Modelling and solving an integrated freight train scheduling and trip planning problem with hazardous materials

This paper investigates the routing and scheduling of rail freight of hazardous materials with train scheduling decisions considering risk-spreading function. We consider the problem of minimizing the weighted sum of the cost of serving the commodities plus risk-spreading function using well-defined measures, either the maximum population exposure, the difference between the maximum and minimum risk, or the mean absolute deviation of the risk while limiting the population exposure below the given risk thresholds. Non-linear-mixed integer programming models and heuristic method are proposed for preparing the shipment plans and determining the schedule of train services. Numerical examples are provided to study and analyse risk-spreading functions.