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A novel bilevel model and solution algorithms for multi-period interdiction problem with fortification

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Abstract

Service systems are in significant danger of terrorist attacks aimed at disrupting their critical components. These attacks seek to exterminate vital assets such as transportation networks, services, and supplies. In the present paper, we propose a multi-period planning based on capacity recovery to allocate fortification/interdiction resources in a service system. The problem involves a dynamic Stackelberg game between a defender (leader) and an attacker (follower). The decisions of the defender are the services provided to customers and the fortification resources allocated to facilities in each period as the total demand-weighted distances are minimized. Following this, the attacker allocates interdiction resources to facilities that resulted in the service capacity reduction in each period. In this model, excess fortification/interdiction budgets and capacity in one period can be used in the next period. Moreover, facilities have a predefined capacity to serve the customers with varying demands during the time horizon. To solve this problem, two different types of approaches are implemented and compared. The first method is an exact reformulation algorithm based on the decomposition of the problem into a restricted master problem (RMP) and a slave problem (SP). The second one is a high performance metaheuristic algorithm, i.e., genetic algorithm (GA) developed to overcome the decomposition method’s impracticability on large-scale problem instances. We also compare the results with some novel metaheuristic algorithms such as teaching learning based optimization (TLBO) and dragonfly algorithm (DA). Computational results show the superiority of GA against TLBO and DA.

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Acknowledgements

The first author would like to thank the research council of Gonbad Kavous University for supporting this research work. The second author would like to appreciate the research council of Shiraz University of Technology for supporting this research.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Gonbad Kavous University, P.O. Box 49717-99151, Gonbad Kavous, Golestan, Iran

    R. Khanduzi

  2. Faculty of Mathematics, Shiraz University of Technology, P.O. Box, 71555-313, Shiraz, Iran

    H. R. Maleki

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  1. R. Khanduzi
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  2. H. R. Maleki
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Correspondence to R. Khanduzi.

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Khanduzi, R., Maleki, H.R. A novel bilevel model and solution algorithms for multi-period interdiction problem with fortification. Appl Intell 48, 2770–2791 (2018). https://doi.org/10.1007/s10489-017-1116-8

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  • DOI: https://doi.org/10.1007/s10489-017-1116-8

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