Technical Note—A Generalized Bounding Method for Multifacility Location Models

Love, Robert F.; Dowling, Paul D.

doi:10.1287/opre.37.4.653

Cited by 11 publications

(2 citation statements)

References 11 publications

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“…derived the geometrical characterizations for the set of efficient, weakly efficient and properly efficient solutions of the Euclidean MFLP when it includes certain convex locational constraints. Love and Yoeng (1981), Hearn (1983), Juel (1984), and Love and Dowling (1989) explored the bounding method that continuously updates a lower bound on the optimal objective function value during each iteration. This method is based on the idea that the convex hull and the current value of the gradient determine an upper bound on the objective function's improvement.…”

Section: Euclidean Distance Minisum Location Problemmentioning

confidence: 99%

Demand Point Aggregation Analaysis for Location Models

Sadigh

Fallah

2009

Facility Location

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Section: Euclidean Distance Minisum Location Problemmentioning

confidence: 99%

Demand Point Aggregation Analaysis for Location Models

Sadigh

Fallah

2009

Facility Location

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“…Finally, since every heuristic method gives a local optimum, a good bounding method is useful in devising termination rules for multistart algorithms. Contributors to bounding methods include Dowling and Love (1986) and Love and Dowling (1989) and the references therein.…”

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confidence: 99%

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

Chen

Hansen

Jaumard

et al. 1998

Operations Research

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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.T he problem of optimally locating new facilities with respect to the locations of existing ones and/or users has many applications in distribution, transportation, and manufacturing. The most studied case is Weber's problem, in which the weighted sum of Euclidean distances between the facility and the users must be minimized. We propose new solution methods for three important generalizations of this problem: (1) the multisource Weber problem, in which several source facilities are to be located simultaneously, with each user at the nearest one; (2) the conditional Weber problem, similar to the previous one, but for the already established source facilities; and (3) the facility location problem with limited distances, in which the distance from a user to the facility is considered to be constant after a given threshold, i.e., the effective service distance. The proposed algorithms use d.-c. programming, concave minimization, and vertex enumeration for polytopes. Detailed computational experience is reported. The new algorithms allow the solution of the multisource Weber problem with up to 10,000 users and two facilities, or 50 users and three facilities. Instances with two facilities are much larger than those previously solved exactly. The conditional Weber problem, with up to 1,000 users, 20 existing facilities and a new one or 200 users, 10 existing facilities and two new ones, and the facility location problem with limited distances, with up to 1,000 users, are solved in moderate computing time. Only results with heuristics were reported previously for these two last problems. They are thus efficiently solved for the first time. Moreover, the potential of d.-c. programming as a new and versatile tool for solving nonconvex location problems is clearly illustrated.Weber's (1909) problem, which consists of locating a single facility in order to minimize the sum of Euclidean distances between t...

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Multifacility Location Problem

Daneshzand

Shoeleh

2009

Facility Location

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Technical Note—A Generalized Bounding Method for Multifacility Location Models

Cited by 11 publications

References 11 publications

Demand Point Aggregation Analaysis for Location Models

Demand Point Aggregation Analaysis for Location Models

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

Multifacility Location Problem

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