The Traveling Repairperson Home Base Location Problem

This paper considers the problem of locating the home base of a traveling server on a network. Calls for service arrive solely at nodes via independent, time-homogeneous Poisson processes. Calls finding the server busy enter a finite capacity queue which is depleted in a First-Come-First-Served (FCFS) manner. The server travels from his/her home base serving calls back-to-back, returning home only when he/she finds the system empty upon the completion of a service. The objective we consider is to minimize the average response time to an accepted call. The queueing system is analyzed via a busy period analysis, which uses a decoupling scheme to simplify the task of optimizing the home base location. Computational experience is discussed and a numerical example is presented. Generalizations of the model are also discussed.