In the competitive p-median problem, two decision makers, the leader and the follower, compete to attract clients from a given market. The leader opens his facilities, anticipating that the follower will react to the decision by opening his/her own facilities. The leader and the follower try to maximize their own profits. This is the Stackelberg game. We present it as a linear bilevel 0–1 probl...

Good heuristic solutions for large Multisource Weber problems can be obtained by solving related p-median problems in which potential locations of the facilities are users locations and then solving Weber problems for the sets of users of each facility. Weber's problem is to locate a facility in the Euclidean plane in order to minimize the sum of its (weighted) distances to the locations of a g...

Lagrangian relaxation is commonly used in combinatorial optimization to generate lower bounds for a minimization problem. We study a modified Lagrangian relaxation which generates an optimal integer solution. We call it semi-Lagrangian relaxation and illustrate its practical value by solving large-scale instances of the p-median problem.

The p-median problem is a graph theory problem that was originally designed for, and has been extensively applied to, facility location. In this bibliography, we summarize the literature on solution methods for the uncapacitated and capacitated p-median problem on a graph or network.

We consider the hub location problem, where p hubs are chosen from a given set of nodes, each nonhub node is connected to exactly one hub and each hub is connected to a central hub. Links are installed on the arcs of the resulting network to route the traffic. The aim is to find the hub locations and the connections to minimize the link installation cost. We propose two formulations and a heuri...

The p-median model is used to locate P facilities to serve a geographically distributed population. Conventionally, it is assumed that the population patronize the nearest facility and that the distance between the resident and the facility may be measured by the Euclidean distance. Carling, Han, and Håkansson (2012) compared two network distances with the Euclidean in a rural region with a spa...

An instance of a p-median problem gives n demand points. The objective is to locate p supply points in order to minimize the total distance of the demand points to their nearest supply point. p-Median is polynomially solvable in one dimension but NP-hard in two or more dimensions, when either the Euclidean or the rectilinear distance measure is used. In this paper, we treat the p-median problem...

1 School of Management, The University of Texas at Dallas, Richardson, Texas. email: [email protected] 2 Department of Management, Oklahoma State University, Stillwater Ok, 74078 email: [email protected] 3 Department of Accounting and MIS, The Ohio State University, Columbus, Ohio 43210 email: [email protected] Abstract. In this paper we describe a visual interactive decision...

The p-median problem is a graph theory problem that was originally designed for, and has been extensively applied to, facility location. In this bibliography, we summarize the literature on solution methods for the uncapacitated and capacitated p-median problem on a graph or network.

The inverse p-median problem with variable edge lengths on graphs is to modify the edge lengths at minimum total cost with respect to given modification bounds such that a prespecified set of p vertices becomes a pmedian with respect to the new edge lengths. The problem is shown to be strongly NP-hard on general graphs and weakly NP-hard on series-parallel graphs. Therefore, the special case on...