Model and Solution Approach for Multi objective-multi commodity Capacitated Arc Routing Problem with Fuzzy Demand

The capacitated arc routing problem (CARP) is one of the most important routing problems with many applications in real world situations. In some real applications such as urban waste collection and etc., decision makers have to consider more than one objective and investigate the problem under uncertain situations where required edges have demand for more than one type of commodity. So, in this research, a new fuzzy chance constrained programming model based on credibility measure for CARP with two objectives: minimizing the number of vehicle and minimizing the total travel cost is formulated. In this model each required edge has demand for more than one type of commodity and also all demands for each commodity are supposed to be triangular fuzzy numbers. Then we develop a multi-objective genetic algorithm using the Pareto ranking technique and hybrid it with stochastic simulation to design an intelligent algorithm to solve the fuzzy chance constrained model. In order to improve the quality of final solutions, we also propose a new heuristic method to generate a good initial solution in initial population of genetic algorithm. Some data sets with fuzzy demand generated randomly are used to evaluate and investigate key characteristics of the new proposed model and solution approach.