Maximum Capacity Path Interdiction Problem with Fixed Costs

Abstract

This paper addresses a network optimization interdiction problem, called the maximum capacity path interdiction problem. The problem is a hierarchical game containing two players: one evader and one interdictor. In a capacitated network, the evader wants to find a simple path from his current position to a target point with maximum capacity to send his forces along it while the interdictor decreases arc capacities under a budget constraint to interdict the advance of the evader’s forces as much as possible. This paper studies the case that each arc has a fixed cost for decreasing its capacity. An algorithm is proposed to solve the problem in strongly polynomial time. Computational experiments on two real-world datasets guarantee the efficiency and accuracy of the algorithm.