Distribution, inventory and production planning is one of the most important plans of big companies. Inventory routing problem is looking for integrating routing and inventory decisions. This problem doesn’t consider production decisions. Lot-Sizing problem with direct shipment, considers production and inventory and distributions decisions with direct shipment. Routing for delivering products is not considered in this problem. Production routing problem with using vender managed inventory method, combines lot-sizing and vehicle routing problem and considers distribution and production and inventory decisions. In this study a production routing integrated model which determines lot-sizing and production sequence simultaneously is proposed. Setup times and setup costs are depented to production sequence. In each period of time horizon multi-product can be produced and production size and sequence of each product is determined. Delivery amount, routing and held inventory in customer and plant warehouse is also determined. Number and capacity of vehicles and capacity of production time are limited. The objective function of proposed model is minimizing sum of setup costs, routing costs, production costs and inventory costs. The results show proposed model lead to reduce costs considerately. Depending setup to production sequence also can lead to increase feasible solutions. Considering the Np-hard complexity of this problem, a meta-heuristic hybrid algorithm based on quantum algorithm and variable neighbourhood search algorithm has been designed for solving problem in large scales. For examining proposed algorithm, results has been compared with results of exact method in small scales of problems and with results of quantum and variable neighbourhood search algorithms in large scales of problem. The results show proper performance of proposed algorithm. a new valid inequality is also proposed that reduces solving time.