Preemptive priority-based algorithms for fuzzy minimal cost flow problem: An application in hazardous materials transportation

This paper studies the minimal cost flow problem (MCFP) with fuzzy link costs, say fuzzy MCFP, to understand the effect of uncertain factors in applied shipment problems. With respect to the most possible case, the worst case and the best case, the fuzzy MCFP can be converted into a 3-objective MCFP. Applying a lexicographical ordering on the objective functions of derived problem, two efficient algorithms are provided to find the preemptive priority-based solution(s), namely p-successive shortest path algorithm and p-network simplex algorithm. In both of them, lexicographical comparison is used which is a natural ordering in many real problems especially in hazardous material transportation where transporting through some links jeopardizes people’s lives. The presented schemes maintain the network structure of problem and so, they are efficiently implementable. A sample network is also given to illustrate the procedure and to compare the computational experiences with those of previously established works. Finally, the presented approach is applied to find an appropriate plan to transit hazardous materials in Khorasan roads network using annual data of accidents.