On nn-facility median problem with facilities subject to failure facing uniform demand

We study the problem of locating nn facilities subject to failure on a unit line segment. The objective is to minimize the expected travel distance assuming that customers have information about the status of each facility ahead of time and thus travel directly to the closest operating facility (if one exists). The problem was previously studied only for the 2 facility case. In the current paper we introduce a new analytical approach that is based on representing the stochastic problem as a linear combination of deterministic median problems for which analytical results are available; this allows us to solve the problem for any number of facilities. Moreover, our approach is also valid when the failures are correlated. Our results confirm and clarify the various optimal location patterns observed in previous work in this area, as well as identify several new insights.