finding the cost of inventory in make to order supply chain under vendor managed inventory program

this study considers a two echelon supply chain system consisting of one manufacturer and one retailer. under vendor managed inventory (vmi) program, the manufacturer is authorized to manage inventories of agreed upon stock keeping units at retail's locations. in this paper, we assume that the manufacturer monitors inventory levels at retailer's location, replenishes her stock under (r,q) policy, and follows make-to-order strategy to respond retailer's order, also the order quantity for the manufacturer is likely to be an integer multiple of the retailer’s replenishment quantity (q= nq, where n is a positive integer). in the other word, when the inventory position at the retailer reaches reorder point, r, the manufacturer initiates production of q units with finite production rate, p, and send the complete batch of q units to the retailer. we develop a renewal reward model for the case of poisson demand, and drive the long run average inventory cost of overall system under vmi program.