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The stochastic interdiction median problem with disruption intensity levels

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Abstract

In this paper we introduce a stochastic interdiction problem for median systems in which the operational state of the system’s disrupted elements in the aftermath of the disruption is uncertain as it is based on the intensity of the disruption. We assume that a disruption disables a facility with a given probability and this probability depends on the intensity of the disruption. The objective of this problem is to identify which disruption scenario entails a maximum overall traveling distance in serving all customers. We show that the initial two stage stochastic formulation can be reformulated into a deterministic counterpart whose size is polynomial in the number of facilities and intensity levels. Then, our ensuing efforts to solve the problem efficiently focus on studying alternative deterministic formulations that allow the solution of realistic size instances of the model. We observe that the most efficient of the deterministic formulations provide great scalability with respect to variations in the input parameters and size of the instances solved. Finally, we analyze the robustness of the optimal solutions due to misestimations in the probability functions that relate disruption intensity levels with the probabilities of facility survivability.

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Acknowledgements

This research was supported by the Engineering and Physical Sciences Research Council (EPSRC) Grant EP/E048552/1. This support is gratefully acknowledged.

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Authors and Affiliations

  1. Kent Business School, University of Kent, Canterbury, UK

    Chaya Losada & M. Paola Scaparra

  2. Geography Department, University of California, Santa Barbara, USA

    Richard L. Church

  3. Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, USA

    Mark S. Daskin

Authors
  1. Chaya Losada
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  2. M. Paola Scaparra
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  3. Richard L. Church
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  4. Mark S. Daskin
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Correspondence to M. Paola Scaparra.

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Losada, C., Scaparra, M.P., Church, R.L. et al. The stochastic interdiction median problem with disruption intensity levels. Ann Oper Res 201, 345–365 (2012). https://doi.org/10.1007/s10479-012-1170-x

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