A GRASP + ILP-based metaheuristic for the capacitated location-routing problem

Abstract

In this paper we present a three-phase heuristic for the Capacitated Location-Routing Problem. In the first stage, we apply a GRASP followed by local search procedures to construct a bundle of solutions. In the second stage, an integer-linear program (ILP) is solved taking as input the different routes belonging to the solutions of the bundle, with the objective of constructing a new solution as a combination of these routes. In the third and final stage, the same ILP is iteratively solved by column generation to improve the solutions found during the first two stages. The last two stages are based on a new model, the location-reallocation model, which generalizes the capacitated facility location problem and the reallocation model by simultaneously locating facilities and reallocating customers to routes assigned to these facilities. Extensive computational experiments show that our method is competitive with the other heuristics found in the literature, yielding the tightest average gaps on several sets of instances and being able to improve the best known feasible solutions for some of them.

Appendix

1.1 Detailed results for different seetings of GRASP+SB

In this appendix we provide a detailed comparison of the performance of method GRASP+SB (i.e., without considering the LIH) for different settings of GRASP and SB on the instances of set $\mathcal F _1$. Table 10 is based on the average values reported in Table 13. Each gap and CPU time reported corresponds to the average on 10 runs of method GRASP+SB.

Table 13 Detailed results for different settings of GRASP+SB

1.2 New best solutions found

In this appendix we provide the best solutions found by our algorithm (including the calibration phase) as reported in Table 12. In each table, the first lines report the loads ($q$) and fixed costs ($cost$) of the open facilities ($f$). The following lines report the loads ($q$), costs ($cost$), facilities ($f$) and customers ($customers$) associated with each route. The customers are listed in their order of visit (See Tables 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, and 30).

Table 14 New solution for instance ppw-100x10-1a with cost 287695

Table 15 New solution for instance ppw-100x10-1b with cost 230989

Table 16 New solution for instance ppw-200x10-1a with cost 475294

Table 17 New solution for instance ppw-200x10-1b with cost 377043

Table 18 New solution for instance ppw-200x10-2a with cost 449115

Table 19 New solution for instance ppw-200x10-2b with cost 374280

Table 20 New solution for instance ppw-200x10-3b with cost 362653

Table 21 New solution for instance Das-150x10 with cost 43952.3

Table 22 New solution for instance P131122 with cost 1823.2

Table 23 New solution for instance P131212 with cost 1964.3

Table 24 New solution for instance P131222 with cost 1792.8

Table 25 New solution for instance P133212 with cost 1198.2

Table 26 New solution for instance P121112 with cost 2243.4

Table 27 New solution for instance P121122 with cost 2138.4

Table 28 New solution for instance P121212 with cost 2209.3

Table 29 New solution for instance P121222 with cost 2222.9

Table 30 New solution for instance P123112 with cost 1954.7