The Multi‐level Location Set Covering Model

Abstract

The classical Location Set Covering Problem involves finding the smallest number of facilities and their locations so that each demand is covered by at least one facility. It was first introduced by Toregas in 1970. This problem can represent several different application settings including the location of emergency services and the selection of conservation sites. The Location Set Covering Problem can be formulated as a 0–1 integer‐programming model. Roth (1969) and Toregas and ReVelle (1973) developed reduction approaches that can systematically eliminate redundant columns and rows as well as identify essential sites. Such approaches can often reduce a problem to a size that is considerably smaller and easily solved by linear programming using branch and bound. Extensions to the Location Set Covering Model have been proposed so that additional levels of coverage are either encouraged or required. This paper focuses on one of the extended model forms called the Multi‐level Location Set Covering Model. The reduction rules of Roth and of Toregas and ReVelle violate properties found in the multi‐level model. This paper proposes a new set of reduction rules that can be used for the multi‐level model as well as the classic single‐level model. A demonstration of these new reduction rules is presented which indicates that such problems may be subject to significant reductions in both the numbers of demands as well as sites.