Integrating the production scheduling and delivery problems by vehicle routing approach with heterogeneous flee

This paper considers production scheduling and delivery problem together and is trying to integrate both of them. Retailers order includes different types of products that have been processed at a distribution center. After completing the order process at the distribution center, products are delivered to the retailer in window time; otherwise the distribution center is required to pay the penalty cost of window time to the retailer. The aim of solving this problem is to determine the production sequence, retailer need to heterogeneous vehicles and the visiting sequence of retailers with respect to the delivery window time. In this paper, a mixed integer linear programming model is provided in which the total cost, including the cost of vehicle routing, fixed costs and penalty costs have been minimized.in order to solve the proposed mathematical model , two approaches of CPLEX solver of GAMS software and Relaxation Lagrangian algorithm have been used. At first, by using different samples, the efficiency of Lagrangian Relaxation algorithm had been confirmed in small sizes, and then it is used in order to obtain an acceptable optimal solution in large sizes in a reasonable period.