A credibilistic goal programming model for inventory routing problem with hazardous materials

Hazardous materials are harmful to both the environment and human health due to their toxic ingredients. However, they are essential to sustain the industrial lifestyle, and frequently appear in the cargo transport. Since the damage is generally huge once an accident occurs, it is very important to evaluate the transportation risk of hazardous materials, and then make the best inventory routing decisions. In this paper, we study a three-level supply chain problem with hazardous materials inventory and transportation among suppliers, manufacturers and retailers. The goal is to obtain the best balance between risk and cost under the assumption that the demands of retailers are fuzzy variables. Considering that the variation of vehicle loading has a significant influence on the transportation risk, we formulate a loading-dependent transportation risk model and propose a credibilistic goal programming model to minimize the positive deviations of expected risk and expected cost from the given risk level and cost level. An improved genetic algorithm whose chromosomes contain two types of genes is designed to handle the goal programming model. Numerical experiments are given to illustrate the efficiency of the proposed model and algorithm.