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Branch and Price and Cut for the Split-Delivery Vehicle Routing Problem with Time Windows and Linear Weight-Related Cost

Author

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  • Zhixing Luo

    (International Center of Management Science and Engineering, School of Management and Engineering, Nanjing University, 210093 Nanjing, China; and Department of Industrial and Systems Engineering, National University of Singapore, Singapore 119260)

  • Hu Qin

    (School of Management, Huazhong University of Science and Technology, 430074 Wuhan, China)

  • Wenbin Zhu

    (School of Business Administration, South China University of Technology, 510640 Guangzhou, China)

  • Andrew Lim

    (Department of Industrial and Systems Engineering, National University of Singapore, Singapore; and International Center of Management Science and Engineering, School of Management and Engineering, Nanjing University, 210093 Nanjing, China)

Abstract

This paper addresses a new vehicle routing problem that simultaneously involves time windows, split delivery, and linear weight-related cost. This problem is a generalization of the split delivery vehicle routing problem with time windows (SDVRPTW), which consists of determining a set of least-cost vehicle routes to serve all customers while respecting the restrictions of vehicle capacity and time windows. The travel cost per unit distance is a linear function of the vehicle weight and the customer demand can be fulfilled by multiple vehicles. To solve this problem, we propose an exact branch-and-price-and-cut algorithm, where the pricing subproblem is a variant of the resource-constrained elementary shortest path problem. We first prove that at least one optimal solution to the pricing subproblem is associated with an extreme delivery pattern, and then we design a tailored and novel label-setting algorithm to solve the pricing subproblem. Computational results show that our proposed algorithm can handle both the SDVRPTW and our new problem effectively.

Suggested Citation

  • Zhixing Luo & Hu Qin & Wenbin Zhu & Andrew Lim, 2017. "Branch and Price and Cut for the Split-Delivery Vehicle Routing Problem with Time Windows and Linear Weight-Related Cost," Transportation Science, INFORMS, vol. 51(2), pages 668-687, May.
    • Handle: RePEc:inm:ortrsc:v:51:y:2017:i:2:p:668-687
    DOI: 10.1287/trsc.2015.0666
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