Journal article
Cover Inequalities for a Vehicle Routing Problem with Time Windows and Shifts
Vrije Universiteit Amsterdam1
Management Science, Department of Technology, Management and Economics, Technical University of Denmark2
Operations Research, Management Science, Department of Technology, Management and Economics, Technical University of Denmark3
Department of Technology, Management and Economics, Technical University of Denmark4
Eindhoven University of Technology5
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.
Language: | English |
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Year: | 2019 |
Pages: | 1354-1371 |
ISSN: | 15265447 and 00411655 |
Types: | Journal article |
DOI: | 10.1287/trsc.2018.0885 |
ORCIDs: | Røpke, Stefan , 0000-0003-0259-0684 and 0000-0003-4766-2346 |