چكيده به لاتين
Nowadays the government’s interest in protection of critical infrastructure has been increased because of appearing terrorism locally and regionally. Identifying critical and vulnerable components of a supply system, then planning for fortifying them and increasing their security against intentional attacks or natural disasters is substantially important for efficient service provision. Critical infrastructure comprises of several physical assets that, when lost, result in significant disruption of the system and degrading its function. A type of mathematical models called interdiction models with fortification are used to identify vulnerable facilities and then fortify and protect them in order to thwart worst-case interdiction patterns. In this study we present a tri-level interdiction median problem with fortification in order to design a supply system and immunize it against attacks and minimize the worst-case losses by hardening and protecting the most vulnerable facilities. Compared with single sourcing models in this proposed model we expand it as multi sourcing and capacitated one, which allows the customer to be supplied by more than one supplier with considering allowed capacity. In the development tri-level formulation, the defender in the first level, as the leader encounter facility location problem, fortifying a certain number of facilities, assignment of demand nodes to the closest opened facilities, opening new immune and safe facilities in order to minimize total costs and maximum damages imposed by attacker. In the second level, the attacker determines the set of facilities that destroying them imposes maximum losses and costs to the defender. Finally, in the lower level, the defender minimizes the damages caused by the disruptive agent in the upper level by means of reduce worst-case losses. We apply a decomposition algorithm via two-layer cutting plane strategy referred to as column-and-constraint generation method to solve mixed-integer nonlinear tri-level programming problem with binary variables in all three levels. The results prove that the attacker strategy and also the attack and defense resources have substantially significant effects on imposed costs and defender response.
Keywords: facility location, fortification, interdiction, tri-level programming, column-and-constraint generation method
