A Bi-Objective Vehicle Routing Problem Considering Distributors' Satisfaction Using Genetic Algorithm and Simulated Annealing

One of the main problems attracted researchers' attentions in recent years is Vehicle Routing Problem (VRP). This paper tends to minimize the covered distance, total travelling time, number of vehicles, delay and transportation costs, and to maximize consumers' satisfaction by utilizing mathematical models. Distributors always tend to gain the maximum cash compared to their competitors and deliver their products to consumers and accomplish the distribution on a defined time. In real world, distributors' income depends on their product distributions amount. If the distribution income becomes less than a specific amount, distributors show no interest in distribution of that product and therefore distributors' satisfaction is zero. Also, if the delivery time exceeds a specific time, distributors' satisfaction is decreased. Moreover, a partial of drivers' benefit is related to amount of their sale thus balance of goods based on the vehicles capacity is important. The purposes of this paper are presenting a model to calculate minimum distributors' satisfaction of product distribution and also maximize distributed goods by vehicles regarding to their capacities. In addition, calculate the maximum present cash flow in the market on a defined time in a way that does not decrease the distributors' satisfaction level. The general limitations of vehicle routing problems considered in this study for each facility are capacity limitation and the number of vehicles. These kinds of problems are NP-Hard and solving them by linear programming is very time consuming. Thus, both Simulated Annealing (SA) and Genetic Algorithm (GA) are proposed to solve the problem. Finally, a wide range of problems have been solved to demonstrate the efficiency of the proposed algorithm, and then the answers are compared with the result of “Lingo8” software. The results show that the proposed models are quite efficient and viable.