anne-laure ladier, gülgün alpan, allen g. greenwood ● *g-scop, grenoble inp, france ●...

Robustness evaluation of an IP-based cross-docking schedule using discrete-event simulationAnne-Laure Ladier*, Gülgün Alpan*, Allen G. Greenwood●

*G-SCOP, Grenoble INP, France● Department of Industrial Engineering, Mississippi State University

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Outline

Context

• Cross docking operations

Optimization

• IP-based cross-docking schedule

Simulation

• Simulation model

• Methodology for robustness assessment

Results and conclusion

• Numerical results

• Proposition of robustness metrics

• Conclusion and perspectives

Context > Optimization > Simulation > Results > Conclusion

Robustness evaluation of an IP-based cross-docking schedule using discrete-event simulation

A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014

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Cross-docking

Less than 24h of temporary

storage

1 color = 1 destination



4

Operations planning

Reservation system:

Minimize Transporteur providers’ insatisfaction Number of pallets temporarily stored

10am-12pm

6am-8am

9am-12pm

6am-7am

7am-9am

6am-9am

11am-12pm

7am-10am



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IP model

Decision variables: # of units moving from point to point (incl. storage) Time window for the trucks

min ( penality on the inbound time windows chosen + penality on the outbound time windows chosen + nb palets put in storage)

Flow conservation (for each destination)

Nb trucks present ≤ nb doors

Outbound truck leave when fully loaded

Storage capacityLadier, Alpan, Scheduling truck arrivals and departures in a crossdock: earliness, tardiness and storage policies. International Conference on Industrial Engineering and Systems Management, October 2013.



6

Research questions

How do random events distort the schedule ? How to assess its robustness? What should be changed in the IP model to

make the schedule more robust?



7

Methodology

Discrete events simulation Simulate complex stochastic processes Add logic to react in unplanned situations Gather data over multiple runs

Software: FlexSim(http://www.flexsim.com)



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Optimization-simulation?

Simulation

Optimization

Optimization

Simulation

Simulation Optimization

SimulationOptimization

Gambardella et al. (1998)

Hauser (2002)Liu and Takakuwa (2009)Wang and Regan (2008)

McWilliams (2005)Aickelin and Adewunmi (2006)



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FlexSim© simulation model

Simulation model

Run the schedule + add random events

IP

Trucks arrival time

Pallet transfer

time

Unloading time

Ladier, Greenwood, Alpan, Hales. Issues in the Complementary use of simulation and optimization modeling. Cahiers Leibniz n°211, January 2014.

Ex: 20% of trucks are late exponential distribution,

=10 min

Ex: triangular distribution cv=0.1min



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Measure robustness

Measurement indicators

Total number of pallets in stock

Error in docking time inbound

Error in docking time outbound

Error in staying time inbound

Error in staying time outbound

Tolerance

1 pallet

5 min

5 min

20 min

20 min

% off-limits

(20

replications, 21 instances)

Deterministic value

% off-limits



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Results / transfer time

0 10 20 30 40 50 600%

10%

20%

30%

40%

50%

Tolerance (minutes)

% o

ff--li

mits

0 1 2 3 4 5 6 7 80

1

Cv = 0,5Cv = 0,4

Cv = 0,2Cv = 0,3

Cv = 0,1Stochastic transfer time



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Results / transfer time

0 10 20 30 40 50 600%

10%

20%

30%

40%

50%

Tolerance (minutes)

% o

ff--li

mits



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Results / truck arrival time

0 50 100 150 2000%

20%

40%

60%

80%

100%

15101530

Tolerance (minutes)

% o

ff-lim

its

Trucks arriving early or lateFollowing an exponential distribution with parameter dHere: 60% late, 33% on time, 7% early

d



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-100% -60% -20% 20% 60% 100%0

50

100

150

200

15102030

Early Late% of trucks

Tolerance (in minutes) to get 10% off-limits

d

Trucks arriving early or lateFollowing an exponential distribution with parameter d



15


0% 40% 80%0

50

100

150

200

15102030

Late% of trucks

d

Trucks arriving early or lateFollowing an exponential distribution with parameter d



0% 40% 80%0

50

100

150

200

10

Late% of trucks

Tolerance (in minutes) to get 10% off-limits

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Robustness metrics



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Correlation analysis

Correlation error on docking time error in staying time

Between 0 et 10

Some trucks stay docked longer but the next ones

are not delayed

1

Some trucks stay docked longer, the next ones are delayed on that

same amount of time

No critical truckAll trucks are

critical

Some trucks are critical

door1

door2

door3



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Conclusion

Original use of a simulation model to assess the performance of an optimization model

Methodology and indicators to measure robustness

Simulation also helps gathering ideas on robustness improvement



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Robust versions of the model?

Minimax

Min objective in the worst case

Robust project schedulingSpecific approach

Critical tasks Critical trucks

Robust optimizationGeneric approach

Resource redundancy

Doors

Time redundancy

Buffer time

Min average nb trucks at the doors

Min nb of doors used every hour

Min nb critical trucks

Insert buffers of equal length

Insert buffers of length prop. to nb successors

Min buffer lengths standard deviations

Max buffer lenths weighted sum

Min

Min expected regret

…



Thank you for your attentionSlides and more info on www.g-scop.fr/~ladiera

This exchange was funded by

anne-laure ladier, gülgün alpan, allen g. greenwood ● *g-scop, grenoble inp, france ●...

Documents

time ladier

greenwood iserc2014

optimization modeling

greenwood iserc2014

docking time error

robustness assessment

discreteevent simulation

offlimits slide

anne-laure ladier*, gülgün alpan*, allen g. greenwood ● *g-scop, grenoble inp, france ●...

anne-laure ladier, gülgün alpan, allen g. greenwood ● *g-scop, grenoble inp, france ●...