Modeling issues when using simulation to test the performance of mathematical programming models under stochastic conditions Anne-Laure LadierUniv. Lyon - DISP - INSA Lyon Allen G. GreenwoodPoznan Univ. of Technology Gülgün AlpanUniv. Grenoble Alpes

Outline Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 2 Modeling issues when using simulation to test the performance of mathematical programming models under stochastic conditions

Simulation and optimization Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 3 Simulation model Optimization model Simulation model Optimization model Simulation model Optimization model Gambardella et al. (1998) Hauser (2002) Liu and Takakuwa (2009) Wang and Regan (2008) McWilliams (2005) Aickelin and Adewunmi (2006) Context Cases description Foundational differences Operational differences Conclusion

Summary of our approach Optimization model Integer programming Optimization model Integer programming System Simulation model FlexSim Simulation model FlexSim Simulation analyses Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 4

Research questions What are the modelling issues raised by this optimization → simulation relationship? How can they be solved or circumvented? Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 5

C ASES DESCRIPTION Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 6

Cross-docking Less than 24h of temporary storage docking unloading scanning transfer loading departing Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 7 1 color = 1 client

Case 1 – General ideas Simulation model Optimization model Truck schedule Truck arrival and departure time Amount in storage Pallet transfer Comparison Logic Random events Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 8

Case 1 – Model demonstration Simulation software: FlexSim Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 9

Case 2 – General ideas Simulation model Optimization model Comparison Random events Employee timetable Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 10

Case 2 – Model overview Unloading Doors Workers Temporary Storage Inbound Docks Outbound Docks Simulation software: FlexSim Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 11

F OUNDATIONAL DIFFERENCES Two modeling approaches represent the system differently Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 12

Time representation Mathematical optimization « Big buckets » time intervals, masked time Discrete-event simulation Events ocur at precise instances of time Shorten time intervals? Increase complexity Measure performance in terms of intervals Time Inbound truck Outbound truck Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 13

Spatial representation Mathematical optimization If spatial considerations are not the core of the problem, ignore! Process times = average rates Discrete-event simulation Add spatial considerations? Increase complexity speed distance Processor for precise control of travel time availability Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 14

Model structure and size Mathematical optimization Execution time exponential in the instance size Discrete-event simulation Execution time linear in the instance size Specify size early in the project Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 15

O PERATIONAL DIFFERENCES Make the operations match Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 16

Task order, batch size, parallelism Mathematical optimization No precise task order unless it is a key consideration Discrete-event simulation 3 ×10 pallets/hour ≠ 1 × 30 pallets/hour Number of pallets at time h Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 17 Order and batch size do have important impacts 1 pallet= 2 min 1 pallet= 6 min

Process logic Mathematical optimization Low granularity: only overall workload in time interval Optimal decision-making Discrete-event simulation High granularity: specific pallets, doors, workers, etc FIFO logic Greedy decision making Operational decisions when deviation from schedule occurs e.g. wait for assigned operator or use available (capable) Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 18

C ONCLUSION Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 19

After model validation… The simulation models were used to assess the robustness of the schedules/timetables obtained by mathematical programming A.-L. Ladier, G. Alpan, and A. G. Greenwood, “Robustness evaluation of an IP-based cross-docking schedule using discrete-event simulation,” in Industrial and Systems Engineering Research Conference, A.-L. Ladier and G. Alpan, “Robust cross-dock scheduling with time windows,” European Journal of Operational Research. Under revision. Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 20

Conclusion Mathematical programming and optimization are complementary decision-support tools Understand their inherent differences in modeling the same system Encourage an increase in the use of discrete-event simulation to assess the performance of optimization models Modelers in sharing their modeling issues/solution to the community Context Cases description Foundational differences Operational differences Conclusion Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester 21

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Pallets transfer