Mercedes Landete

New formulations for the uncapacitated multiple allocation hub location problem

In this paper we review the integer linear formulations of the uncapacitated multiple allocation hub location problem, we study the scope of validity of these formulations and give new ones that generalize the older formulations. Our formulations allow one or two visits to hubs and include a more general cost structure that needs not satisfy the triangle inequality. We prove that the constraints defined by cliques of a related (intersection) graph are tighter constraints than the classical ones. We also discuss a pre-processing of the problem, which is very useful for reducing its size. Finally, we check the strength of the new formulations and compare them with others in the literature by solving instances of two commonly used data sets: the CAB (Civil Aeronautics Board) and AP (Australian Post), and also randomly generated instances. Our computational results clearly show that our formulations outperform all others previously used for small and medium problems.

On the facets of the simple plant location packing polytope

We introduce new classes of facet-defining inequalities for the polytope Ppd associated with the set packing formulation of the simple plant location problem (SPLP) with p plants and d destinations. The inequalities are obtained by identifying subgraphs of the intersection graph G(p,d) of SPLP that are facet-defining, and lifting their associated facets if it is necessary. To this end, we find subfamilies of previously known structured families of facet-defining graphs, like fans and wheels, inside G(p,d). We also characterize a class of facets of SPLP and summarize the previous polyhedral results on this problem.

New formulation and a branch-and-cut algorithm for the multiple allocation p-hub median problem

This article deals with the uncapacitated multiple allocation p-hub median problem, where p facilities (hubs) must be located among n available sites in order to minimize the transportation cost of sending a product between all pairs of sites. Each path between an origin and a destination can traverse any pair of hubs.

A branch-and-cut algorithm for the Winner Determination Problem

The Winner Determination Problem is the problem of maximizing the benefit when bids can be made on a group of items. In this paper, we consider the set packing formulation of the problem, study its polyhedral structure and then propose a new and tighter formulation. We also present new valid inequalities which are generated by exploiting combinatorial auctions peculiarities. Finally, we implement a branch-and-cut algorithm which shows its efficiency in a big number of instances.

Design and analysis of hybrid metaheuristics for the Reliability p-Median Problem

In the p-Median Problem, it is assumed that, once the facilities are opened, they may not fail. In practice some of the facilities may become unavailable due to several factors. In the Reliability p-Median Problem some of the facilities may not be operative during certain periods. The objective now is to find facility locations that are both inexpensive and also reliable. We present different configurations of two hybrid metaheuristics to solve the problem, a genetic algorithm and a scatter search approach. We have carried out an extensive computational experiment to study the performance of the algorithms and compare its efficiency solving well-known benchmark instances.

New facets for the set packing polytope

We introduce a family of graphs, named grilles, and a facet of the set packing polytope associated with a grille. The proof is based on a new facet generating procedure which is valid in a wider context. We also obtain new facets for the simple plant location polytope.

Facet Obtaining Procedures for Set Packing Problems

New results concerning the facial structure of set packing polyhedra are presented. In particular, new methods are given to obtain facets from the subgraphs of the intersection graph associated with a set packing polyhedron that properly subsume several other methods in the literature. A new class of facet defining graphs, termed fans, is also introduced, as well as a procedure to link any graph to a certain claw K1,k in order to obtain a new graph and an associated facet.

The multiple vehicle pickup and delivery problem with LIFO constraints

This paper approaches a pickup and delivery problem with multiple vehicles in which LIFO conditions are imposed when performing loading and unloading operations and the route durations cannot exceed a given limit. We propose two mixed integer formulations of this problem and a heuristic procedure that uses tabu search in a multi-start framework. The first formulation is a compact one, that is, the number of variables and constraints is polynomial in the number of requests, while the second one contains an exponential number of constraints and is used as the basis of a branch-and-cut algorithm. The performances of the proposed solution methods are evaluated through an extensive computational study using instances of different types that were created by adapting existing benchmark instances. The proposed exact methods are able to optimally solve instances with up to 60 nodes.

Strengthening the reliability fixed-charge location model using clique constraints

The Reliability Fixed-Charge Location Problem is an extension of the Simple Plant Location Problem that considers that some facilities have a probability of failure. In this paper we reformulate the original mathematical programming model of the Reliability Fixed-Charge Location Problem as a set packing problem. We study certain aspects of its polyhedral properties, identifying all the clique facets. We also discuss how to obtain facets of the Reliability Fixed-Charge Location Problem from facets of the Simple Plant Location Problem. Subsequently, we study some conditions for optimal solutions. Finally, we propose an improved compact formulation for the problem and we check its performance by means of an extensive computational study.

Looking for edge-equitable spanning trees

This paper studies the Ordered Spanning Tree Problem, where the weights of the edges of the tree are sorted and then linearly combined using a previously given coefficients vector. Depending on the coefficients, several objectives can be incorporated to the problem. We pay special attention to the search of spanning trees with balanced weights, i.e., where the differences among the weights are, in some sense, minimized. To solve the problem, we propose two Integer Programming formulations, one based on flow and the other one on the Miller-Tucker-Zemlin constraints. We analyze several potential improvements for both the formulations whose behaviors are checked by means of a computational experiment. Finally, we show how both the formulations can be adapted to incorporate to the objective non-linear functions of the weights.