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The gradual covering problem
Author(s) -
Drezner Zvi,
Wesolowsky George O.,
Drezner Tammy
Publication year - 2004
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.20030
Subject(s) - constant (computer programming) , extreme point , point (geometry) , mathematical optimization , minimum distance , function (biology) , signed distance function , zero (linguistics) , mathematics , computer science , linear programming , algorithm , combinatorics , geometry , linguistics , philosophy , evolutionary biology , biology , programming language
In this paper we investigate the gradual covering problem. Within a certain distance from the facility the demand point is fully covered, and beyond another specified distance the demand point is not covered. Between these two given distances the coverage is linear in the distance from the facility. This formulation can be converted to the Weber problem by imposing a special structure on its cost function. The cost is zero (negligible) up to a certain minimum distance, and it is a constant beyond a certain maximum distance. Between these two extreme distances the cost is linear in the distance. The problem is analyzed and a branch and bound procedure is proposed for its solution. Computational results are presented. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004