A defensive maximal covering problem on a network

Consider a situation where p facilities need to be located by a leader, on the nodes of a network, to provide maximum coverage of demand generated at nodes of the network. At some point in the future it is expected that one of the links of the network will become unusable either due to a terrorist attack or a natural disaster (by the follower). The follower's objective is which link to remove. The leader's objective is to cover the most demand following such a damage to a link. The problem is formulated and analyzed from the leader's perspective. An efficient approach to solving the follower's problem is constructed. The leader's problem is solved heuristically by an ascent algorithm, simulated annealing, and tabu search, using the efficient algorithm for the solution of the follower's problem. Computational experiments on 40 test problems ranging between 100 and 900 nodes and 5–200 facilities provided good results.

[1]  Frank Plastria,et al.  Polynomial algorithms for parametric minquantile and maxcovering planar location problems with locational constraints , 1998 .

[2]  Polly Bart,et al.  Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph , 1968, Oper. Res..

[3]  John E. Beasley,et al.  OR-Library: Distributing Test Problems by Electronic Mail , 1990 .

[4]  Oded Berman,et al.  The generalized maximal covering location problem , 2002, Comput. Oper. Res..

[5]  G. O. Wesolowsky,et al.  The gradual covering problem , 2004 .

[6]  Richard L. Church,et al.  A bilevel mixed-integer program for critical infrastructure protection planning , 2008, Comput. Oper. Res..

[7]  Lawrence V. Snyder,et al.  Reliability Models for Facility Location: The Expected Failure Cost Case , 2005, Transp. Sci..

[8]  R. Kevin Wood,et al.  Deterministic network interdiction , 1993 .

[9]  Zvi Drezner,et al.  Heuristic Solution Methods for Two Location Problems with Unreliable Facilities , 1987 .

[10]  Zvi Drezner,et al.  Locating service facilities whose reliability is distance dependent , 2003, Comput. Oper. Res..

[11]  Richard L. Church,et al.  BEAMR: An exact and approximate model for the p-median problem , 2008, Comput. Oper. Res..

[12]  Fred W. Glover,et al.  Future paths for integer programming and links to artificial intelligence , 1986, Comput. Oper. Res..

[13]  Zvi Drezner,et al.  The variable radius covering problem , 2009, Eur. J. Oper. Res..

[14]  Richard L. Church,et al.  The maximal covering location problem , 1974 .

[15]  Mark S. Daskin,et al.  A Hierarchical Objective Set Covering Model for Emergency Medical Service Vehicle Deployment , 1981 .

[16]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[17]  Mark S. Daskin,et al.  A Maximum Expected Covering Location Model: Formulation, Properties and Heuristic Solution , 1983 .

[18]  Zvi Drezner,et al.  The facility and transfer points location problem , 2005, Int. Trans. Oper. Res..

[19]  Richard L. Church,et al.  Protecting Critical Assets: The r-interdiction median problem with fortification , 2007 .

[20]  Reza Barkhi,et al.  A REVIEW OF COVERING PROBLEMS IN FACILITY LOCATION. , 1993 .

[21]  Zvi Drezner,et al.  The gradual covering decay location problem on a network , 2003, Eur. J. Oper. Res..

[22]  Frank Plastria,et al.  Undesirable facility location with minimal covering objectives , 1999, Eur. J. Oper. Res..

[23]  Richard L. Church,et al.  Locating and protecting critical reserve sites to minimize expected and worst-case losses , 2007 .

[24]  Rajan Batta,et al.  The Maximal Expected Covering Location Problem: Revisited , 1989, Transp. Sci..

[25]  Mark S. Daskin,et al.  Planning for Disruptions in Supply Chain Networks , 2006 .

[26]  Shine-Der Lee,et al.  On solving unreliable planar location problems , 2001, Comput. Oper. Res..

[27]  Richard D. Wollmer,et al.  Removing Arcs from a Network , 1964 .

[28]  Charles ReVelle,et al.  Applications of the Location Set‐covering Problem , 2010 .