Sequential location of two facilities: comparing random to optimal location of the first facility

We investigate sequential location of two facilities. One strategy is to locate the first facility at its single facility optimum. A second strategy is to randomly locate the first facility. The second facility is then located at its optimal location given the first facility’s location. We investigate which of these two strategies is better. Three objectives are tested: minisum, minimax, and competitive. We considered three environments: uniform demand in a square, discrete demand in the plane, and demand at nodes of a network. For the competitive objective we obtained what might be considered the expected result of locating the first facility optimally is better. For the minisum and minimax objectives, we found a surprising result: it is better to locate the first facility at random. We investigate the reasons behind these results which support the principle of add‐heuristics and the greedy randomized adaptive search procedure where the search does not necessarily select the best solution in a greedy sequential approach.