Design of a reliable multi-modal multi-commodity model for hazardous materials transportation under uncertainty

In this paper, we propose a new mathematical model for designing a reliable hazardous material (HAZMAT) transportation network (RHTND) on the basis of hub location topology under uncertainties, in which hub nodes may be disrupted by external events, as well as HAZMATs incidents. Hub locations and HAZMAT transportation routes using different transportation modes are simultaneously optimized to obtain minimum risk of incidents. A mixed integer nonlinear programing model is developed. To cope with the uncertainties in the model, we provide a solution framework based on an integration of the well-known chance-constrained programing with a possibilistic programing approach. Small size problems are solved to optimality. In order to solve large size instances, a meta-heuristic algorithm was applied and its performance is evaluated in comparison with a new lower bound approach through analysis of a real case-study of a HAZMAT transportation network.