Multi-class hazmat distribution network design with inventory and superimposed risks

Transportation and inventory are essential to hazardous materials logistics, while different classes of hazardous materials are often transported over a network simultaneously. Despite their in-transit and storage incompatibility, the superimposed risks among different materials, which results from possible chemical reaction once accidents (e.g., leakage, explosion) happen, further complicate the comprehensive plans. In this study, we introduce a new multi-class hazmat distribution network design problem with inventory and superimposed risks (MHND) in a multi-echelon supply chain, where the planning of locations, inventory, and routes are made together. The long-term detour cost/risk and the cyclic time windows penalty costs under the time-dependent (periodic) road closure policy are explicitly formulated. We further propose a new population-based risk definition that evaluates the risk for the population at any location and any time with respect to its multi-class hazmat logistics system. In particular, to capture the interactions between different types of materials, we introduce risk superposition coefficients to capture possible superimposed risks among different hazmat that accommodate a general system with more than two hazmat types. We develop a knowledge-based NSGA-II algorithm with cyclic dissimilarity-based elitist selection (NSGA-II-CD) to solve the problem. The devised cyclic dissimilarity-based elitist selection (CD) operator can tackle the issue of speeding proliferation, which greatly improves the solution quality. Our model is applied to a metropolitan-wide real-world case study in Guangzhou, China. The results suggest that, from the perspective of the traffic management sector, the periodic road closures policy in Guangzhou could be possibly upgraded to a full-time prohibition. Moreover, the results provide the following insights to authorities (1) there is a positive convex relation between risk minimization and risk equilibration. The authorities should not try to find a perfect distribution of risk, and they should make a trade-off between the risk equity and total exposed risk; (2) there is a positive correlation between the level of service and total risk. Thus, in practice, the agencies should make a trade-off between economic viability of the system, exposed risk, and maintaining good service for customers; and (3) the interactions between different types of hazmat considerably affect the distribution network design; specifically, the route overlapping ratio for different types of hazmat decreases when their interactions intensify.