Yolanda Hinojosa

A multiperiod two-echelon multicommodity capacitated plant location problem

Abstract In this paper we deal with a facility location problem where one desires to establish facilities at two different distribution levels by selecting the time periods. Our model intends to minimize the total cost for meeting demands for all the products specified over the planning horizon at various customer locations while satisfying the capacity requirements of the production plants and intermediate warehouses. We address this problem by means of a formulation as a mixed integer programming problem. A Lagrangean relaxation is proposed to solve the problem, together with a heuristic procedure that constructs feasible solutions of the original problem from the solutions at the lower bounds obtained by the relaxed problems. Computational tests are provided showing the good performance of this approach for a wide range of problems.

Dynamic supply chain design with inventory

In this paper, we deal with a facility location problem where we build new facilities or close down already existing facilities at two different distribution levels over a given time horizon. In addition, we allow to carry over stock in warehouses between consecutive periods. Our model intends to minimize the total costs, including transportation and inventory holding costs for products as well as fixed and operating costs for facilities. After formulating the problem, we propose a Lagrangian approach which relaxes the constraints connecting the distribution levels. A procedure is developed to solve the resulting, independent subproblems and, based on this solution, to construct a feasible solution for the original problem.

The multi-period incremental service facility location problem

In this paper we introduce the multi-period incremental service facility location problem where the goal is to set a number of new facilities over a finite time horizon so as to cover dynamically the demand of a given set of customers. We prove that the coefficient matrix of the allocation subproblem that results when fixing the set of facilities to open is totally unimodular. This allows to solve efficiently the Lagrangean problem that relaxes constraints requiring customers to be assigned to open facilities. We propose a solution approach that provides both lower and upper bounds by combining subgradient optimization to solve a Lagrangean dual with an ad hoc heuristic that uses information from the Lagrangean subproblem to generate feasible solutions. Numerical results obtained in the computational experiments show that the obtained solutions are very good. In general, we get very small percent gaps between upper and lower bounds with little computation effort.

Single facility location problems with unbounded unit balls

Abstract.In this paper we consider a new class of continuous location problems where the “distances” are measured by gauges of closed (not necessarily bounded) convex sets. These distance functions do not satisfy the definiteness property and therefore they can be used to model those situations where there exist zero-distance regions. We prove a geometrical characterization of these measures of distance as the length of shortest paths between points using only a subset of directions of their unit balls. We also characterize the complete set of optimal solutions for this class of continuous single facility location problems and we give resolution methods to solve them. Our analysis allows to consider new models of location problems and generalizes previously known results.

The reliable p-median problem with at-facility service

This paper deals with a discrete facility location model where service is provided at the facility sites. It is assumed that facilities can fail and customers do not have information on failures before reaching them. As a consequence, they may need to visit more than one facility, following an optimized search scheme, in order to get service. The goal of the problem is to locate p facilities in order to minimize the expected total travel cost. The paper presents two alternative mathematical programming formulations for this problem and proposes a matheuristic based on a network flow model to provide solutions to it. The computational burden of the presented formulations is tested and compared on a test-bed of instances.

When centers can fail

This paper presents the p-next center problem, which aims to locate p out of n centers so as to minimize the maximum cost of allocating customers to backup centers. In this problem it is assumed that centers can fail and customers only realize that their closest (reference) center has failed upon arrival. When this happens, they move to their backup center, i.e., to the center that is closest to the reference center. Hence, minimizing the maximum travel distance from a customer to its backup center can be seen as an alternative approach to handle humanitarian logistics, that hedges customers against severe scenario deteriorations when a center fails.For this extension of the p-center problem we have developed several different integer programming formulations with their corresponding strengthenings based on valid inequalities and variable fixing. The suitability of these formulations for solving the p-next center problem using standard software is analyzed in a series of computational experiments. These experiments were carried out using instances taken from the previous discrete location literature.