Multi commodity maximum flow network interdiction problem considering uncertainty

This study investigates the multi-commodity maximum flow network interdiction problem (MC-MFNIP) consisting of two opposite sides who have conflicting aims in the presence of uncertainty regarding arc capacities. In this problem, while the follower tries to maximize the multi-commodity flow throughout the network, the leader attempts to minimize the total flow quantity that the follower has achieved using the limited interdiction resource. In this study, the MC-MFNIP is studied under a fuzzy environment for the first time. To this end, the fuzzy-based optimization model is formulated to allow considering multiple-source & multiple-sink nodes for the commodities and prioritizing the commodities. Following that, computational analyses are performed through a set of cases regarding the different sized networks and α-cut levels to test the model performance and track the changes in the flow quantities. It is highlighted that the model is efficient to plan fortification strategies versus interdictions at an operational level because the model provides optimal information about the most vital (interdicted) arcs within seconds in all generated networks in terms of tractability.