Modeling issues when using simulation to test the performance of mathematical programming models under stochastic conditions Anne-Laure LadierUniv. Lyon

Modeling issues when using simulation

to test the performance of mathematical programming

models under stochastic conditions

Anne-Laure Ladier Univ. Lyon - DISP - INSA LyonAllen G. Greenwood Poznan Univ. of TechnologyGülgün Alpan Univ. Grenoble Alpes

2

Outline

Context

Cases

description

Foundational

differences

Operation

al differences

Conclusion

Anne-Laure Ladier, Allen G. Greenwood, Gülgün Alpan | ESM'2015, Leicester

Modeling issues when using simulation to test the performance of mathematical programming models under stochastic conditions

3

Simulation and optimization


Simulation

model

Optimization

model

Optim

izatio

n

mod

el

Simulation

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

4

Summary of our approach

Optimization

model

Integer

programming

System

Simulation

model

FlexSim Sim

ula

tion

anal

yses





5

Research questions

What are the modelling issues raised by this optimization → simulation relationship?

How can they be solved or circumvented?





6

CASES DESCRIPTION





7

Cross-docking

Less than 24h of

temporary storage

docking

unloading

scanning

transfer

loading

departing





1 color = 1 client

8

Case 1 – General ideas

Simulation model

Optimization

model

Truck schedule

Truck arrival and departure timeAmount in storagePallet transfer

Comparison

Logic

Logic

Random

events





9

Case 1 – Model demonstration

Simulation software: FlexSim





10

Case 2 – General ideas

Simulation model

Optimization

model

Comparison

Random

events

Employee timetable





11

Case 2 – Model overview

Unloading Doors

Workers

Temporary Storage

Inbound Docks

Outbound Docks

Simulation software: FlexSim





12

FOUNDATIONAL DIFFERENCES

Two modeling approaches represent the system differently





13

Time representationMathematical 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





14

Spatial representationMathematical optimization If spatial

considerations are not the core of the problem, ignore!

Process times = average rates


Add spatial considerations?

Increase complexity

speed

distance

Processor for precise control of travel time

availability





15

Model structure and sizeMathematical optimization

Execution time exponential in the instance size


Execution time linear in the instance size

Specify size early in the project





16

OPERATIONAL DIFFERENCESMake the operations match





17

Task order, batch size, parallelismMathematical optimization

No precise task order unless it is a key consideration


3 ×10 pallets/hour≠

1 × 30 pallets/hourNumber of pallets at time h





Order and batch size do have important impacts

1 pallet= 2 min

1 pallet= 6 min

18

Process logicMathematical 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)





19

CONCLUSION





20

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, 2014.

A.-L. Ladier and G. Alpan, “Robust cross-dock scheduling with time windows,” European Journal of Operational Research. Under revision.





21

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





Thank you for your attention!

anne-laure-ladier.fr

Pallets transfer

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Modeling issues when using simulation to test the performance of mathematical programming models under stochastic conditions Anne-Laure LadierUniv. Lyon