A Median Location Model with Nonclosest Facility Service

This paper deals with the location of service facilities on a transportation network where the closest (in distance, time or cost) facility is known not to service some significant portion of demand. The concept of vector assignment of demand nodes to facilities is introduced to account for nonclosest facility service. A generalized formulation of the p-median problem incorporating vector assignment is presented. It is shown that an optimal solution to this vector assignment p-median problem exists which consists entirely of nodes of the graph; however, there may be more than one facility per node. Three different solution procedures are discussed for the vector assignment p-median problem. Computational experiments for three different moderately sized data sets give encouraging results. A locational example is included which gives a comparison of an optimal p-median solution and an optimal p-median solution with vector assignment.