When centers can fail: A close second opportunity

Abstract

a b s t r a c tThis 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.

A Weighting-Based Tabu Search Algorithm for the p-Next Center Problem

“…z ∈ R + is the upper bound of the assignment cost, i.e., the length of the longest path. Based on the above notations, the classical mixed-integer programming (MIP) model [Albareda-Sambola et al, 2015] for the pNCP can be formulated as follows.…”

“…In that case, the clients served by the center have to turn to another center from the current center as quickly as possible. Therefore, Albareda-Sambola et al [2015] introduced the p-next center problem (pNCP), which occurs in many industrial applications and has been proven to be NP-hard. It requires locating p centers from a set of candidate centers and assigning a reference center and a backup center to each client.…”

A Multi-Objective Parallel Iterated Greedy for Solving the p-Center and p-Dispersion Problem

“…A total of 165 instances were considered. We generated the instances by selecting the first n points of each instance and varying the values of p following the indications in [8]. See Table 1, where all the combinations of n and p are shown and the number of possible feasible solutions are calculated.…”

“…Among the most extended criteria are the maximization of dispersion among facilities, which was originally defined in [4], and it has been recently studied in [5], the minimization of the distance between the demand points and their closest facility, defined in [6] and tackled with a totally novel approach in [7], or even the minimization of the distance between the demand points to their closest facility and their second closest facility with the aim of being able to overcome a facility failure. This problem was recently presented and solved with an exact approach [8], but it has also been studied from a heuristic point of view [9].…”

The reliable p -median problem with at-facility service

“…Therefore, having contingency plans is important to improve efficiency. This kind of situation was given, for example, in May 11, 2011, in the Spanish town of Lorca: After two consecutive earthquakes nine people were killed, three hundred were injured and the local hospital had to be evacuated due to the risk of collapse [2]. In all those cases, simply moving to the next closest facility from the one that has failed would make a shortsighted decision.…”