Order-Guided Non-Conservative Maximum Flow in Uncertain Network Interdiction Problem with Budget Constraint

Abstract

Probability theory in decision science fails in the absence of sufficient data. In these situations, uncertainty theory is applied to the problem-solving process, taking into account the opinions of the domain experts. In order to minimize the maximum flow carried by the evader, we describe an interdiction problem in an uncertain network with intermediate storage and resource constraints. Such approaches would help law enforcement combat drug-related and smuggling activities. This work first converts the bi-level deterministic conservative model of the interdictor vs evader problem (IEP) into a non-conservative deterministic IEP. With intermediate storage, a binary interdiction variable, and an interdiction resource constraint, the model is further transformed into an uncertain measure-based model. Then, utilizing uncertainty theory, the uncertain model is again converted into its deterministic equivalent. We have presented two techniques to identify the arc that the interdictor needs to block and to direct the order-guided maximum flow that the evader needs to deliver to the target. The models’ and algorithms’ efficacy is confirmed by an example. Lastly, a graphic representation of the shifting trend of the value of the objective function (VOF) is shown for a range of confidence levels.