CAPACITATED VEHICLE ROUTING PROBLEM

Ibrahim A.A; Lo N.; Abdulaziz R.O; Ishaya J.A

doi:10.29121/granthaalayah.v7.i3.2019.976

Authors

Ibrahim A.A Department of Mathematical Science, African Institute for Mathematical Science, Senegal
Lo N. Department of Mathematical Science, African Institute for Mathematical Science, Senegal
Abdulaziz R.O Department of Energy Engineering, PAUWES, University of Tlemcen, Algeria
Ishaya J.A Department of Mathematical Science, African Institute for Mathematical Science, Senegal

DOI:

https://doi.org/10.29121/granthaalayah.v7.i3.2019.976

Keywords:

Vehicle Routing Problem, CVRP, Column Generation, Google’s OR tool, Reinforcement Learning; Python; Gourbi

Abstract [English]

Cost of transportation of goods and services is an interesting topic in today’s society. The Capacitated vehicle routing problem, which is been consider in this research, is one of the variants of the vehicle routing problem. In this research we develop a reinforcement learning technique to find optimal paths from a depot to the set of customers while also considering the capacity of the vehicles, in order to reduce the cost of transportation of goods and services. Our basic assumptions are; each vehicle originates from a depot, service the customers and return to the depot, the vehicles are homogeneous. We solve the CVRP with an exact method; column generation, goole’s operation research tool and reinforcement learning and compare their solutions. Our objective is to solve a large-size of vehicle routing problem to optimality.

Downloads

Download data is not yet available.

References

Paolo Toth and Daniele Vigo, An Overview of Vehicle Routing Problems, The Vehicle Routing problem, SIAM, 2002, pp. 1–26. DOI: https://doi.org/10.1137/1.9780898718515.ch1

George B Dantzig and John H Ramser, The Truck Dispatching Problem, Management Science 6 (1959), no. 1, 80–91.

Michael Berliner Pedersen, OB Madsen, and OA Nielsen, Optimization Models and Solution Methods for Intermodal Transportation, Centre for Traffic and Transport, Technical University of Denmark, 2005.

Stefan Ropke, Heuristic and Exact Algorithms for Vehicle Routing Problems, Unpublished PhD thesis, Computer Science Department, University of Copenhagen (2005).

Ricardo Fukasawa, Humberto Longo, Jens Lysgaard, Marcus Poggi de Aragão, Marcelo Reis, Eduardo Uchoa, and Renato F Werneck, Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem, Mathematical Programming 106 (2006), no. 3, 491–511.

Bruce L Golden, Subramanian Raghavan, and Edward A Wasil, The Vehicle Routing Problem: Latest Advances and New Challenges, vol. 43, Springer Science & Business Media, 2008. DOI: https://doi.org/10.1007/978-0-387-77778-8

Michel Gendreau, Francois Guertin, Jean-Yves Potvin, and René Séguin, Neighborhood Search Heuristics for a Dynamic Vehicle Dispatching Problem with Pick-ups and Deliveries, Transportation Research Part C: Emerging Technologies 14 (2006), no. 3, 157–174.

GDH Claassen and Th HB Hendriks, An application of special ordered sets to a periodic milk collection problem, European Journal of Operational Research 180 (2007), no. 2,754–769.

Geoff Clarke and John W Wright, Scheduling of vehicles from a central depot to a number of delivery points, Operations research 12 (1964), no. 4, 568–581.

Martin Desrochers, Jacques Desrosiers, and Marius Solomon, A new optimization algorithm for the vehicle routing problem with time windows, Operations research 40 (1992), no. 2,342–354.

Niklas Kohl, Jacques Desrosiers, Oli BG Madsen, Marius M Solomon, and Francois Soumis, 2-path Cuts for the Vehicle Routing Problem with Time Windows, Transportation Science 33 (1999), no. 1, 101–116.

Roberto Baldacci and Aristide Mingozzi, Lower Bounds and an Exact Method for the Capacitated Vehicle Routing Problem, Service Systems and Service Management, 2006 International Conference on, vol. 2, IEEE, 2006, pp. 1536–1540. DOI: https://doi.org/10.1109/ICSSSM.2006.320764

Mohammadreza Nazari, Afshin Oroojlooy, Lawrence V Snyder, and Martin Takáč, Deep Re-inforcement Learning for Solving the Vehicle Routing Problem, arXiv preprint arXiv:1802.04240(2018).

Frédéric Semet, Paolo Toth, and Daniele Vigo, Chapter 2: Classical Exact Algorithms for the Capacitated Vehicle Routing Problem, Vehicle Routing: Problems, Methods, and Applications, Second Edition, SIAM, 2014, pp. 37–57. DOI: https://doi.org/10.1137/1.9781611973594.ch2

GPT van Lent, Using Column Generation for the Time Dependent Vehicle Routing Problem with Soft Time Windows and Stochastic Travel Times, Master’s thesis, 2018.

Inc. google. google’s optimization tools, 2019, webpage, https://github.com/google/or-tools, 2019.

Ilya Sutskever, Oriol Vinyals, and Quoc V Le, Sequence to Sequence Learning with Neural Networks, Advances in Neural Information Processing Systems, 2014, pp. 3104–3112.

Inc. Gurobi Optimization. gurobi optimizer reference manual, 2019, url, http://www.gurobi.com, 2019.