Freight transportation planning for regular and hazmat materials with simplified risk functions

Routing regular and dangerous commodities in railway freights transportation is discussed in this paper. Based on a link-based modeling approach, a mixed integer nonlinear programing model is developed. The model takes into account weather stability conditions of urban and rural areas and spatial distribution of risk at yards and around links as it impacts these zones along the routes. This paper also discusses the advantages of using bifurcation of flows on risk-cost tradeoffs and route planning decisions. The widely used nonlinear risk function is linearized and then the problem was solved to optimality using a commercial software. Results of the experiments on two hypothetical networks and one based on the rail network of the Province of Quebec in Canada are presented and analyzed. Routing decisions associated with both variants of the proposed model with bifurcation of the material flows are compared to obtain managerial insights on the model in solving hazmat freight routing problems.