Equitable location of facilities in a region with probabilistic barriers to travel

•Proposed heuristic produces high-quality solutions in reasonable run-times.•Recognizing presence of barrier leads to a better solution of new facility locations.•Distribution of barrier location has a dramatic impact on new facility locations.•Recognizing probabilistic barrier has a dramatic impact on maximum travel distance. This paper studies a planar multi-facility location problem that considers the presence of a restricted region with probabilistic position. This problem seeks to locate facilities in an equitable manner by minimizing the maximum expected distance traveled from demand points to access a facility, as well as distances between locations of new facilities. We propose a heuristic to solve this problem that combines a bounding approach with a split-divide-and-conquer strategy. Computational study shows that this heuristic produces high-quality solutions in reasonable run-times. We report findings from a case-study involving locating police facilities in Kingston-Upon-Thames.