Locating capacitated facilities to maximize captured demand

We consider the problem of locating a set of facilities on a network to maximize the expected number of captured demand when customer demands are stochastic and congestion exists at facilities. Customers travel to their closest facility to obtain service. If the facility is full (no more space in the waiting room), they attempt to obtain service from the next-closest facility not yet visited from its current position on the network. A customer is lost either when the closest facility is located too far away or all facilities have been visited. After formulating the model, we propose two heuristic procedures. We combine the heuristics with an iterative calibration scheme to estimate the expected demand rate faced by the facilities: this is required for evaluating objective function values. Extensive computational results are presented.