A proposed multi-objective model in vehicle routing problems employing both exact and approximate approaches

Putting Distribution under study as a core process of the Supply Chain Management, Vehicle Routing Problem (VRP) has been recognized as an influential problem in transportation section. In the study, it has been tried to solve a very critical type of the problem known as Bi-Objective Capacitated Vehicle routing problem (CVRP), with two objectives of optimization of travelled tours and also the number of vehicles, with both exact and approximate approaches. As an approximate evaluation, Meta-Heuristic methods known as Ant Colony Optimization (ACO) and also an exact one, a Mixed Integer Linear Programming (MILP), are applied to compare the results. In addition, another Crucial problem, Vehicle Routing Problem with Flexible Time Windows (VRPFlexTW) , is modelled with the overall aim of first minimizing the cost through minimizing the tour length, the number of vehicles and the penalties must be paid due to not punctual deliveries and then increasing customer satisfaction through improvement of service Level . The results are being validated through two separate ways:(1) a real case study of a dairy company which delivers products to supermarkets all over the city of Tehran; and (2) available Benchmark instances in the Capacitated Vehicle Routing Problem Library (CVRPLIB).