Locations on time-varying networks

We begin by examining the dynamic behavior of a facility location such as a 1-median or a 1-center on a network when the parameters of the network are known functions of time. The parameters of the network include the lengths of the edges and the demands at the nodes. In our formulation, time is considered a discrete variable and it is assumed that the facility can only serve customers while it is stationary and that the demands at time t are fully satisfied before time t + 1. In particular, if x(t) denotes the location of the facility for t = 1, 2, the cost would be the sum of the costs of satisfying the demands at the various times plus the cost of moving the facility along its route implied by x(t). We also examine certain path (route) selection problems in dynamic networks. Recent past literature is surveyed. Various extensions including the multifacility versions of the above problems are studied.