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A Multi-Depot Vehicle Routing Problem with Stochastic Road Capacity and Reduced Two-Stage Stochastic Integer Linear Programming Models for Rollout Algorithm

Author

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  • Wadi Khalid Anuar

    (Department of Logistics and Transportation, School of Technology Management and Logistics, Universiti Utara Malaysia, Sintok 06010, Kedah, Malaysia
    Laboratory of Computational Statistics and Operations Research, Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia)

  • Lai Soon Lee

    (Laboratory of Computational Statistics and Operations Research, Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia
    Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia)

  • Hsin-Vonn Seow

    (Faculty of Arts and Social Sciences, Nottingham University Business School, University of Nottingham Malaysia Campus, Jalan Broga, Semenyih 43500, Selangor, Malaysia)

  • Stefan Pickl

    (Fakultät für Informatik, Universität der Bundeswehr München, 85577 Neubiberg, Germany)

Abstract

A matheuristic approach based on a reduced two-stage Stochastic Integer Linear Programming (SILP) model is presented. The proposed approach is suitable for obtaining a policy constructed dynamically on the go during the rollout algorithm. The rollout algorithm is part of the Approximate Dynamic Programming (ADP) lookahead solution approach for a Markov Decision Processes (MDP) framed Multi-Depot Dynamic Vehicle Routing Problem with Stochastic Road Capacity (MDDVRPSRC). First, a Deterministic Multi-Depot VRP with Road Capacity (D-MDVRPRC) is presented. Then an extension, MDVRPSRC-2S, is presented as an offline two-stage SILP model of the MDDVRPSRC. These models are validated using small simulated instances with CPLEX. Next, two reduced versions of the MDVRPSRC-2S model (MDVRPSRC-2S1 and MDVRPSRC-2S2) are derived. They have a specific task in routing: replenishment and delivering supplies. These reduced models are to be utilised interchangeably depending on the capacity of the vehicle, and repeatedly during the execution of rollout in reinforcement learning. As a result, it is shown that a base policy consisting of an exact optimal decision at each decision epoch can be obtained constructively through these reduced two-stage stochastic integer linear programming models. The results obtained from the resulting rollout policy with CPLEX execution during rollout are also presented to validate the reduced model and the matheuristic algorithm. This approach is proposed as a simple implementation when performing rollout for the lookahead approach in ADP.

Suggested Citation

  • Wadi Khalid Anuar & Lai Soon Lee & Hsin-Vonn Seow & Stefan Pickl, 2021. "A Multi-Depot Vehicle Routing Problem with Stochastic Road Capacity and Reduced Two-Stage Stochastic Integer Linear Programming Models for Rollout Algorithm," Mathematics, MDPI, vol. 9(13), pages 1-44, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1572-:d:588192
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    1. Shiripour, Saber & Mahdavi-Amiri, Nezam, 2019. "Optimal distribution of the injured in a multi-type transportation network with damage-dependent travel times: Two metaheuristic approaches," Socio-Economic Planning Sciences, Elsevier, vol. 68(C).
    2. Bertazzi, Luca & Secomandi, Nicola, 2018. "Faster rollout search for the vehicle routing problem with stochastic demands and restocking," European Journal of Operational Research, Elsevier, vol. 270(2), pages 487-497.
    3. B. Zhao, 2016. "April 2015 Nepal earthquake: observations and reflections," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 80(2), pages 1405-1410, January.
    4. Nicola Secomandi, 2001. "A Rollout Policy for the Vehicle Routing Problem with Stochastic Demands," Operations Research, INFORMS, vol. 49(5), pages 796-802, October.
    5. Yi, Wei & Ozdamar, Linet, 2007. "A dynamic logistics coordination model for evacuation and support in disaster response activities," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1177-1193, June.
    6. Moshe Dror & Gilbert Laporte & Pierre Trudeau, 1989. "Vehicle Routing with Stochastic Demands: Properties and Solution Frameworks," Transportation Science, INFORMS, vol. 23(3), pages 166-176, August.
    7. Richard Bellman, 1954. "Some Applications of the Theory of Dynamic Programming---A Review," Operations Research, INFORMS, vol. 2(3), pages 275-288, August.
    8. Claudia Archetti & Martin W. P. Savelsbergh & M. Grazia Speranza, 2006. "Worst-Case Analysis for Split Delivery Vehicle Routing Problems," Transportation Science, INFORMS, vol. 40(2), pages 226-234, May.
    9. Davood Shiri & Vahid Akbari & F. Sibel Salman, 2020. "Online routing and scheduling of search-and-rescue teams," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(3), pages 755-784, September.
    10. Dror, Moshe, 1993. "Modeling vehicle routing with uncertain demands as a stochastic program: Properties of the corresponding solution," European Journal of Operational Research, Elsevier, vol. 64(3), pages 432-441, February.
    11. Novoa, Clara & Storer, Robert, 2009. "An approximate dynamic programming approach for the vehicle routing problem with stochastic demands," European Journal of Operational Research, Elsevier, vol. 196(2), pages 509-515, July.
    12. Keyju Lee & Junjae Chae & Bomi Song & Donghyun Choi, 2020. "A Model for Sustainable Courier Services: Vehicle Routing with Exclusive Lanes," Sustainability, MDPI, vol. 12(3), pages 1-19, February.
    13. Zhen, Lu & Ma, Chengle & Wang, Kai & Xiao, Liyang & Zhang, Wei, 2020. "Multi-depot multi-trip vehicle routing problem with time windows and release dates," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 135(C).
    14. Sha-lei Zhan & Liang Chen & Ping-Kuo Chen & Yong Ye, 2019. "A Vehicle Route Planning Method of Two-Phase Large-Scale Crowd Evacuation in Typhoon Relief Activities," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-9, August.
    15. Ferrer, José M. & Martín-Campo, F. Javier & Ortuño, M. Teresa & Pedraza-Martínez, Alfonso J. & Tirado, Gregorio & Vitoriano, Begoña, 2018. "Multi-criteria optimization for last mile distribution of disaster relief aid: Test cases and applications," European Journal of Operational Research, Elsevier, vol. 269(2), pages 501-515.
    16. Bertazzi, Luca & Bosco, Adamo & Laganà, Demetrio, 2015. "Managing stochastic demand in an Inventory Routing Problem with transportation procurement," Omega, Elsevier, vol. 56(C), pages 112-121.
    17. Richard Bellman, 1954. "On some applications of the theory of dynamic programming to logistics," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(2), pages 141-153, June.
    18. Justin C. Goodson & Jeffrey W. Ohlmann & Barrett W. Thomas, 2013. "Rollout Policies for Dynamic Solutions to the Multivehicle Routing Problem with Stochastic Demand and Duration Limits," Operations Research, INFORMS, vol. 61(1), pages 138-154, February.
    19. Haghani, Ali & Oh, Sei-Chang, 1996. "Formulation and solution of a multi-commodity, multi-modal network flow model for disaster relief operations," Transportation Research Part A: Policy and Practice, Elsevier, vol. 30(3), pages 231-250, May.
    20. Marlin W. Ulmer & Justin C. Goodson & Dirk C. Mattfeld & Marco Hennig, 2019. "Offline–Online Approximate Dynamic Programming for Dynamic Vehicle Routing with Stochastic Requests," Service Science, INFORMS, vol. 53(1), pages 185-202, February.
    21. Justin C. Goodson & Barrett W. Thomas & Jeffrey W. Ohlmann, 2016. "Restocking-Based Rollout Policies for the Vehicle Routing Problem with Stochastic Demand and Duration Limits," Transportation Science, INFORMS, vol. 50(2), pages 591-607, May.
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