Formulations and relaxations for a multi-echelon capacitated location-distribution problem

Authors:
Bernard Gendron;Frédéric Semet
Affiliations:
Département d'informatique et de recherche opérationnelle and Centre de recherche sur les transports Université de Montréal C.P. 6128, succ. Centre-ville Montreal, Que., Canada ...;LAMIH, Université de Valenciennes et du Hainaut-Cambrésis Le Mont Houy, 59313 Valenciennes Cedex 9, France
Venue:
Computers and Operations Research
Year:
2009

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Abstract

We consider a multi-echelon location-distribution problem arising from an actual application in fast delivery service. We present and compare two formulations for this problem: an arc-based model and a path-based model. We show that the linear programming (LP) relaxation of the path-based model provides a better bound than the LP relaxation of the arc-based model. We also compare the so-called binary relaxations of the models, which are obtained by relaxing the integrality constraints for the general integer variables, but not for the 0-1 variables. We show that the binary relaxations of the two models always provide the same bound, but that the path-based binary relaxation appears preferable from a computational point of view, since it can be reformulated as an equivalent simple plant location problem (SPLP), for which several efficient algorithms exist. We also show that the LP relaxation of this SPLP reformulation provides a better bound than the LP relaxation of the path-based model.