Ensuring sustainable strategies for achieving multi-commodity maximum flow on a fuzzy network under interdictions

Document Type : Article

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Department of Industrial Engineering, Karadeniz Technical University, 61080 Trabzon, Turkey

Abstract

This paper addresses the multi-commodity maximum flow network interdiction problem (MC-MFNIP) which involves two opposite sides with conflicting objectives in the presence of uncertain arc capacities. In this problem, one party, follower tries to maximize the multi-commodity flow throughout the network, while the other party, leader, attempts to minimize the total flow quantity that the follower achieves using the limited interdiction resources. To tackle this challenge, this study presents an exact fuzzy-based optimization model that, for the first time, considers the prioritization of multiple-source and multiple-sink nodes for commodities while addressing the uncertainties inherent in arc capacities. The model also considers the feasibility degree that specify the level of risk the decision-maker is willing to accept for the MC-MFNIP, in which arc capacities are defined using triangular fuzzy numbers. The computational analyses are performed through a set of cases regarding the various sized networks and α-cut levels to test the model’s performance and track changes in flow quantities. It is worth noting that the model is efficient for devising fortification strategies against interdictions at an operational level. This is because the model quickly provides optimal information about the most critical arcs within seconds in all generated networks, ensuring tractability.

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Scientia Iranica

Articles in Press, Accepted Manuscript
Available Online from 27 January 2024

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