT • Schedule Packing Univ. Nebraska 9

11. Heuristic Search • A heuristic prefers some choices over others • Search explores heuristically preferred options Univ. Nebraska 10

12. Limited Discrepancy Search • Better model of how heuristic search fails Univ. Nebraska 11

13. Limited Discrepancy Search • LDS-n deviates from heuristic exactly n times on path from root to leaf LDS-0 LDS-1 Univ. Nebraska 12

14. Schedule Packing • Post-processing to exploit opportunities 1 1 2 2 Univ. Nebraska 13

15. Schedule Packing • schedule longest chains first • starting from right 1 1 2 2 1 1 2 2 Univ. Nebraska 14

16. Schedule Packing • repeat, starting from the left 1 1 2 2 1 1 2 2 Univ. Nebraska 15

17. Squeaky Wheel Optimization • Key insight: scheduling involves two major decisions: • which task to assign next • where to assign it in the schedule • Create a dual search space • priority space • schedule space Univ. Nebraska

18. Priority Space • Coupled search space P S P’ S’ Priority Space Solution Space Univ. Nebraska

19. Architecture • Construct Analyze Prioritize loop Construct P S Analyze Prioritize P’ Construct S’ Priority Space Solution Space Univ. Nebraska

20. Construct P S Analyze Prioritize P’ Construct S’ Priority Space Solution Space Construction • Construct a solution taking each task in sequence Univ. Nebraska

21. Analysis • Assign blame problem elements, relatively simple Construct P S Analyze Prioritize P’ Construct S’ Priority Space Solution Space Univ. Nebraska

22. Prioritization • Adjust priority sequence according to blame Construct P S Analyze Prioritize P’ Construct S’ Priority Space Solution Space Univ. Nebraska

23. Large Coherent Moves • High priority tasks handled well lower tasks fill in. Construct P S Analyze Prioritize P’ Construct S’ Priority Space Solution Space Univ. Nebraska

24. Mission 1234 AAR 234 SEAD 34 Construct Mission 4567 Squeaky Wheel Optimization Univ. Nebraska

25. “High attrition rate” “Outside target time window” “Low success rate” “Not attacked” Squeaky Wheel Optimization Analyze Univ. Nebraska

26. Squeaky Wheel Optimization Prioritize Univ. Nebraska

27. Squeaky Wheel Optimization Prioritize Univ. Nebraska

28. Construct Squeaky Wheel Optimization Univ. Nebraska

29. 25 % Over Best Solution 20 15 TABU LP/IP SWO 10 5 0 0 100 50 150 200 250 300 Number of Tasks Scalability

30. Applications Univ. Nebraska 16

31. Aircraft Assembly McDonnell Douglas / Boeing • ~570 tasks, 17 resources, various capacities • MD’s scheduler took 2 days to schedule • needed: • better schedules (1 day worth $200K–$1M) • rescheduler that can get inside production cycles Univ. Nebraska 17

32. Problem Specification • Task/precedence specification • mostly already existed for regulatory reasons Univ. Nebraska 18

33. Problem Specification • Task/precedence specification • mostly already existed for regulatory reasons • Resource capacity profiles • labor profile available from staffing information • others determined from SOPs, etc. Univ. Nebraska 19

34. Problem Specification • Task/precedence specification • mostly already existed for regulatory reasons • Resource capacity profiles • labor profile available from staffing information • others determined from SOPs, etc. • Optimization criterion • simple makespan minimization Univ. Nebraska 20

35. Problem Specification • Task/precedence specification • mostly already existed for regulatory reasons • Resource capacity profiles • labor profile available from staffing information • others determined from SOPs, etc. • Optimization criterion • simple makespan minimization • Solution checker • available from in-house scheduling efforts Univ. Nebraska 21

36. The Optimizer • LDS to generate seed schedules • Schedule packing to optimize • intensification improves convergence speed • etc. Univ. Nebraska 22

37. Performance • ~570 tasks, 17 resources, various capacities • about 1 second to first solution • about 1 minute to within 2% of best known • about 30 minutes to best schedule known Univ. Nebraska 23

38. Performance • ~570 tasks, 17 resources, various capacities • about 1 second to first solution • about 1 minute to within 2% of best known • about 30 minutes to best schedule known • 10-15% shorter makespan than best in-house • 4 to 6 days shorter schedules Univ. Nebraska 24

39. Performance • ~570 tasks, 17 resources, various capacities • about 1 second to first solution • about 1 minute to within 2% of best known • about 30 minutes to best schedule known • 10-15% shorter makespan than best in-house • 4 to 6 days shorter schedules • 2 orders of magnitude faster scheduling • scheduler runs inside production cycle • less need for rescheduler Univ. Nebraska 25

40. Extensions Boeing: • multi-unit assembly • interruptible tasks • persistent assignments • multiple objectives • e.g., time to first completion, average makespan, time to completion • fast enough to use for “what-iffing” • discovered improved PM schedule • Noise is your friend!!! Univ. Nebraska 26

41. Submarine Construction General Dynamics / Electric Boat • 7000 activities per hull, approx 125 resource types • Electric Boat’s scheduler takes 6 weeks • needed: • cheaper schedules • faster schedules to deal with contingencies Univ. Nebraska 27

42. Problem Specification • reschedule shipyard operations to reduce wasted labor expenses • efficient management of labor profiles • reduce overtime and idle time • hiring and RIF costs Univ. Nebraska

43. Optimizer • ARGOS is new technology developed specifically with these goals in mind Univ. Nebraska

44. Performance: One Boat • Labor costs of existing schedule: $155m • Time to produce existing schedule: ~6 weeks • 15% reduction in cost, 50x reduction in schedule development time Iteration Time Savings 1 2 min 8.4% $13.0M 7 10 min 11.4% $17.7M 20 34 min 11.8% $18.2M Ultimate ~24hrs 15.5% $24.0M Univ. Nebraska

45. Performance: Whole Yard • All hulls, about 5 years of production • Estimated cost of existing schedule: $630M • No existing software package can deal with the yard coherently Iteration Time Savings 1 24 min 7.8% $49M 7 60 min 10.2% $65M 20 4 hours 10.7% $68M Ultimate 4 days 11.5% 73M Univ. Nebraska

46. Extensions • Shared resources • dry dock • cranes • Sub-assemblies • provided by different yards and suppliers • Repair • dealing with new jobs Univ. Nebraska

47. Future Applications • Workflow management • STRATCOM checklist manager • IBM • E-Business • supply chain management • Military • air expeditionary forces • logistics Univ. Nebraska

48. Future Work • Robustness • Distributed scheduling • Common task description Univ. Nebraska

49. Penalty Box Scheduling • Sub-set of the tasks with higher probability of success. • 90% probability of destroying 90% of the targets? • 96% probability of destroying 75% of the targets? • Inability to resource leads to a task “squeak” • Blame score related to user priority and “uniqueness” • Reduce the target percentage until no significant improvement is found Univ. Nebraska

50. Semi-Flexible Constraints • The time constraints provided by the users tended to be ad-hoc and imprecise • heuristics based on sortie rate, no of targets, etc • this is what we did last time so it must be right!! • Not a preference • this is what I want until you can prove otherwise!! • Two algorithms were investigated • pointer based • ripple based Univ. Nebraska