Uncertain Network Interdiction Problem

Published in Journal of Uncertain Systems, 2018


Indeterminacy is an intrinsic characteristic of a decision making process. Sometimes there are no samples, and historical data are not enough for estimating an appropriate probability distribution for an indeterminate variable. In these situations, an option could be referring to an expert on the subject, and uncertainty theory is a potentially powerful framework to manage this sort of indeterminacy. In this theory, an undetermined input parameter is referred to as an uncertain variable and its distribution is constructed based on the opinion of an expert. This is the case in many practical problems such as in the smuggling networks and drug-trafficking networks. This paper considers the network interdiction problem that aims to minimize the maximum flow through a capacitated network from a source to a sink where the arc capacities are uncertain variables. It is proved that there exists an equivalent deterministic model to the uncertain network interdiction problem. The proposed method is applied on a test problem, and the results are compared with the associated deterministic counterpart.