Location Modeling Utilizing Maximum Service Distance Criteria

Richard L. Church · Michael E. Meadows

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Facility Location and Emergency Management Complexity and Algorithms in Graphs Vehicle Routing Optimization Methods

Abstract

The location set‐covering problem (LSCP) and the maximal covering location problem (MCLP) have been the subject of considerable interest. As originally defined, both problems allowed facility placement only at nodes. This paper deals with both problems for the case when facility placement is allowed anywhere on the network. Two theorems are presented that show that when facility placement is unrestricted, for either the LSCP or MCLP at least one optimal solution exists that is composed entirely of points belonging to a finite set of points called the network intersect point set (NIPS). Optimal solution approaches to the unrestricted site LSCP and MCLP problems that utilize the NIPS and previously developed solution methodologies are presented. Example solutions show that considerable improvement in the amount of coverage or the number of facilities needed to insure total coverage can be achieved by allowing facility placement along arcs of the network. In addition, extensions to the arc‐covering model and the ambulance‐hospital model of ReVelle, Toregas, and Falkson are developed and solved .

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References

1974THE MAXIMAL COVERING LOCATION PROBLEM 1971The Location of Emergency Service Facilities 1970An Analysis of Private and Public Sector Location Models 1972OPTIMAL LOCATION UNDER TIME OR DISTANCE CONSTRAINTS 1976Applications of the Location Set‐covering Problem

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