A Probabilistic Analysis of the Maximal Covering Location Problem

Under a variety of different random models of the maximal covering location problem, we show that the relative error of a randomly generated solution converges to zero in expectation as problem size grows. We prove similar results for the relative error between the optimal integer and fractional solutions to the problem. Suppose that randomly generated instances of this problem are used to test heuristics. One consequence of our results is that we should expect the mean relative error of a heuristic to be better than that of randomly generated solutions, if the heuristic is to be considered useful.