Stochastic location models applied to multipurpose shopping trips

In a competitive multi-purpose (MP) trips model, it is assumed that the proportion of customers that do MP trips is given. In this paper, we investigate a model with a stochastic proportion of MP trips. Five decision analysis criteria are analyzed for finding the best location for a new facility under these circumstances. We first design a general approach that can be applied to many location problems. We then prove that by the optimistic rule, the solution is one of the extreme cases and construct solution algorithms to solve problems based on the other four rules optimally. The approach is demonstrated on the MP trips model. We performed computational experiments on instances between 100 and 20,000 demand points on five different models and two distance decay functions. The largest problem was solved within a given accuracy in about 8 h for the most time-consuming model. Our general approach can be applied to other location models (not necessarily competitive) when a parameter of such models is stochastic.