Two new approaches for the bi-objective shortest path with a fuzzy objective applied to HAZMAT transportation

This work proposes two algorithms to the Bi-objective Shortest Path (BSP) problem, considering a fuzzy objective. Such approaches originally extend two classic label setting algorithms to solve BSP, in particular, the first one using a modified Gandibleux revision of Martin's algorithm and the second one based on the A* algorithm acceleration technique. The proposed extensions differ from the previous classic approaches for two main aspects: the two methods solve BSP problems with a linear objective function and a min-max objective function; the max-min objective considered in the BSP is a fuzzy objective function. This latter aspect represents the main contribution of this paper. The proposed approaches, applied to the selection of paths for the road transport of hazardous materials, generate the set of Pareto optimal solutions among which the decision makers have to evaluate the trade-off between paths with minimum cost and paths with minimum (or min-max) risk. In this paper, a real life case study related to the delivery of petrol from a depot to refueling stations is finally illustrated to compare the effectiveness of the proposed approaches.