Fractional location problems

In this paper we analyze some variants of the classical uncapacitated facility location problem with a ratio as an objective function. Using basic concepts and results of fractional programming, we identify a class of one-level fractional location problems which can be solved in polynomial time in terms of the size of the problem. We also consider the fractional two-echelon location problem, which is a special case of the general two-level fractional location problem. For this two-level fractional location problem we identify cases for which its solution involves decomposing the problem into several one-level fractional location problems.discrete location;fractional program

Solving Multi-Objective Hub Location Problems with Robustness

Hub location problems (HLP) are considered in many logistic, telecommunications, and computer problems, where the design of these networks are optimized based on some objective(s) related to the cost or service. In those cases, direct routing between any origin and destination is not viable due to economic or technological constraints. From the seminal work of O'Kelly~\cite{OKelly86}, a huge number of works have been published in the literature. Early contributions were focused on analogue facility location problems, considering some assumptions to simplify the network design. Recent works have studied more complex models by incorporating additional real-life features and relaxing some assumptions, although the input parameters are still assumed to be known in most of the HLPs considered in the literature. This assumption is unrealistic in practice, since there is a high uncertainty on relevant parameters of real problems, such as costs, demands, or even distances. Consequently, a decision maker usually prefer several solutions with a low uncertainty in their objectives functions instead of the optimum solution of an assumed deterministic objective function. In this work we use a three-objective Integer Linear Programming model of the p-hub location problem where the average transportation cost, its variance, and the processing time in the hubs are minimized. The number of variables is $O(n^4)$ where $n$ is the number of nodes of the graph. ILP solvers can only solve small instances of the problems and we propose in this work the use of a recent hybrid algorithm combining a heuristic and exact methods: Construct, Merge, Solve, and AdaptUniversidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Anytime Algorithms for Multi-Objective Hub Location Problems

In many logistic, telecommunications and computer networks, direct routing of commodities between any origin and destination is not viable due to economic and technological constraints. Hub locations problems (HLPs) are considered in that cases, where the design of these networks are optimized based on some objective(s) related on the cost or service. A huge number of papers have been published since the seminal work of O’Kelly. Early works were focused on analogue facility location problems, considering some assumptions to simplify network design. Recent works have studied more complex models that relax some of these assumptions and incorporate additional real-life features. In most HLPs considered in the literature, the input parameters are assumed to be known and deterministic. However, in practice, this assumption is unrealistic since there is a high uncertainty on relevant parameters, such as costs, demands or even distances. As a result, a decision maker usually prefer several solutions with a low uncertainty in their objectives functions. In this work, anytime algorithms are proposed to solve the multi-objective hub location problems with uncertainty. The proposed algorithms can be stopped at any time, yielding a set of efficient solutions (belonging to the Pareto front) that are well spread in the objective space.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Fractional location problems

In this paper we analyze some variants of the classical uncapacitated facility location problem with a ratio as an objective function. Using basic concepts and results of fractional programming, we identify a class of one-level fractional location problems which can be solved in polynomial time in terms of the size of the problem. We also consider the fractional two-echelon location problem, which is a special case of the general two-level fractional location problem. For this two-level fractional location problem we identify cases for which its solution involves decomposing the problem into several one-level fractional location problems

Reference priors in non-normal location problems

Bayesian Statistics;Statistical Distribution

Solving multi-objective hub location problems by hybrid algorithms

In many logistic, telecommunications and computer networks, direct routing of commodities between any origin and destination is not viable due to economic and technolog- ical constraints. In that cases, a network with centralized units, known as hub facilities, and a small number of links is commonly used to connect any origin-destination pair. The purpose of these hub facilities is to consolidate, sort and transship e ciently any commodity in the network. Hub location problems (HLPs) consider the design of these networks by locating a set of hub facilities, establishing an interhub subnet, and routing the commodities through the network while optimizing some objective(s) based on the cost or service. Hub location has evolved into a rich research area, where a huge number of papers have been published since the seminal work of O'Kelly [1]. Early works were focused on analogue facility location problems, considering some assumptions to simplify network design. Recent works [2] have studied more complex models that relax some of these assumptions and in- corporate additional real-life features. In most HLPs considered in the literature, the input parameters are assumed to be known and deterministic. However, in practice, this assumption is unrealistic since there is a high uncertainty on relevant parameters, such as costs, demands or even distances. In this work, we will study the multi-objective hub location problems with uncertainty.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec