The service system design problem arises in the design of telecommunication networks, refuse collection and disposal networks in public sector, transportation planning, and location of emergency medical facilities. The problem seeks to locate service facilities, determine their capacities and assign users to those facilities under time varying demand conditions. The objective is to minimize total costs that comprises the costs of accessing facilities by users and waiting for service at these facilities as well as the cost of setting up and operating the facilities. We consider a system where a central dispatcher assigns the user to the service facility. Under Poisson demand arrival rates and general service time distributions at the facilities, the problem is setup as a network of spatially distributed facilities, modelled as M/G/1 queues and formulated as a nonlinear integer programming model. Using simple transformation and piecewise linear approximation, we present a linear reformulation of the model with large number of constraints. We compute tight upper and lower bounds and use them in an iterative constraint generation algorithm based exact solution approach. Computational results indicate that the exact approach provides optimal solution in reasonable computational times.
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View Location and Allocation of Service Units on a Congested Network with Time Varying Demand Rates