Nonemergency single facility location on a network with elastic demands

Abstract

The problem of locating a nonemergency public service facility on a general network with discrete node demands(customers) as well as link demands is considered. The facility has customers who live only in the area within a prespecified distance. The problem does consider two different demand patterns classified due to customers`` inclination such as a constant demand pattern (Model 1) and a decreasing convex demand pattern (Model 2). The objective of each problem is to find a location point that maximizes the sum of potential (arriving) customers within the prespecified distance from the location point. The customers are assumed to be distributed in discrete numbers over all nodes but uniformly distributed over links of the network. For Model 1, the objective function is characterized that an optimal point exists in a finite set of points on the network, and that such a finite set can easily be generated. Model 2 is considered as an extension but difficult to find an optimal location point. Several alternative solution approaches to find an optimal location are suggested.