The maximal covering location disruption problem

Abstract

This research sets forth and examines a new sequential, competitive location problem. The maximal covering location disruption problem is a zero-sum Stackelberg game comprised of two stages. A leader denies access to at most $q$ out of $n$ possible facility locations in the first stage and, in the second stage, a follower solves a maximal covering location problem while emplacing at most $p$ facilities. Identifying this problem as both relevant and unaddressed in the current literature, this research examines properties of the bilevel programming formulation to inform heuristic development, subsequently evaluating the efficacy and efficiency of two variants each of an iterative, bounding heuristic (IBH) and a reformulation-based construction heuristic (RCH) over a two sets collectively consisting of 2160 test instances representing a breadth of relative parametric values. Although we illustrate that each heuristic may not identify an optimal solution, computational testing demonstrates the superlative and generally excellent performance of the RCH variants. For the 12.4% of instances for which the RCH does not readily verify the optimality of its solution, lower-bounding procedures characterize solution quality. Both of the RCH variants attain solutions with an average 4.08% relative optimality gap, and they scaled well over different parametric value combinations, solving instances in an average of 98.0 and 123.6 seconds, respectively.