Ensuring feasibility in location problems with stochastic demands and congestion

A location problem with stochastic demand and congestion where mobile servers respond to service calls originating from nodes is considered. The problem is of the set-covering type: only servers within the coverage radius of the demand-generating node may respond to a call. The service level constraint requires that at least one server must be available to respond to an arriving call, with some prespecified probability. The objective is to minimize the total number of servers. It is shown that earlier models quite often overestimate servers' availability and thus may lead to infeasible solutions (i.e., solutions that fail to satisfy the service level constraint). System stability conditions and lower bounds on system availability are developed by analyzing the underlying partially accessible queueing system. These lead to the development of two new models for which feasibility is guaranteed. Simulation-based computational experiments show that the proposed models achieve feasibility without significantly increasing the total number of servers.