Groupe d’études et de recherche en analyse des décisions

# Solution of the Multisource Weber and Conditional Weber Problems by D.-C. Programming

## Pey-Chun Chen, Pierre Hansen, Brigitte Jaumard et H Tuy

D.-c. programming is a recent technique of global optimization, which allows the solution of problems whose objective function and constraints can be expressed as differences of convex (i.e., d.-c.) functions. Many such problems arise in continuous location theory. The problem first considered is to locate a known number of source facilities so as to minimize the sum of weighted Euclidean distances between fixed location of users and the source facility closest to location of each user. We also apply d.-c. programming to the solution of the conditional Weber problem, an extension of the multisource Weber Problem, in which some facilities are assumed to be already established. In addition, we consider a generalization of the Weber's problem, the facility location problem with limited distances, where the effective service distance becomes a constant when the actual distance attains a given value. Computational results for problems with up to ten thousand users and two new facilities; fifty users and three new facilities; one thousand users, twenty existing facilities and one new facility or two hundred users, ten existing and two new facilities are reported.

, 35 pages

Ce cahier a été révisé en janvier 1996