The multicommodity assignment problem: a network aggregation heuristic

AbstractWe present a network-based heuristic procedure for solving a class of large non-unimodular assignment-type problems. The procedure is developed from certain results concerning multi-commodity network flows and concepts of node-aggregation in networks. Computational experience indicates that problems with over fifteen thousand integer variables can be solved in well under ten seconds using state-of-the-art network optimization software

Equipment control in container shipping

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1994.Includes bibliographical references (p. 133-134).by Okinobu Hatsgai.M.S

Linear Mathematical Model to Optimize Buying, Shipping and Storing Oil Field Tubulars

This study develops a mathematical model to assist oil companies in buying, shipping, and storing tubulars at the minimum cost. The equations developed were to utilize existing information which the materials sections of these companies were presently collecting. The model to be developed must be solvable using existing computer codes. The model developed in this report can be solved using a branch and bound technique for linear models. The size of the model is potentially very large. Through reasonable constraints, the size of the model can be reduced to a size easily solved on any large computer system. In addition, the model can be adapted to commodities other than tubulars.Business Administratio

Analysis of large scale linear programming problems with embedded network structures: Detection and solution algorithms

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Linear programming (LP) models that contain a (substantial) network structure frequently arise in many real life applications. In this thesis, we investigate two main questions; i) how an embedded network structure can be detected, ii) how the network structure can be exploited to create improved sparse simplex solution algorithms. In order to extract an embedded pure network structure from a general LP problem we develop two new heuristics. The first heuristic is an alternative multi-stage generalised upper bounds (GUB) based approach which finds as many GUB subsets as possible. In order to identify a GUB subset two different approaches are introduced; the first is based on the notion of Markowitz merit count and the second exploits an independent set in the corresponding graph. The second heuristic is based on the generalised signed graph of the coefficient matrix. This heuristic determines whether the given LP problem is an entirely pure network; this is in contrast to all previously known heuristics. Using generalised signed graphs, we prove that the problem of detecting the maximum size embedded network structure within an LP problem is NP-hard. The two detection algorithms perform very well computationally and make positive contributions to the known body of results for the embedded network detection. For computational solution a decomposition based approach is presented which solves a network problem with side constraints. In this approach, the original coefficient matrix is partitioned into the network and the non-network parts. For the partitioned problem, we investigate two alternative decomposition techniques namely, Lagrangean relaxation and Benders decomposition. Active variables identified by these procedures are then used to create an advanced basis for the original problem. The computational results of applying these techniques to a selection of Netlib models are encouraging. The development and computational investigation of this solution algorithm constitute further contribution made by the research reported in this thesis.This study is funded by the Turkish Educational Council and Mugla University

Um modelo de fluxo em rede para solução de problemas de distribuição de produtos compostos

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Engenharia de Produção.Neste trabalho é proposto um modelo linear de Fluxo em Redes para o problema de minimização de custos de produção e distribuição de Múltiplos Produtos Compostos. Neste modelo, restrições de acoplamento são consideradas para tratar a proporcionalidade existente entre os diversos fluxos que formam o produto composto, bem como as restrições de capacidade dos arcos pelos quais estes fluxos percorrem. A metodologia utilizada para solucionar o problema é baseada na estratégia de particionamento da matriz básica, e na implementação de uma especialização do método simplex dual para solucionar o problema particionado primal. Como solução inicial, é utilizada uma base construída por meio de um método heurístico que aloca fluxos em caminhos de custo mínimo. Para realização das operações de troca de base, a matriz ciclo é armazenada na forma produto da inversa, de modo a manter a esparsidade e a dimensão. Testes computacionais, contendo em torno de 200.000 restrições e 370.000 variáveis, aplicados à distribuição de produtos compostos de uma indústria do setor petroquímico, foram realizados com sucesso. Os resultados obtidos demonstram a eficiência computacional do algoritmo desenvolvido e a aplicabilidade do modelo formulado. Finalmente, recomendações são apresentadas para desenvolvimento de trabalhos futuros