Bilevel maximal covering problem for location, relocation and protection planning of public service facilities

Abstract

In this study, we consider the design problem of a public service facility network with existing facilities when there is a threat of possible terrorist attacks. The aim of the system planner, who is responsible for the operation of the network, is to open new facilities, relocate existing ones if necessary, and protect some of the facilities to ensure a maximum coverage of the demand that is assumed to be aggregated at customer zones. By doing so, the system planner anticipates that a number of unprotected facilities will be rendered out-of-service by terrorist attacks. It is assumed that the sum of the fixed costs of opening new facilities, the relocation costs, and the protection costs cannot exceed a predetermined budget level. Adopting the notion of gradual (partial) coverage, we formulate a bilevel programming model where the system planner is the leader and the attacker is the follower. The objective of the former is the maximization of the total service coverage, whereas the latter wants to minimize the same measure. We propose a heuristic solution procedure based on tabu search where the search space consists of the decisions of the system planner, and the corresponding objective value is computed by optimally solving the attacker’s problem using CPLEX. To assess the quality of the solutions produced by the Tabu search heuristic, we also develop binary enumeration tree method, which explores all the possible combinations of opening new facilities, relocating existing ones, and protecting them. Since its time complexity is exponential, it can only be employed for relatively small instances.