Locating Mobile Servers on a Network with Markovian Processes

Abstract

The median problem has been generalized to the case in which facilities can be moved, at a cost, on the network in response to changes in the state of the network. Such changes are brought about by changes in travel times on the links of the network due to the occurrence of probabilistic events. For the case examined here, transitions among states of the network are assumed to be Markovian. The problem is examined for an objective which is a weighted function of demand travel times and of facility relocation costs. It is shown that when these latter costs are a concave function of travel time, an optimal set of facility locations exists solely on the nodes of the network. The location-relocation problem is formulated as an integer programming problem and its computational complexity is discussed. An example illustrates the basic concepts of this paper.