The competitive facility location problem under disruption risks

•We investigate a facility location problem incorporating service competition and disruption risks.•We develop a new binary bilevel linear programming (BBLP) model.•We design a variable neighborhood decomposition search matheuristic embedded with variable fixing and cut generation.•Exhaustive experiments prove the efficiency of our methods and draw interesting managerial insights.•Proposed methods can be extended to general BBLPs, preserving all fathoming and branching rules. Two players sequentially locate a fixed number of facilities, competing to capture market share. Facilities face disruption risks, and each customer patronizes the nearest operational facility, regardless of who operates it. The problem therefore combines competitive location and location with disruptions. This combination has been absent from the literature. We model the problem as a Stackelberg game in which the leader locates facilities first, followed by the follower, and formulate the leader’s decision problem as a bilevel optimization problem. A variable neighborhood decomposition search heuristic which includes variable fixing and cut generation is developed. Computational results suggest that high quality solutions can be found quickly. Interesting managerial insights are drawn.