Multipurpose shopping trips and location

We locate a single competing facility in a particular retail category competing for customers who plan a visit to such a facility. Suppose that there is a probability that customers patronize in the same trip a second retail facility of a different category. In the standard competitive location model the probability of a multipurpose trip is zero. The estimated market share is calculated with an appropriately formulated gravity model and this is embedded in a locational decision model. An efficient implementation is devised. We show that multipurpose activity impacts all aspects of the solution: market share captured increases with this rate, and locational choices reflect an increasing interest in clustered co-location as the percentage of multipurpose trip activity increases. These results are both consistent with long standing theory and at the same time new because we are able to compute a locational trajectory for a large range of optimization scenarios. The core results hold over a wide variety of parameter variations. We solved optimally problems with up to 20,000 groups of customers in reasonable run time. The optimal location of the new facility moves from the optimal location of standard gravity models to locations close to clusters of facilities that sell different product types. At the optimal location, the market share can be more than doubled compared with the market share (including multiple trips in the calculation of the market share) captured at the location found by traditional models. Ignoring multipurpose trips results in a much inferior facility location.