An optimal algorithm for the multiproduct capacitated facility location problem with a choice of facility type

doi:10.1016/0305-0548(91)90087-8

Computers & Operations Research

Volume 18, Issue 2, 1991, Pages 167-182

https://doi.org/10.1016/0305-0548(91)90087-8 Get rights and content

Abstract

Consider a generalization of the multiproduct capacitated facility location problem in which each facility capacity has to be chosen from a given set of admissible levels. The objective is to select a set of facilities to open, along with their capacities, and to assign customer demands to them so as to minimize the total cost. In this model, in addition to a fixed cost for opening a facility, a fixed cost is incurred for each product that a facility is equipped to produce. Also, transportation costs are incurred for satisfying each customer's requirement for a particular product at each chosen facility. Benders' decomposition provides a natural partitioning of this model which defines a master problem for selecting a set of open facilities and equipment (or machines) and a subproblem in which the optimal assignment of demand to a specific facility is determined. A solution algorithm based on Benders' decomposition is developed, implemented and applied to a numerical example to discuss the behavior of the cutting planes generated in Benders' decomposition. Computational results of this algorithm are quite satisfactory and encouraging.

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This model considers a fixed cost for opening facilities such as a plant or a distribution centre as well as unit transportation cost between the facilities in a supply chain. Lee (1991) reports the distribution problem of several products required by customers with a choice of facility type. The model considers facility-to-customer transportation costs and fixed cost for opening a facility.
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However, several papers address the variant in which a customer may be served by several facilities. Lee solved this problem via Bender׳s decomposition [5] and via a combination of Bender׳s decomposition and Lagrangean relaxation [6]. Mazzola and Neebe [7] developed Lagrangean heuristics for the variant in which facilities of different types may be opened at a location.
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^∗: Dr Choong Y. Lee is an Assistant Professor of Business Administration at Pittsburg State University, Kans. He received his B.Sc. in Engineering from Seoul National University, Korea, and his M.Sc. in Industrial and Management Engineering, M.Sc. in Mathematics and Ph.D. in Management Science from the University of Iowa. Dr Lee has taught at the University of Iowa and the University of Wisconsin at River Falls.

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An optimal algorithm for the multiproduct capacitated facility location problem with a choice of facility type

Abstract

Ann. Discr. Math.

Eur. J. opl Res.

Eur. J. opl Res.

Eur. J. opl Res.

Eur. J. opl Res.

Eur. J. opl Res.

A dual-based procedure for uncapacitated facility location

Ops Res.

A branch-bound algorithm for plant location

Ops Res.

An efficient branch-and-bound algorithm for the warehouse location problem

Mgmt Sci.

The capacitated warehouse location problem: a review

A survey of the capacitated plant location problem

An efficient branch-and-bound algorithm for the capacitated warehouse location problem

Mgmt Sci.

Lagrangian relaxation applied to capacitated facility location problems

AIIE Trans.

An improved algorithm for the capacitated facility location problem

Ops Res.

A branch-and-bound algorithm for the capacitated facilities location problem

Nav. Res. Logist. Q.

Linear relaxations of the capacitated warehouse location problem

J opl Res. Soc.

Multicommodity distribution system design by Benders decomposition

Mgmt Sci.