The design of a public service facility network under terrorist attack

1. The design of a public service facility network under terrorist attack A BilevelProgramming Model Serhat Keçici Necati Aras Vedat Verter YAEM 2010 – June 2

2. Problem Motivation • Terrorist activities rising all over the world • More planned attacks with the aim of giving maximum harm • Security issues becoming more vital • Most critical facilities are already being protected • Attacks shifted towards infrastructure networks with manyfacilities

3. Problem Motivation Mobile-Phone Towers Are Taliban's New Target • “Destruction of the telecommunication towers will affect thousands of phone users in southern Afghanistan.” • “Local tribal leaders have offered to help protect such areas.” March 03, 2008

4. Problem Motivation Arsonists target ambulance station • “Attacks on the ambulance service are on the increase.” • “The station has had to betemporarily shut down because of the attack.” June 25, 1999

5. Outline • Problem Motivation • Bilevel Programming • The Model • Solution Approach • Results • Further Work

6. Problem Motivation • Public Service Facility Networks: • Aim is the maximization of service coverage • Attacks on facilities causes service failure • There are many facilities • Which facilities to protect? • Protectiondecision in the design stage of the network • Examples: • Wireless communication networks • Emergency services networks • Banking ATM networks

7. Problem Motivation • Classical Maximal Coverage Model except; • Bilevel Programming: There is an attacker • Protection decision • There are existing facilities • Relocation decision • Gradual Coverage

8. Bilevel Programming • What is Bilevel Programming? • Optimization problems where one optimization problem is embedded in another one. Max F(x,y) st. G(x,y)=B Max f(x,y) st. g(x,y)=b xєX Leader’s problem yєY Follower’s problem

9. Bilevel Programming

10. Bilevel Facility Location Model • Our Model • Leader (government) • Objective: Maximize post-attack service coverage • Decision: Location, relocation and protection of facilities • Follower (attacker) • Objective: Minimize post-attack service coverage • Decision: Destruction of open&unprotected facilities

11. Bilevel Facility Location Model k є K: Set of customers i,jє I : Set of facility locations • Parameters:

12. Bilevel Facility Location Model N1: Set of existing facility locations N2:Set of potential facility locations • Decision variables:

13. (2) Bilevel Facility Location Model Relocation – location constraints Budget constraint (2) (4) (6) (7) Attack – coverage constraints Budget like constraint (8)

14. Solution Approach • Meta-Heuristic Method • Tabu Search and Cplex solver • Challenge: There is still an optimization problem in the second level • Exact Method • Special Branch and Bound and Cplex solver • Main aim is to solve small problem instances • Challenge: There are too many alternative feasible solutions: location x relocation x protection

15. Exact Solution Method New facility location alternatives Stop if budget overrun Protection alternatives Relocation alternatives - Stop if excess budget - Stop if UB < Best Cplex Solver Attackers Response

16. Tabu Search Method • There are two extremes in the solution space • Protecting all facilities • Protecting “minority” of the facilities • How to deal with that? • Tabu moves • Two initial points

17. Results • Real life data • OR-Library • São José dos Campos city in Brazil • 324 customers and 818 customers • Customer locations and demands • Random and adapted data • Random potential facility locations; n=10 and 15 • 2 existing facilities in good locations • Number of attacks; r=2 • Same budget in all trials • Random fixed costs for location, relocation and protection • Visual C# software used for runs

18. SJC 324 Optimal Results n=10 n=15

19. SJC 324 Tabu - Exact Comparison n=10 n=15

20. SJC 818 Tabu - Exact Comparison n=10 n=15

21. Further Work • Parameter analysis to observe any trend or pattern • When to protect? • Network criticality • Leaders behavior vs. increasing budget • Leaders behavior vs. effects of fixed costs

22. Thank you! Questions and Comments s_kecici@yahoo.com