Lagrangian Bounds and a Heuristic for the Two-Stage Capacitated Facility Location Problem

Abstract

In the two-stage capacitated facility location problem, a single product is produced at some plants in order to satisfy customer demands. The product is transported from these plants to some depots and then to the customers. The capacities of the plants and depots are limited. The aim is to select cost minimizing locations from a set of potential plants and depots. This cost includes fixed cost associated with opening plants and depots, and variable cost associated with both transportation stages. In this work, two different mixed integer linear programming formulations are considered for the problem. Several Lagrangian relaxations are analyzed and compared, and a Lagrangian heuristic producing feasible solutions is presented. The results of a computational study are reported.

Hybrid metaheuristics to solve a multiproduct two‐stage capacitated facility location problem

“…Relaxation-based heuristics were proposed by Litvinchev and Ozuna (2012) to solve the SP-TSCFLP considering instances with up to 10 plants and depots and 100 customers, while metaheuristcs were recently employed by Fernandes et al (2014) A wide set of large-sized instances was proposed by Fernandes et al (2014), who also proposed a GA to solve the SP-TSCFLP. Two heuristics proposed by Litvinchev and Ozuna (2012) (state of the art so far) were also applied to the new proposed set of instances, as well as a commercial solver. The authors demonstrated that GA was capable of outperforming both heuristics and solver.…”

“…In addition, we note a lack of research in applying metaheuristics to solve the problem. Litvinchev and Ozuna (2012) proposed a mathematical model for SP-TSCFLP. The same model was used by Rabello et al (2016) and Biajoli et al (2019).…”

A simple and effective genetic algorithm for the two-stage capacitated facility location problem

“…Moreover, the latter work considers that the number of depots to locate is known beforehand. The TSCFLP version considered in this paper is the same of Litvinchev and Ozuna (2012) who proposed several Lagrangian relaxations for the problem. Feasible solutions are constructed from those of the Lagrangian subproblems by applying simple heuristic procedures.…”

Determination of Network Configuration Considering Inventory Cost in a Supply Chain

“…Among some publications involving location and inventory problems we can mention the work of Tancrez [5], which incorporates the Economic Order Quantity Model (EOQ) into the facility location problem, assuming deterministic demand and fixing the lot size. References [4,6,7,8] present similar problems, but assume stochastic demands. Hernández et al [9] develop an algorithm to solve multi item inventory decisions.…”

“…Regarding to solution methods, the literature is not very extensive. The Lagrangian relaxation is the most appealed tool for solving problems with similar characteristics [8], but heuristics have also been used [7,10].…”