A new fuzzy approach of vehicle routing problem for disaster-stricken zones

Route planning problems are among the activities that have the highest impact in emergency logistical planning, goods transportation and facility location-distribution because of their effects on efficiency in resource management, service levels and client satisfaction. In the extreme conditions, such as disaster-stricken zones, the difficulty of vehicle movement between nearest different affected areas (demand points) on planning routes cause the imprecision of time of movement and the uncertainty of feasibility of movement. In this paper, the imprecision is presented by triangular fuzzy numbers and the uncertainty is presented by a possibility measure. A new two-stage, fuzzy bi-criterion optimization approach for the vehicle routing problem (VRP) is considered. On the first stage, the sample of so-called "promising" closed routes are selected based on a "constructive" approach. On the second stage, triangular fuzzy valued Choquet aggregation (TFCA) operator is constructed for the selected closed routes. The evaluation of constructed routes, levels of failure and possibility of vehicle movement on the roads are aggregated by the TFCA operator by the new criterion - minimization of infeasibility of movement. The new criterion together with the classic criterion - minimization of the total distance traveled - creates a bi-criteria fuzzy VRP. The constructed VRP is reduced to the bi-criteria fuzzy partitioning problem, and an -constraint approach is developed for solving it. For numerical experiments, a parallel algorithm is created on the basis of D. Knuth's algorithm of Dancing Links (DLX). An example is presented with the results of our approach for the VRP, where all Pareto-optimal solutions are found from the set of promising routes. The optimal solutions tend to avoid roads that are problematic because of extreme situations.