Optimizing dynamic investment decisions for railway systems protection

Past and recent events have shown that railway infrastructure systems are particularly vulnerable to natural catastrophes, unintentional accidents and terrorist attacks. Protection investments are instrumental in reducing economic losses and preserving public safety. A systematic approach to plan security investments is paramount to guarantee that limited protection resources are utilized in the most efficient manner. In this paper, we present an optimization model to identify the railway assets which should be protected to minimize the impact of worst case disruptions on passenger flows. We consider a dynamic investment problem where protection resources become available over a planning horizon. The problem is formulated as a bilevel mixed-integer model and solved using two different decomposition approaches. Random instances of different sizes are generated to compare the solution algorithms. The model is then tested on the Kent railway network to demonstrate how the results can be used to support efficient protection decisions.

[1]  Richard L. Church,et al.  The stochastic interdiction median problem with disruption intensity levels , 2012, Ann. Oper. Res..

[2]  Alan T. Murray,et al.  Modeling s-t path availability to support disaster vulnerability assessment of network infrastructure , 2010, Comput. Oper. Res..

[3]  Claudio Sterle,et al.  Optimizing Investment Decisions for Railway Systems Protection , 2015 .

[4]  Halil Bayrak,et al.  Shortest path network interdiction with asymmetric information , 2008, Networks.

[5]  Lili Du,et al.  A Stochastic Optimization Model to Reduce Expected Post-Disaster Response Time Through Pre-Disaster Investment Decisions , 2014 .

[6]  Hossein Taghizadeh Kakhki,et al.  Maximum dynamic network flow interdiction problem: New formulation and solution procedures , 2013, Comput. Ind. Eng..

[7]  Maria Paola Scaparra,et al.  Hedging against disruptions with ripple effects in location analysis , 2012 .

[8]  Gregory Levitin,et al.  Resource Distribution in Multiple Attacks Against a Single Target , 2010, Risk analysis : an official publication of the Society for Risk Analysis.

[9]  Gregory Levitin,et al.  Parallel systems under two sequential attacks , 2009, Reliab. Eng. Syst. Saf..

[10]  David P. Morton,et al.  Stochastic Network Interdiction , 1998, Oper. Res..

[11]  Marianthi G. Ierapetritou,et al.  Resolution method for mixed integer bi-level linear problems based on decomposition technique , 2009, J. Glob. Optim..

[12]  Johannes O. Royset,et al.  Solving the Bi-Objective Maximum-Flow Network-Interdiction Problem , 2007, INFORMS J. Comput..

[13]  R. Kevin Wood,et al.  Shortest‐path network interdiction , 2002, Networks.

[14]  Jacques F. Benders,et al.  Partitioning procedures for solving mixed-variables programming problems , 2005, Comput. Manag. Sci..

[15]  Gregory Levitin,et al.  Parallel systems under two sequential attacks with imperfect detection of the first attack outcome , 2012, J. Oper. Res. Soc..

[16]  M. Naceur Azaiez,et al.  Optimal resource allocation for security in reliability systems , 2007, Eur. J. Oper. Res..

[17]  Richard L. Church,et al.  A Framework for Modeling Rail Transport Vulnerability , 2008 .

[18]  J. C. Smith,et al.  Algorithms for discrete and continuous multicommodity flow network interdiction problems , 2007 .

[19]  Delbert Ray Fulkerson,et al.  Maximizing the minimum source-sink path subject to a budget constraint , 1977, Math. Program..

[20]  Gregory Levitin,et al.  Defence resource distribution between protection and decoys for constant resource stockpiling pace , 2013, J. Oper. Res. Soc..

[21]  Pierre Hansen,et al.  New Branch-and-Bound Rules for Linear Bilevel Programming , 1989, SIAM J. Sci. Comput..

[22]  Jonathan Cole Smith,et al.  Exact interdiction models and algorithms for disconnecting networks via node deletions , 2012, Discret. Optim..

[23]  Alan T. Murray,et al.  Critical network infrastructure analysis: interdiction and system flow , 2007, J. Geogr. Syst..

[24]  Deniz Aksen,et al.  A bilevel partial interdiction problem with capacitated facilities and demand outsourcing , 2014, Comput. Oper. Res..

[25]  Jesse R. O'Hanley,et al.  Optimizing system resilience: A facility protection model with recovery time , 2012, Eur. J. Oper. Res..

[26]  Justo Puerto,et al.  Revisiting a game theoretic framework for the robust railway network design against intentional attacks , 2013, Eur. J. Oper. Res..

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

[28]  B. Karimi,et al.  Solving the p-hub Median Problem Under Intentional Disruptions Using Simulated Annealing , 2013 .

[29]  Maria Paola Scaparra,et al.  Optimal Allocation of Protective Resources in Shortest-Path Networks , 2011, Transp. Sci..

[30]  Kenneth Sörensen,et al.  MISTRAL: A game-theoretical model to allocate security measures in a multi-modal chemical transportation network with adaptive adversaries , 2015, Reliab. Eng. Syst. Saf..

[31]  Özlem Ergun,et al.  The Maximum Flow Network Interdiction Problem: Valid inequalities, integrality gaps, and approximability , 2010, Oper. Res. Lett..

[32]  Necati Aras,et al.  A Bilevel p-median model for the planning and protection of critical facilities , 2013, J. Heuristics.

[33]  Gregory Levitin,et al.  Resource distribution in multiple attacks with imperfect detection of the attack outcome. , 2012, Risk analysis : an official publication of the Society for Risk Analysis.

[34]  Kjell Hausken,et al.  Governments' and Terrorists' Defense and Attack in a T-Period Game , 2011, Decis. Anal..

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

[36]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[37]  Sujeevraja Sanjeevi,et al.  A length-based, multiple-resource formulation for shortest path network interdiction problems in the transportation sector , 2013, Int. J. Crit. Infrastructure Prot..

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

[39]  Nancy R. Mead,et al.  Survivable Network Systems: An Emerging Discipline , 1997 .

[40]  David L. Woodruff,et al.  Interdicting Stochastic Networks with Binary Interdiction Effort , 2003 .

[41]  Kjell Hausken,et al.  The timing and deterrence of terrorist attacks due to exogenous dynamics , 2012, J. Oper. Res. Soc..

[42]  Mustapha Nourelfath,et al.  Protection of warehouses and plants under capacity constraint , 2015, Reliab. Eng. Syst. Saf..

[43]  Alan T. Murray,et al.  Comparative Approaches for Assessing Network Vulnerability , 2008 .

[44]  Mark S. Daskin,et al.  Stochastic p-robust location problems , 2006 .

[45]  Gilbert Laporte,et al.  A game theoretic framework for the robust railway transit network design problem , 2010 .

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

[47]  Richard L. Church,et al.  Identifying Critical Infrastructure: The Median and Covering Facility Interdiction Problems , 2004 .

[48]  Morton E. O'Kelly,et al.  A geographic perspective on commercial Internet survivability , 2003, Telematics Informatics.

[49]  Richard L. Church,et al.  Production , Manufacturing and Logistics An exact solution approach for the interdiction median problem with fortification , 2008 .

[50]  Gregory Levitin,et al.  Defense resource distribution between protection and redundancy for constant resource stockpiling pace. , 2011, Risk analysis : an official publication of the Society for Risk Analysis.

[51]  Kjell Hausken,et al.  Defending Against a Stockpiling Terrorist , 2011 .

[52]  Necati Aras,et al.  A Matheuristic for Leader-Follower Games Involving Facility Location-Protection-Interdiction Decisions , 2013 .

[53]  M. P. Scaparra,et al.  Optimizing Protection Strategies for Supply Chains: Comparing Classic Decision-Making Criteria in an Uncertain Environment , 2011 .

[54]  Jesse R. O'Hanley,et al.  Designing robust coverage networks to hedge against worst-case facility losses , 2008, Eur. J. Oper. Res..

[55]  Derek P Molle,et al.  Defending Critical Infrastructure as Cyber Key Terrain , 2016 .

[56]  Massimo Marchiori,et al.  Error and attacktolerance of complex network s , 2004 .