Dynamic Location Problems with Discrete Expansion and Reduction Sizes of Available Capacities

 

Joana Dias^†

M. Eugénia Captivo^‡

João Clímaco^†

 

 ^†Faculdade de Economia and INESC-Coimbra

Universidade de Coimbra, Av. Dias da Silva, 165, 3004 -512 Coimbra

joana@fe.uc.pt

jclimaco@inescc.pt

^‡Universidade de Lisboa, Faculdade de Ciências Centro de Investigação Operacional, Campo Grande, Bloco C6, Piso 4, 1749-016 Lisboa mecaptivo@fc.ul.pt

 

Abstract

In this paper a dynamic location problem is formulated that considers the possibility of expanding or reducing the maximum available capacity at any given location during the planning horizon. The expansion (or reduction) of available capacity at a given location is achieved through the opening (or closure) of one or more facilities with different discrete capacities. The mixed-integer linear model developed considers fixed costs for opening the first facility at any location, plus additional fixed costs for every open facility in a location with already existing facilities. It is possible to open, close and reopen any facility at any location more than once during the planning horizon. It is also possible to consider different assignment costs depending on the size of the facility that is assigned to each client. This is important, because, in general, smaller facilities have smaller fixed costs but greater unitary operating costs. A primal‑dual heuristic is developed that is able to find primal feasible solutions to the problem here described, and computational results are presented.

Keywords: dynamic location problems, primal-dual heuristics, capacity planning

 

Resumo

Neste artigo considera-se um problema de localização dinâmica, em que é possível aumentar ou reduzir a capacidade máxima disponível numa dada localização, num determinado período de tempo, através da abertura ou fecho de um ou mais equipamentos, de iguais ou diferentes capacidades. O modelo de programação linear inteira mista desenvolvido considera os custos fixos de abrir o primeiro equipamento numa dada localização, e custos fixos associados à localização de outros equipamentos, para além do primeiro. É possível abrir, fechar e reabrir qualquer equipamento em qualquer localização, mais do que uma vez durante o horizonte temporal considerado. É também possível considerar custos de afectação que podem variar consoante a dimensão do equipamento. Foi desenvolvida uma heurística primal-dual capaz de resolver este problema, que aqui se descreve, e apresentam-se alguns resultados computacionais.

 

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