‎A‎ ‎tri‎-level programming approach for location-fortification-interdiction in a hierarchical network

Document Type : Original Paper

Author

Department of mathematics and statistics, Faculty of science, Gonbad Kavous University, Gonbad Kavous, Golestan, Iran

10.22055/jamm.2025.48153.2321

Abstract

The importance of locating critical facilities in hierarchical service delivery systems and fortification them against intentional attacks is the main subject of many researches, which helps the stability of the service system during intentional attacks by making appropriate decisions on location and fortification.‎ In this paper , for the first time , the problem of locating hierarchical facilities with regard to the fortification and interdiction operations in a tri-level programming model between system designer , defender and attacker has been proposed.‎‎ The aim of the system designer at the first level is to minimize the location cost and service distance between the demand points and two categories of facilities.‎ The defender's objective is to adopt appropriate fortification operations at the second level in order to minimize the distance between customers and the nearest facility to receive primary services and referrals for secondary services according to available location resources.‎ Meanwhile, the attacker in the third level of the model, as a follower, seeks to make decisions to assign customers to two categories of facilities and interdiction operations in order to maximize the service system distances.‎ To solve the new problem, a hybrid metaheuristic method based on genetic algorithm, simulated annealing algorithm and CPLEX has been proposed, and by solving several numerical examples, the the analysis of the results and the relation between the model parameters and the goals of the hierarchical service system is investigated.

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