## Contributed Session Mon.1.H 0106

#### Monday, 10:30 - 12:00 h, Room: H 0106

**Cluster 13: Logistics, traffic, and transportation** [...]

### Facility location and p-median problems

**Chair: Sergio Garcia Quiles**

**Monday, 10:30 - 10:55 h, Room: H 0106, Talk 1**

**Sergio Garcia Quiles**

On the *p*-median problem with uncertainty in the cost matrix

**Coauthor: Laureano F. Escudero**

**Abstract:**

It has been shown that the deterministic p-median problem can be solved with just a column generation approach that is embedded in a branch-and-bound framework. Large-scale instances have been solved efficiently in a small computing time. However, quite often, the cost matrix coefficients are random variables. The aim of this paper is twofold. First, a model is presented to minimize the expected cost over a set of scenarios of the outlook of the random variables while satisfying the first order stochastic dominance constraints (sdc) for a set of profiles in order to reduce the risk of the cost impact of the solution in non-wanted scenarios. And second, a scheme to obtain the solution of the stochastic p-median problem is developed by considering the splitting variable representation of the static Deterministic Equivalent Model (DEM) of the stochastic one. This scheme dualizes the non-anticipativity constraints and treats with a special procedure the sdc for each profile (since those constraints have variables from different scenarios). A computational experience is reported.

**Monday, 11:00 - 11:25 h, Room: H 0106, Talk 2**

**Vinicius Layter Xavier**

Solving the Fermat-Weber location problem by the hyperbolic smoothing approach

**Coauthors: Felipe Franca, Priscila Lima, Adilson Elias Xavier**

**Abstract:**

The Fermat-Weber problem considers the optimum location of a given number of facilities. The problem corresponds to the minimization of the sum of the euclidean distances of each city to the its nearest facility weighted by relative importance of each one. The mathematical modeling of this problem leads to a min-sum-min formulation which in addition to its intrinsic bi-level nature, has the significant characteristic of being strongly non-differentiable and non-convex problem, with a large number of local minima. The hyperbolic smoothing strategy solves a sequence of low dimension differentiable unconstrained optimization sub-problems, which gradually approaches the original problem. The reliability and efficiency of the method are illustrated via a set of computational experiments by using traditional instances presented in the literature.

**Monday, 11:30 - 11:55 h, Room: H 0106, Talk 3**

**Haldun Sural**

The dynamic p-median problem with relocation

**Coauthor: Huseyin Guden**

**Abstract:**

The dynamic location problem considers changes of demand amounts over the horizon and minimizes the location and service costs. In any period new facilities can be opened in addition to the operating facilities and some of the operating ones can be relocated or abolished. We develop exact and heuristic methods for solving the dynamic p-median problem. The former is a branch-and-price algorithm using the reduced size form of an integer programming formulation based on discretization of the number of different distances between facilities and demand points. The latter effort explores the dynamic structure of the problem to find upper bounds on the problem objective function. Our computational results are presented to assess the performance our methods on test instances derived from the p-median literature.