A multi-objective transportation routing problem

This paper presents a variant of vehicle routing problem, incorporating factors of transportation costs in conjunction with adverse situations. The effects of hazardous materials (HazMat) transportation are examined on air-pollution exposure levels, as well as the risk and damage in the case of accidents. In an urban network, the various weights that can be are assigned to each road of a route are associated to the following factors: time, cost, pollution exposure levels, and the risk of damage in HazMat transportation. These weights express the travel cost and the estimated provoked adverse consequences at each road of a vehicle transit route between two disparate points of the network concerning the pollution and risk of unforeseen accident during hazardous materials transportation. The sum of the weights assigned to every road of a route represents the route value according to the corresponding factors. We introduce an optimization criterion in order to select the optimal route among all vehicle transition routes joining any given pair of the network points that does not surpass a predefined threshold route value for each factor. The predefined weights for each factor are a percentage increment of its corresponding shortest route value. The optimal location of a central depot is determined where each vehicle serves a customer using one specific route with respect to the posed restrictions. Subsequently, a suitable partition into sub-networks is carried out in the case of large urban areas and a depot is assigned to each sub-network by applying a specific optimization criterion. A branch and bound tree search algorithm is developed for the determination of the optimal routes while the locations of the depots are investigated within the framework of graph theory. Finally, small numerical examples are given.