A branch-and-price approach to p-median location problems

This paper describes a branch-and-price algorithm for the p-median location problem. The objective is to locate p facilities (medians) such as the sum of the distances from each demand point to its nearest facility is minimized. The traditional column generation process is compared with a stabilized approach that combines the column generation and Lagrangean/surrogate relaxation. The Lagrangean/surrogate multiplier modifies; the reduced cost criterion, providing the selection of new productive columns at the search tree. Computational experiments are conducted considering especially difficult instances to the traditional column generation and also with some large-scale instances. (C) 2004 Elsevier Ltd. All rights reserved.

Calculating the Best Dual Bound for Problems with Multiple Lagrangian Relaxations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A decomposition heuristic for the maximal covering location problem

This paper proposes a cluster partitioning technique to calculate improved upper bounds to the optimal solution of maximal covering location problems. Given a covering distance, a graph is built considering as vertices the potential facility locations, and with an edge connecting each pair of facilities that attend a same client. Coupling constraints, corresponding to some edges of this graph, are identified and relaxed in the Lagrangean way, resulting in disconnected subgraphs representing smaller subproblems that are computationally easier to solve by exact methods. The proposed technique is compared to the classical approach, using real data and instances from the available literature. © 2010 Edson Luiz França Senne et al.

Abordagens complementares para problemas de p-medianas

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Integração de modelos de localização a sistemas de informações geográficas

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A column generation approach to capacitated p-median problems

The Capacitated p-median problem (CPMP) seeks to solve the optimal location of p facilities, considering distances and capacities for the service to be given by each median. In this paper we present a column generation approach to CPMP. The identified restricted master problem optimizes the covering of 1-median clusters satisfying the capacity constraints, and new columns are generated considering knapsack subproblems. The Lagrangean/surrogate relaxation has been used recently to accelerate subgradient like methods. In this work the Lagrangean/surrogate relaxation is directly identified from the master problem dual and provides new bounds and new productive columns through a modified knapsack subproblem. The overall column generation process is accelerated, even when multiple pricing is observed. Computational tests are presented using instances taken from real data from Sao Jose dos Campos' city.

Um algoritmo de busca tabu para problemas de localização não capacitados

In this work, a tabu search algorithm for solving uncapacitated location problems is presented. The uncapacitated location problem is a classic problem of localization and occurs in many practical situations. The problem consists in determining in a network, at the minimum possible cost, the better localization, in a network, for the installation of facilities in order to attend the customers' associated demands, at the minimum possible cost. One admits that there exists a cost associated with the opening of a facility and a cost of attendance of each customer by any open facilities. In the particular case of the uncapacitated location problem there is no capacity limitation to attend the customers’ demands. There are some parameters in the algorithm that influence the solution’s quality. These parameters were tested and optimal values for them were obtained. The results show that the proposed algorithm is able to find the optimal solution for all small tested problems keeping the compromise between solution’s quality and computational time. However, to solve bigger problems, the structure of the algorithm must be changed in its structure. The implemented algorithm is integrated to a computational platform for solution of logistic problems

A hybrid method for the probabilistic maximal covering location-allocation problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Two-level network design with intermediate facilities: An application to electrical distribution systems

We consider the two-level network design problem with intermediate facilities. This problem consists of designing a minimum cost network respecting some requirements, usually described in terms of the network topology or in terms of a desired flow of commodities between source and destination vertices. Each selected link must receive one of two types of edge facilities and the connection of different edge facilities requires a costly and capacitated vertex facility. We propose a hybrid decomposition approach which heuristically obtains tentative solutions for the vertex facilities number and location and use these solutions to limit the computational burden of a branch-and-cut algorithm. We test our method on instances of the power system secondary distribution network design problem. The results show that the method is efficient both in terms of solution quality and computational times. © 2010 Elsevier Ltd.

A priori reformulations for joint rolling-horizon scheduling of materials processing and lot-sizing problem

In many production processes, a key material is prepared and then transformed into different final products. The lot sizing decisions concern not only the production of final products, but also that of material preparation in order to take account of their sequence-dependent setup costs and times. The amount of research in recent years indicates the relevance of this problem in various industrial settings. In this paper, facility location reformulation and strengthening constraints are newly applied to a previous lot-sizing model in order to improve solution quality and computing time. Three alternative metaheuristics are used to fix the setup variables, resulting in much improved performance over previous research, especially regarding the use of the metaheuristics for larger instances. © 2013 Elsevier Ltd. All rights reserved.

Reformulações e relaxação Lagrangiana para o problema de dimensionamento de lotes com várias plantas

Pós-graduação em Matemática - IBILCE

Formulações fortes para o problema de dimensionamento de lotes com várias plantas

This paper considers the multi-plant lot sizing problem. Each item can be produced in any plant and it is possible to meet the demand of a particular plant with production from one (or several) other plants, in this case, incurs a transfer cost. The objective is todevelop strong formulations for this problem. Reformulations that based on the shortest path problem and facility location problem are investigated. Finally, some computational results are presented comparing all the proposed formulations.

Simulations under Ideal and Nonideal Conditions for Characterization of a Passive Doppler Geographical Location System Using Extension of Data Reception Network

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The Impact on Geographic Location Accuracy due to Different Satellite Orbit Ephemerides

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Problems related to the employment of thin uranium films as neutron dosimeters

Thin uranium films built on muscovite mica basis and obsidian samples having known ages were irradiated with thermal neutrons at the IPEN/CNEN reactor, São Paulo. Comparing thin film performance with the obsidian one, it was observed that the latter feel a greater neutron fluence. Nominal fluences at the used facility are in agreement with the results obtained analysing the obsidian samples. A probable hypothesis to explain this disagreement, namely, the uranium loss from the thin films, was ruled out. © 1995.