J Heuristics DOI 10.1007/s10732-011-9163-5 A Bilevel p-median model for the planning and protection of critical facilities Deniz Aksen · Necati Aras · Nuray Piyade © Springer Science+Business Media, LLC 2011 Abstract The bilevel p-median problem for the planning and protection of critical facilities involves a static Stackelberg game between a system planner (defender) and a potential attacker. The system planner determines firstly where to open p critical service facilities, and secondly which of them to protect with a limited protection budget. Following this twofold action, the attacker decides which facilities to inter- dict simultaneously, where the maximum number of interdictions is fixed. Partial protection or interdiction of a facility is not possible. Both the defender’s and the at- tacker’s actions have deterministic outcome; i.e., once protected, a facility becomes completely immune to interdiction, and an attack on an unprotected facility destroys it beyond repair. Moreover, the attacker has perfect information about the location and protection status of facilities; hence he would never attack a protected facility. We formulate a bilevel integer program (BIP) for this problem, in which the de- fender takes on the leader’s role and the attacker acts as the follower. We propose and compare three different methods to solve the BIP. The first method is an optimal exhaustive search algorithm with exponential time complexity. The second one is a two-phase tabu search heuristic developed to overcome the first method’s impracti- cality on large-sized problem instances. Finally, the third one is a sequential solution method in which the defender’s location and protection decisions are separated. The efficiency of these three methods is extensively tested on 75 randomly generated in- stances each with two budget levels. The results show that protection budget plays D. Aksen ( ) College of Administrative Sciences and Economics, Koç University, Rumelifeneri Yolu, Sarıyer, ˙ Istanbul, Turkey e-mail: daksen@ku.edu.tr N. Aras · N. Piyade Department of Industrial Engineering, Bo˘ gaziçi University, Bebek, ˙ Istanbul, Turkey N. Aras e-mail: arasn@boun.edu.tr