Stochastic Maximum Flow Network Interdiction with Endogenous Uncertainty

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SADEGHI SOMAYEH; Seifi Abbas

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Journal Paper

Paper Information

Journal: International Journal of Supply and Operations Management Year:2019 | Volume:6 | Issue:3 Page(s): 200-212

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Title

Stochastic Maximum Flow Network Interdiction with Endogenous Uncertainty

Author(s)

SADEGHI SOMAYEH | Seifi Abbas | Issue Writer Certificate

Keywords

Network Interdiction

Maximum Flow

Endogenous Uncertainty

Benders’

Decomposition

Stackelberg Game

Abstract

We described the two-stage Maximum Flow Network Interdiction problem under endogenous stochastic interdiction. Our model consists of two adversary agent playing a Stackelberg Game. A smuggler who wishes to maximize the expected flow of some illicit commodities (same as drugs), can be transmitted between a source node and a sink node without being detected. On the other hand, an attacker tries to minimize the objective of the smugglers by installing some detectors or adding some security controls on critical arcs to increase the probability of detection. Most previous stochastic Network Interdiction problems in the literature deal with exogenous uncertainty, while we consider stochastic programs under Endogenous Uncertainty in which the interdictor’ s decisions can alter the probability measures. The problem can be formulated as a bi-level program, at the top level the attacker by a limited budget, choosing critical arcs to install detectors and enhance the interdiction probability of those arcs endogenously. The bottom level problem is a two-stage problem which is solved to find the Maximum Flow in the network by smugglers. In the first stage, he chooses some links to transmit the flow. In the second stage an indicator variable is used to show if he would be detected under each scenario. The bi-level Decomposition algorithm has been applied to solve the problem by adding some Benders’; cuts iteratively. We applied a successive method, to deal with non-linearity rise in the probability measure of each path. A case study of drug trafficking network is applied to recognize which countries have the most significant effect in interdicting the drug trafficking network. The police can concentrate on those areas to decline the amount of drug flow. Our results demonstrate that if the critical arcs are chosen wisely and the probability of drug seizers decreases slightly, a significant decrease in the expected total flow of drugs can be achieved.

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APA: Copy

SADEGHI, SOMAYEH, & Seifi, Abbas. (2019). Stochastic Maximum Flow Network Interdiction with Endogenous Uncertainty. INTERNATIONAL JOURNALS OF SUPPLY AND OPERATIONS MANAGEMENT, 6(3), 200-212. SID. https://sid.ir/paper/665503/en

Vancouver: Copy

SADEGHI SOMAYEH, Seifi Abbas. Stochastic Maximum Flow Network Interdiction with Endogenous Uncertainty. INTERNATIONAL JOURNALS OF SUPPLY AND OPERATIONS MANAGEMENT[Internet]. 2019;6(3):200-212. Available from: https://sid.ir/paper/665503/en

IEEE: Copy

SOMAYEH SADEGHI, and Abbas Seifi, “Stochastic Maximum Flow Network Interdiction with Endogenous Uncertainty,” INTERNATIONAL JOURNALS OF SUPPLY AND OPERATIONS MANAGEMENT, vol. 6, no. 3, pp. 200–212, 2019, [Online]. Available: https://sid.ir/paper/665503/en

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