A commonly occurring problem in distribution system design is the optimal location of intermediate distribution facilities between plants and customers. A multicommodity capacitated single-period version of this problem is formulated as a mixed integer linear program. A solution technique based on Benders Decomposition is developed, implemented, and successfully applied to a real problem for a major food firm with 17 commodity classes, 14 plants, 45 possible distribution center sites, and 121 customer zones. An essentially optimal solution was found and proven with a surprisingly small number of Benders cuts. Some discussion is given concerning why this problem class appears to be so amenable to solution by Benders’ method, and also concerning what we feel to be the proper professional use of the present computational technique.

Multicommodity Distribution System Design by Benders Decomposition

https://www.cirrelt.ca/DocumentsTravail/CIRRELT-2008-36.pdf

The Design of Robust Value-Creating Supply Chain Networks: A Critical Review †

Dynamic multi-commodity capacitated facility location: a mathematical modeling framework for strategic supply chain planning

Facility location models for distribution planning

A multi-commodity, multi-plant, capacitated facility location problem: formulation and efficient heuristic solution

It is demonstrated that mixed-integer programming can be applied successfully to the solution of certain practical site location problems. A mixed-integer model of a frequently occurring form of warehouse location problem is presented. Experience with models of this type is described with examples of computational performance. The flexibility of mixed-integer models and the approach to their use as aids to decision-making are discussed.

D. G. Elson

Papers

Site Location via Mixed-integer Programming