The p-median problem is a classic discrete location problem with numerous applications. It aims to open p sites while minimizing the sum of the distances of each client to its nearest open site. We study a Benders dec...
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The p-median problem is a classic discrete location problem with numerous applications. It aims to open p sites while minimizing the sum of the distances of each client to its nearest open site. We study a Benders decomposition of the most efficient formulation in the literature. We show that the Benders cuts can be separated in linear time. The Benders reformulation leads to a compact formulation for the p-median problem. We implement a two-phase Benders decomposition algorithm that outperforms state-of-the-art methods on benchmark instances by an order of magnitude and allows to exactly solve for the first time several instances among which are large TSP instances and BIRCH instances. We also show that our implementation easily applies to the uncapacitated facility location problem.(c) 2022 Elsevier B.V. All rights reserved.
In this paper we are interested in the separation problem of the so-called rounded capacity inequalities which are involved in the two-index formulation of the CVRP (Capacitated Vehicle Routing Problem) polytope. In a...
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In this paper we are interested in the separation problem of the so-called rounded capacity inequalities which are involved in the two-index formulation of the CVRP (Capacitated Vehicle Routing Problem) polytope. In a recent work (Diarrassouba, 2015, [1]), we have investigated the theoretical complexity of that problem in the general case. Several authors have devised heuristic separationalgorithms for rounded capacity inequalities for solving the CVRP. In this paper, we investigate the conditions under which this separation problem can be solved in polynomial time, and this, in the context of the CVRP or for solving other combinatorial optimization problems in which rounded capacity inequalities are involved. We present four cases in which they can be separated in polynomial time and reduce the problem to O(n(2)) maximum flow computations. (C) 2016 Elsevier B.V. All rights reserved.
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