Today, due to the expansion of demand on the one hand and the increase of market competitiveness, on the other hand, distribution and logistics management as a requirement for distribution companies and companies to raise profits and reduce costs is raised. In this research, the mathematical model of vehicle-based routing problem based on put out and the impression approach is developed at the same time. The goal is to determine the best route with minimal shipping cost and maximize customer demand. In the routing problem, both demand for receipt and delivery of commodity with each other, requiring the receipt of a certain amount of commodity from Depot, and also the commodity to be sent from customers to Depot. On the other hand, customer satisfaction is commensurate with the amount of demand for each customer that is satisfied, the higher the demand for a customer, the greater the satisfaction. Therefore, this research is to introduce a vehicle routing model with simultaneous and simultaneous withdrawal with the aim of maximizing customer demand supply to increase customer satisfaction. In order to solve the proposed mathematical model, a precise method of solving the problem using the GAMS software was performed in addition to experimental and model issues. Also, by examining the behavior of the two functions relative to each other, it is understood that because the first objective function is rating the cost of routing and the second objective function is to maximize customer demand supply, so these two objective functions behave vice versa and when one of them decrease another one will increase, which indicates the validity of the model. On the other hand, the results of sensitivity analysis indicate that with decreasing and increasing the parameter of the traversing routes cost and customer demand, the objective function is increased or decrease, respectively.