The gradual covering problem

TLDR

The gradual covering problem models coverage that is full within a minimum distance, absent beyond a maximum distance, and varies linearly in between, with a cost that is zero up to a minimum distance, constant beyond a maximum, and linear in the intermediate range. The study investigates the gradual covering problem. The authors reformulate the problem as a Weber problem with a specially structured cost function and propose a branch‑and‑bound algorithm to solve it. Computational results are presented. © 2004 Wiley Periodicals, Inc., Naval Research Logistics, 2004.

Abstract

Abstract 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