en Mathematical Modeling and Applications of OR Mathematical Modeling and Applications of OR پژوهشی Original <p>In general, any system may be at risk in a case of losing the critical facilities by natural disasters or terrorist attacks. This paper focuses on identifying the critical facilities and planning to reduce the effect of this event. A three-level model is suggested in the form of a defender-attacker-defender. It is assumed that the facilities are hierarchical and capable of nesting. Also, the attacker budget for the interdiction and defender budget for fortification is limited. At the first level, a defender locates facilities in order to enhance the system capability with the lowest possible cost and full covering customer demand before any interdiction. The worst-case scenario losses are modeled in the second-level. At the third level, a defender is responsible for satisfying the demand of all customers while minimizing the total transportation and outsourcing costs. We use two different approaches to solve this model. In the first approach, the third level of the presented model is coded in Gams software, its second level is solved by an explicit enumeration method, and the first level is solved by tabu search (TS). In the second approach the first level is solved by the bat algorithm (BA). Finally, the conclusion is provided.</p> r-interdiction median three-level model, hierarchical facility location, integer programming, Meta-heuristics. 58 72 http://iors.ir/journal/browse.php?a_code=A-10-10-7&slc_lang=en&sid=1 Maryam Akbari-Jafarabadi maryamakbari.math@gmail.com 00031947532846001506 00031947532846001506 No University of Science and Ttechnology of Mazandaran Reza Tavakkoli-Moghaddam tavakoli@ut.ac.ir 00031947532846001507 00031947532846001507 Yes University of Tehran Mehdi Mahmoodjanloo mehdi.janloo@yahoo.com 00031947532846001508 00031947532846001508 No University of Science and Ttechnology of Mazandaran Yaser Rahimi yaser.ie87@gmail.com 00031947532846001509 00031947532846001509 No University of Tehran