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W e consider two capacity choice scenarios for the optimal location of facilities with fixed servers, stochastic demand, and congestion. Motivating applications include virtual call centers, consisting of geographically dispersed centers, walk-in health clinics, motor vehicle inspection stations, automobile emissions testing stations, and internal service systems. The choice of locations for such facilities influences both the travel cost and waiting times of users. In contrast to most previous research, we explicitly embed both customer travel/ connection and delay costs in the objective function and solve the location-allocation problem and choose facility capacities simultaneously. The choice of capacity for a facility that is viewed as a queueing system with Poisson arrivals and exponential service times could mean choosing a service rate for the servers (Scenario 1) or choosing the number of servers (Scenario 2). We express the optimal service rate in closed form in Scenario 1 and the (asymptotically) optimal number of servers in closed form in Scenario 2. This allows us to eliminate both the number of servers and the service rates from the optimization problems, leading to tractable mixed-integer nonlinear programs. Our computational results show that both problems can be solved efficiently using a Lagrangian relaxation optimization procedure.

This article categorizes existing maximum coverage optimization models for locating ambulances based on whether the models incorporate uncertainty about (1) ambulance availability and (2) response times. Data from Edmonton, Alberta, Canada are used to test five different models, using the approximate hypercube model to compare solution quality between models. The basic maximum covering model, which ignores these two sources of uncertainty, generates solutions that perform far worse than those generated by more sophisticated models. For a specified number of ambulances, a model that incorporates both sources of uncertainty generates a configuration that covers up to 26% more of the demand than the configuration produced by the basic model.

The hub covering flow problem (HCFP) seeks to find the minimal cost hub-and-spoke network by optimally locating hub nodes and assigning non-hub nodes to the hub nodes subject to a coverage constraint. The cost of establishing such a hub network is based on a fixed cost of opening hubs and the cost of transporting demand flow through the network. We also present an extension called the multiaircraft HCFP. The results from computational experiments are presented and discussed.

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