This research introduces methods of stochastic decision processes into location analysis. The specific model concerns making dynamic relocation decisions for a new facility (server) that must interact with existing facilities (customers) whose relocations are stochastic processes. The model is an infinite-horizon Markov decision chain whose solution gives a server relocation policy that minimizes the expected discounted sum of costs. Costs are location-dependent and are incurred in two ways: when the server makes choice relocations and when the server interacts with customers. The model captures the essence of a variety of familiar dynamic location decision situations. Some methodological developments that allow solution of large problems are reported.