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

Pey-Chun Chen, Pierre Hansen, Brigitte Jaumard and Hoang Tuy
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Pey-Chun Chen: AT&T Laboratories, Holmdel, New Jersey
Pierre Hansen: GERAD and École des Hautes Études Commerciales, Montréal, Canada
Brigitte Jaumard: GERAD and École Polytechnique de Montreál, Montreál, Canada
Hoang Tuy: Institute of Mathematics, Hanoi, Vietnam

Operations Research, 1998, vol. 46, issue 4, 548-562

Abstract: D.-c. programming is a recent technique of global optimization that 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 to minimize the sum of weighted Euclidean distances between a user's fixed location and the source facility closest to the 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 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 are reported for problems with up to 10,000 users and two new facilities, 50 users and three new facilities, 1,000 users, 20 existing facilities and one new facility or 200 users, 10 existing and two new facilities.

Keywords: Facilities/equipment planning; continuous location theory; Nonlinear programming; d.-c. programming; concave minimization; algorithm; application; Linear programming; vertex enumeration (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (18)

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