1. Anne-Laure Ladier*, Gülgün Alpan*, Allen G. Greenwood ● *G-SCOP, Grenoble INP, France ● Department of Industrial Engineering, Mississippi State University

2. 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 2A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014

3. Cross-docking Less than 24h of temporary storage 1 color = 1 destination Context > Optimization > Simulation > Results > Conclusion 3A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014

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 Context > Optimization > Simulation > Results > Conclusion 4A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014

5. 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 loadedStorage capacity Ladier, Alpan, Scheduling truck arrivals and departures in a crossdock: earliness, tardiness and storage policies. International Conference on Industrial Engineering and Systems Management, October 2013. Context > Optimization > Simulation > Results > Conclusion 5A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014

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? Context > Optimization > Simulation > Results > Conclusion 6A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014

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) Context > Optimization > Simulation > Results > Conclusion 7A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014

8. Optimization-simulation? Simulation Optimization Simulation Optimization Simulation Optimization Gambardella et al. (1998) Hauser (2002) Liu and Takakuwa (2009) Wang and Regan (2008) McWilliams (2005) Aickelin and Adewunmi (2006) Context > Optimization > Simulation > Results > Conclusion 8A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014

9. 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 c v =0.1min Context > Optimization > Simulation > Results > Conclusion 9A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014

10. 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 20 min % off- limits (20 replications, 21 instances) Deterministic value  % off-limits Context > Optimization > Simulation > Results > Conclusion 10A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014

11. Results / transfer time Stochastic transfer time Context > Optimization > Simulation > Results > Conclusion 11A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014

12. Results / transfer time Context > Optimization > Simulation > Results > Conclusion 12A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014

13. Results / truck arrival time Trucks arriving early or late Following an exponential distribution with parameter  Here: 60% late, 33% on time, 7% early  Context > Optimization > Simulation > Results > Conclusion 13A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014

14. Results / truck arrival time  Trucks arriving early or late Following an exponential distribution with parameter  Context > Optimization > Simulation > Results > Conclusion 14A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014

15. Results / truck arrival time  Trucks arriving early or late Following an exponential distribution with parameter  Context > Optimization > Simulation > Results > Conclusion 15A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014 Tolerance (in minutes) to get 10% off-limits

16. Robustness metrics Context > Optimization > Simulation > Results > Conclusion 16A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014

17. Correlation analysis Correlation error on docking time  error in staying time Between 0 et 1 0 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 truck All trucks are critical Some trucks are critical door1 door2 door3 Context > Optimization > Simulation > Results > Conclusion 17A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014

18. 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 Context > Optimization > Simulation > Results > Conclusion 18A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014

19. Robust versions of the model? Minimax Min objective in the worst case Robust project scheduling Specific approach Critical tasks  Critical trucks Robust optimization Generic 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 … Context > Optimization > Simulation > Results > Conclusion 19A-L. Ladier, G. Alpan, A.G. Greenwood | ISERC2014

20. Thank you for your attention Slides and more info on www.g-scop.fr/~ladiera This exchange was funded by