Robust Optimization for the Hazardous Materials Transportation Network Design Problem

Abstract

We consider the problem of designing a transportation network for hazardous materials (HTNDP). For HTNDP, it was shown that deciding whether there exists an optimal path of risk 0 is NP-hard. A natural way to handle NP-hard problems is approximation solutions or FPT algorithms. We prove that HTNDP does not admit any approximation, neither any FPT algorithm, unless P=NP. The hazmat network design problem faces significant uncertainty in conflicting numbers of edge risk reported by different researchers and many factors affecting edge risk could induce different results since the edge risk is often difficult to characterize. In this paper, we use maximum regret criterion robust optimization to model the problem as a bi-level integer programming problem under edge risk uncertainty where an interval of possible risk values is associated with each arc. We present a heuristic approach that always finds a robust and stable hazmat network. At the end, we test our method on a random instance on a network of Guangdong province in China to illustrate the efficiency of our model and algorithm. Our experimental tests illustrate that the robust interval risk scenario network performs very well, and can handle the risk change better compared with the deterministic scenario network. Overall, the numerical analysis reveals that the maximum regret criterion robust optimization used in HTNDP is more conservative but has the merit of robustness.