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Cover Inequalities for a Vehicle Routing Problem with Time Windows and Shifts

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  • Said Dabia

    (School of Business and Economics, VU University Amsterdam, 1081 HV Amsterdam, Netherlands; Eyefreight B.V., 3981 AJ Bunnik, Netherlands;)

  • Stefan Ropke

    (Department of Management Engineering, Technical University of Denmark, 2800 Copenhagen, Denmark;)

  • Tom van Woensel

    (School of Industrial Engineering, Eindhoven University of Technology, 5612 AZ Eindhoven, Netherlands)

Abstract

This paper introduces the vehicle routing problem with time windows and shifts (VRPTWS). At the depot, several shifts with nonoverlapping operating periods are available to load the planned trucks. Each shift has a limited loading capacity. We solve the VRPTWS exactly by a branch-and-cut-and-price algorithm. The master problem is a set partitioning with an additional constraint for every shift. Each constraint requires the total quantity loaded in a shift to be less than its loading capacity. For every shift, a pricing subproblem is solved by a label-setting algorithm. Shift capacity constraints define knapsack inequalities; hence we use valid inequalities inspired from knapsack inequalities to strengthen the linear programming relaxation of the master problem when solved by column generation. In particular, we use a family of tailored robust cover inequalities and a family of new nonrobust cover inequalities. Numerical results show that nonrobust cover inequalities significantly improve the algorithm.

Suggested Citation

  • Said Dabia & Stefan Ropke & Tom van Woensel, 2019. "Cover Inequalities for a Vehicle Routing Problem with Time Windows and Shifts," Transportation Science, INFORMS, vol. 53(5), pages 1354-1371, September.
    • Handle: RePEc:inm:ortrsc:v:53:y:2019:i:5:p:1354-1371
    DOI: 10.1287/trsc.2018.0885
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