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Advanced Scheduling and Optimization: Cutting the Costs of Manufacturing Brian Drabble Computational Intelligence Research Advanced Scheduling and Optimization: Cutting the Costs of Manufacturing Brian Drabble Computational Intelligence Research Laboratory www. cirl. uoregon. edu drabble@cirl. uoregon. edu & On Time Systems, Inc www. otsys. com 26 th Nov 2001 Univ. Nebraska 1

Overview • Constraint based scheduling • Algorithms – LDS and Schedule Pack – Squeaky Overview • Constraint based scheduling • Algorithms – LDS and Schedule Pack – Squeaky Wheel Optimization • Applications – Aircraft assembly – Ship construction • Future Directions • Summary 26 th Nov 2001 Univ. Nebraska 2

Constraint Based Scheduling • Problem characteristics • Search based techniques 26 th Nov 2001 Constraint Based Scheduling • Problem characteristics • Search based techniques 26 th Nov 2001 Univ. Nebraska 3

Problem Characteristics – Task details: • resource requirements • deadlines/release times • value 26 Problem Characteristics – Task details: • resource requirements • deadlines/release times • value 26 th Nov 2001 Univ. Nebraska 3 4

Problem Characteristics – Task details – Resource characteristics: • • type capacity availability speed, Problem Characteristics – Task details – Resource characteristics: • • type capacity availability speed, etc. 26 th Nov 2001 Univ. Nebraska 4 5

Problem Characteristics ¨ ¨ ¨ Task details Resource characteristics Precedences: – necessary orderings between Problem Characteristics ¨ ¨ ¨ Task details Resource characteristics Precedences: – necessary orderings between tasks 26 th Nov 2001 Univ. Nebraska 5 6

Problem Characteristics – Constraints: ¨ Task details ¨ Resource characteristics ¨ Precedences 26 th Problem Characteristics – Constraints: ¨ Task details ¨ Resource characteristics ¨ Precedences 26 th Nov 2001 • • Univ. Nebraska 6 setup costs exclusions reserve capacity union rules/business rules 7

Problem Characteristics – Constraints ¨ Task details ¨ Resource characteristics ¨ Precedences 26 th Problem Characteristics – Constraints ¨ Task details ¨ Resource characteristics ¨ Precedences 26 th Nov 2001 – Optimization criteria: • makespan, lateness, cost, throughput Univ. Nebraska 7 8

Optimization Techniques • Operations Research (OR) – LP/IP solvers • seem to be near 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 26 th Nov 2001 Univ. Nebraska 8 9

Search-based Techniques • Systematic – explore all possibilities • Depth-First Search • Limited Discrepancy Search-based Techniques • Systematic – explore all possibilities • Depth-First Search • Limited Discrepancy Search • Nonsystematic – explore only “promising” possibilities • Walk. SAT • Schedule Packing 26 th Nov 2001 Univ. Nebraska 9 10

Heuristic Search – A heuristic prefers some choices over others – Search explores heuristically Heuristic Search – A heuristic prefers some choices over others – Search explores heuristically preferred options 26 th Nov 2001 Univ. Nebraska 10 11

Limited Discrepancy Search – Better model of how heuristic search fails 26 th Nov Limited Discrepancy Search – Better model of how heuristic search fails 26 th Nov 2001 Univ. Nebraska 11 12

Limited Discrepancy Search – LDS-n deviates from heuristic exactly n times on path from Limited Discrepancy Search – LDS-n deviates from heuristic exactly n times on path from root to leaf LDS-0 26 th Nov 2001 LDS-1 Univ. Nebraska 12 13

Schedule Packing – Post-processing to exploit opportunities 1 1 2 26 th Nov 2001 Schedule Packing – Post-processing to exploit opportunities 1 1 2 26 th Nov 2001 2 Univ. Nebraska 13 14

Schedule Packing – schedule longest chains first • starting from right 1 1 2 Schedule Packing – schedule longest chains first • starting from right 1 1 2 26 th Nov 2001 Univ. Nebraska 14 2 15

Schedule Packing – repeat, starting from the left 1 1 2 26 th Nov Schedule Packing – repeat, starting from the left 1 1 2 26 th Nov 2001 2 Univ. Nebraska 15 16

Squeaky Wheel Optimization Mission 1234 AAR 234 SEAD 34 Construct Mission 4567 26 th Squeaky Wheel Optimization Mission 1234 AAR 234 SEAD 34 Construct Mission 4567 26 th Nov 2001 Univ. Nebraska 17

Squeaky Wheel Optimization A n a l y z e “High attrition rate” “Outside Squeaky Wheel Optimization A n a l y z e “High attrition rate” “Outside target time window” “Low success rate” “Not attacked” 26 th Nov 2001 Univ. Nebraska 18

Squeaky Wheel Optimization P r i o r i t i z e 26 Squeaky Wheel Optimization P r i o r i t i z e 26 th Nov 2001 Univ. Nebraska 19

Squeaky Wheel Optimization P r i o r i t i z e 26 Squeaky Wheel Optimization P r i o r i t i z e 26 th Nov 2001 Univ. Nebraska 20

Squeaky Wheel Optimization Construct 26 th Nov 2001 Univ. Nebraska 21 Squeaky Wheel Optimization Construct 26 th Nov 2001 Univ. Nebraska 21

Scalability 25 % Over Best Solution 20 15 TABU LP/IP SWO 10 5 0 Scalability 25 % Over Best Solution 20 15 TABU LP/IP SWO 10 5 0 0 26 th Nov 2001 50 100 Univ. Nebraska 150 Number of Tasks 200 250 300 22

Applications 26 th Nov 2001 Univ. Nebraska 16 23 Applications 26 th Nov 2001 Univ. Nebraska 16 23

Aircraft Assembly Mc. Donnell Douglas / Boeing – ~570 tasks, 17 resources, various capacities Aircraft Assembly Mc. Donnell Douglas / Boeing – ~570 tasks, 17 resources, various capacities – MD’s scheduler took 2 days to schedule – needed: • better schedules (1 day worth $200 K–$1 M) • rescheduler that can get inside production cycles 26 th Nov 2001 Univ. Nebraska 17 24

Problem Specification – Task/precedence specification • mostly already existed for regulatory reasons 26 th Problem Specification – Task/precedence specification • mostly already existed for regulatory reasons 26 th Nov 2001 Univ. Nebraska 18 25

Problem Specification – Task/precedence specification • mostly already existed for regulatory reasons – Resource 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. 26 th Nov 2001 Univ. Nebraska 19 26

Problem Specification – Task/precedence specification • mostly already existed for regulatory reasons – Resource 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 26 th Nov 2001 Univ. Nebraska 20 27

Problem Specification – Task/precedence specification • mostly already existed for regulatory reasons – Resource 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 26 th Nov 2001 Univ. Nebraska 21 28

The Optimizer • LDS to generate seed schedules • Schedule packing to optimize – The Optimizer • LDS to generate seed schedules • Schedule packing to optimize – intensification improves convergence speed • etc. 26 th Nov 2001 Univ. Nebraska 22 29

Performance – ~570 tasks, 17 resources, various capacities • about 1 second to first 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 26 th Nov 2001 Univ. Nebraska 23 30

Performance – ~570 tasks, 17 resources, various capacities • about 1 second to first 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 26 th Nov 2001 Univ. Nebraska 24 31

Performance – ~570 tasks, 17 resources, various capacities • about 1 second to first 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 26 th Nov 2001 Univ. Nebraska 25 32

Extensions Boeing: – – multi-unit assembly interruptible tasks persistent assignments multiple objectives • e. 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 26 th Nov 2001 Univ. Nebraska 26 33

Submarine Construction General Dynamics / Electric Boat – 7000 activities per hull, approx 125 Submarine Construction General Dynamics / Electric Boat – 7000 activities per hull, approx 125 resources – Electric Boat’s scheduler takes 6 weeks – needed: • cheaper schedules • faster schedules of contingencies 26 th Nov 2001 Univ. Nebraska 27 34

Problem Specification • reschedule shipyard operations to reduce wasted labor expenses • efficient management Problem Specification • reschedule shipyard operations to reduce wasted labor expenses • efficient management of labor profiles – reduce overtime and idle time – hiring and RIF costs 26 th Nov 2001 Univ. Nebraska 35

Optimizer • ARGOS is new technology developed specifically with these goals in mind 26 Optimizer • ARGOS is new technology developed specifically with these goals in mind 26 th Nov 2001 Univ. Nebraska 36

Performance: One Boat • Labor costs of existing schedule: $155 m • Time to Performance: One Boat • Labor costs of existing schedule: $155 m • Time to produce existing schedule: ~6 weeks Iteration Time Savings 1 2 min 8. 4% $13. 0 M 7 10 min 11. 4% $17. 7 M 20 34 min 11. 8% $18. 2 M Ultimate ~24 hrs 15. 5% $24. 0 M • 15% reduction in cost, 50 x reduction in schedule development time 26 th Nov 2001 Univ. Nebraska 37

Performance: Whole Yard • All hulls, about 5 years of production • Estimated cost Performance: Whole Yard • All hulls, about 5 years of production • Estimated cost of existing schedule: $630 M Iteration 1 7 20 Time 24 min 60 min 4 hours Ultimate 4 days Savings 7. 8% $49 M 10. 2% $65 M 10. 7% $68 M 11. 5% 73 M • No existing software package can deal with the yard coherently 26 th Nov 2001 Univ. Nebraska 38

Extensions • Shared resources – dry dock – cranes • Sub-assemblies – provided by Extensions • Shared resources – dry dock – cranes • Sub-assemblies – provided by different yards and suppliers • Repair – dealing with new jobs 26 th Nov 2001 Univ. Nebraska 39

Future Applications • Workflow management – STRATCOM checklist manager – IBM • E-Business – Future Applications • Workflow management – STRATCOM checklist manager – IBM • E-Business – supply chain management • Military – air expeditionary forces – logistics 26 th Nov 2001 Univ. Nebraska 40

Future Work • Robustness • Distributed scheduling • Common task description 26 th Nov Future Work • Robustness • Distributed scheduling • Common task description 26 th Nov 2001 Univ. Nebraska 41

Penalty Box Scheduling • Sub-set of the tasks with higher probability of success. – 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 26 th Nov 2001 Univ. Nebraska 42

Semi-Flexible Constraints • The time constraints provided by the users tended to be ad-hoc 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 26 th Nov 2001 Univ. Nebraska 43

Semi-Flexible Constraints: Pointer Based “Attack the IAD before power system” IAD-E 0 IAD-L Power-E Semi-Flexible Constraints: Pointer Based “Attack the IAD before power system” IAD-E 0 IAD-L Power-E 3000 Power-L 6000 Time (Minutes) 26 th Nov 2001 Univ. Nebraska 44

Semi-Flexible Constraints: Pointer Based “Attack the IAD before power system” IAD-E 0 IAD-L Power-E Semi-Flexible Constraints: Pointer Based “Attack the IAD before power system” IAD-E 0 IAD-L Power-E 3000 Power-L 6000 Time (Minutes) 26 th Nov 2001 Univ. Nebraska 45

Semi-Flexible Constraints: Pointer Based “Attack the IAD before power system” IAD-E 0 IAD-L Power-E Semi-Flexible Constraints: Pointer Based “Attack the IAD before power system” IAD-E 0 IAD-L Power-E 3000 Power-L 6000 Time (Minutes) 26 th Nov 2001 Univ. Nebraska 46

Semi-Flexible Constraints: Ripple Based “Attack the IAD before power system” IAD-E 0 IAD-L Power-E Semi-Flexible Constraints: Ripple Based “Attack the IAD before power system” IAD-E 0 IAD-L Power-E Power-L 3000 6000 Time (Minutes) 26 th Nov 2001 Univ. Nebraska 47

Semi-Flexible Constraints: Ripple Based “Attack the IAD before power system” IAD-E 0 Power-E IAD-L Semi-Flexible Constraints: Ripple Based “Attack the IAD before power system” IAD-E 0 Power-E IAD-L 3000 Power-L 6000 Time (Minutes) 26 th Nov 2001 Univ. Nebraska 48

Semi-Flexible Constraints: Ripple Based “Attack the IAD before power system” IAD-E 0 Power-E IAD-L Semi-Flexible Constraints: Ripple Based “Attack the IAD before power system” IAD-E 0 Power-E IAD-L 3000 Power-L 6000 Time (Minutes) 26 th Nov 2001 Univ. Nebraska 49

Semi-Flexible Constraints: Ripple Based “Attack the IAD before power system” IAD-E 0 IAD-L Power-E Semi-Flexible Constraints: Ripple Based “Attack the IAD before power system” IAD-E 0 IAD-L Power-E 3000 Power-L 6000 Time (Minutes) 26 th Nov 2001 Univ. Nebraska 50

Common Task Model Plan Ready Fly 30 mins 20 mins P P P R Common Task Model Plan Ready Fly 30 mins 20 mins P P P R F F F E E R 60 mins R Bomb Depot P AAR AWACS P 26 th Nov 2001 5 mins R “Drop 120, MK-84 s from 3 B-52 s at location X, Y at 22. 00 on D+5” Recover 40 mins R R Execute P F E R P R R R F F F E E CAP Flight Univ. Nebraska E R R R SEAD Flight B-52 Flight Weapon Loader Information & Control 51

Example Problem (2) • The AWACS aborts on take off! P P P R Example Problem (2) • The AWACS aborts on take off! P P P R R R F F F E E R Bomb Depot P AAR AWACS P 26 th Nov 2001 R R P F E R P R R R F F F E E E R R R SEAD Flight B-52 Flight Weapon Loader CAP Flight Univ. Nebraska 52

Summary Advances in search technology: – – 1993: 1996: 1999: 2001: Tasks 64 ~570 Summary Advances in search technology: – – 1993: 1996: 1999: 2001: Tasks 64 ~570 1000 s 10000 s Resources 6 17 dozens hundreds Type Job Shop RCPS Feasible? X barely • Search works! – search-based technology has matured – large, real-world, problems are solvable – tech-transfer path is short 26 th Nov 2001 Univ. Nebraska 53

Questions ? 26 th Nov 2001 Univ. Nebraska 54 Questions ? 26 th Nov 2001 Univ. Nebraska 54