Optimal mathematical programming for the warehouse location problem with Euclidean distance linearization

The warehouse location problem (WLP) involves determining one (or multiple) locations as the materials/products collecting/distributing centers for serving a group of customers scattered geographically in a region, at a minimum total transportation cost. The most conventional and widely used approach for solving the WLP is the weighted k-means algorithm. However, this is not a global approach, because it always traps into local optima and is sensitive to the initial settings. Our numeric examples demonstrated that the solutions obtained by the weighted k-means could depart from the optimal values by as much as 16.8% on average. In this paper, we present an optimal programming approach based on mixed-integer linear programming (MILP) for the WLP, which is irrelative to the initial solution and can be optimally solved by commercial solvers. For large-sized datasets, we developed an MILP-based dynamic iterative partial optimization (MILP-DIPO) to search for the near-optimal results with controllable computational time. Experiments on 14 datasets, including 6 small-sized synthesized datasets and 8 variants of the known benchmark datasets in the UEF repository, were performed to validate the proposed model and heuristics. The computational results confirm that improvements with the proposed method could be as great as –22.9% (−14.0% on average) for small-sized datasets. For the eight benchmark datasets, the MILP-DIPO algorithm delivered near-optimal solutions in a reasonable computational time, with up to −8.0% (−2.6% on average) improvement compared to the results obtained by the conventional weighted k-means algorithm.