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.

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.

Abordagens complementares para problemas de p-medianas

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

Métodos de geração de colunas para problemas de atribuição

Este trabalho apresenta métodos de geração de colunas para dois importantes problemas de atribuição: o Problema Generalizado de Atribuição (PGA) e o Problema de Atribuição de Antenas a Comutadores (PAAC). O PGA é um dos mais representativos problemas de Otimização Combinatória e consiste em otimizar a atribuição de n tarefas a m agentes, de forma que cada tarefa seja atribuída a exatamente um agente e a capacidade de cada agente seja respeitada. O PAAC consiste em atribuir n antenas a m comutadores em uma rede de telefonia celular, de forma a minimizar os custos de cabeamento entre antenas e comutadores e os custos de transferência de chamadas entre comutadores. A abordagem tradicional de geração de colunas é comparada com as propostas neste trabalho, que utilizam a relaxação lagrangeana/surrogate. São apresentados testes computacionais que demonstram a efetividade dos algoritmos propostos.

A linear optimization approach to the combined production planning model

Two fundamental processes usually arise in the production planning of many industries. The first one consists of deciding how many final products of each type have to be produced in each period of a planning horizon, the well-known lot sizing problem. The other process consists of cutting raw materials in stock in order to produce smaller parts used in the assembly of final products, the well-studied cutting stock problem. In this paper the decision variables of these two problems are dependent of each other in order to obtain a global optimum solution. Setups that are typically present in lot sizing problems are relaxed together with integer frequencies of cutting patterns in the cutting problem. Therefore, a large scale linear optimizations problem arises, which is exactly solved by a column generated technique. It is worth noting that this new combined problem still takes the trade-off between storage costs (for final products and the parts) and trim losses (in the cutting process). We present some sets of computational tests, analyzed over three different scenarios. These results show that, by combining the problems and using an exact method, it is possible to obtain significant gains when compared to the usual industrial practice, which solve them in sequence. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

The integrated lot sizing and cutting stock problem in a furniture factory

This work studies the integrated lot sizing and cutting stock problem, where the goal is to capture the dependency that exists between two important decisions in the production process, in order to economize raw materials and also reduce production and inventory costs. The integrated lot sizing and cutting stock problem is studied in a small furniture factory that produces wardrobes, dressing tables and cupboards and the lot sizing and cutting stock decisions are taken by the production manager. A column-generation technique is used to solve a linear relaxation of the proposed model. The computational results, using real data from the factory, show that it is possible to reduce total inventory and raw material costs when integrated planning is used. © 2013 IFAC.

Aplicação de técnicas de decomposição em problemas de corte de estoque

Pós-graduação em Matemática - IBILCE

Propostas de solução para o problema de corte de estoque bidimensional de uma fábrica de móveis de pequeno porte

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Problemas de corte e empacotamento na indústria de móveis: um estudo de caso

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Problema integrado de dimensionamento de lotes e corte de estoque na indústria moveleira

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

O problema de corte de estoque com uso e venda de retalhos: uma proposta de otimização para a sustentabilidade ambiental

Pós-graduação em Engenharia de Produção - FEB

The role of the vagus nerve in the generation of cardiorespiratory interactions in a neotropical fish, the pacu, Piaractus mesopotamicus

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On-line redox speciation analysis of antimony using L-proline immobilized on controlled pore glass and hydride generation inductively coupled plasma optical emission spectrometry for detection

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

Aperfeiçoamento do método clause-column table para a geração eficiente de implicantes primos

Pós-graduação em Engenharia Elétrica - FEIS