For the p-median problem we study complexity of finding a local minimum in the worst and the average cases. We introduce several neighborhoods and show that the corresponding local search problems are PLS-complete. In the average case we note that standard local descent algorithm is polynomial. A relationship between local optima and 0–1 local saddle points is presented.

In this paper we present a hybrid heuristic for the capacitated pmedian problem (CPMP). This problem considers a set of n points, each of them with a known demand, the objective consists of finding p medians and assign each point to exactly one median such that the total distance of assigned points to their corresponding medians is minimized, and the a capacity limit on the medians may not be e...

Due to absence of an universally acceptable magnitude of the Type I error in various Ž elds, p values are used as a wellrecognized tool in decision making in all areas of statistical practice. The distribution of p values under the null hypothesis is uniform. However, under the alternative hypothesis the distribution of the p values is skewed. The expected p value (EPV) has been proposed by aut...

The p-median model is used to locate P facilities to serve a geographically distributed population. Conventionally, it is assumed that the population always travels to the nearest facility. Drezner and Drezner (2006, 2007) provide three arguments on why this assumption might be incorrect, and they introduce the extended the gravity p-median model to relax the assumption. We favour the gravity p...

We consider the problem of approximating the branch and size dependent demand of a fashion discounter with many branches by a distributing process being based on the branch delivery restricted to integral multiples of lots from a small set of available lot-types. We propose a formalized model which arises from a practical cooperation with an industry partner. Besides an integer linear programmi...

In this paper we consider a well-known class of valid inequalities for the p-median and the uncapacitated facility location polytopes, the odd cycle inequalities. It is known that their separation problem is polynomially solvable. We give a new polynomial separation algorithm based on a reduction from the original graph. Then, we define a non-trivial class of graphs, where the odd cycle inequal...

In this paper we present a hybrid approach to integrative clustering based on the p-median problem with clients’ preferences. We formulate the problem of simultaneous clustering of a set of objects, characterized by two sets of features, as a bi-level p-median model. An exact approach involving a branchand-cut method combined with the simulated annealing algorithm is used, that allows one to fi...

This paper presents an exact algorithm, a constructive heuristic algorithm, and a metaheuristic for the Hamiltonian p-Median Problem (HpMP). The exact algorithm is a branch-and-cut algorithm based on an enhanced p -median based formulation, which is proved to dominate an existing p -median based formulation. The constructive heuristic is a giant tour heuristic, based on a dynamic programming fo...

The p-median problem, like most location problems, is classified as NP -hard, and so, heuristic methods are usually used for solving it. The pmedian problem is a basic discrete location problem with real application that have been widely used to test heuristics. Metaheuristics are frameworks for building heuristics. In this survey, we examine the p-median, with the aim of providing an overview ...

Given n customers and a set F of m potential facilities, the p-median problem consists in finding a subset of F with p facilities such that the cost of serving all customers is minimized. This is a well-known NPcomplete problem with important applications in location science and classification (clustering). We present here a GRASP (Greedy Randomized Adaptive Search Procedure) with path-relinkin...