An Integrated Production-Inventory Model for a Dual-Channel Supply Chain

In this paper a dual-channel supply chain with one retailer and one manufacturer is considered. The manufacturer produces in a lot to supply an integer number of the retailer’s order and ships his product to the retailer in equal-sized batches. The manufacturer has also an online channel to meet the demand directly. It is assumed that two members have integrated production-inventory system to minimize the total cost. A procedure is developed to find the optimal solution based on the convexity of the total cost. A numerical example is provided to clarify the characteristics of the model. The results show that the optimal number of the shipments from the manufacturer to the retailer is very sensitive to the holding cost of the manufacturer. When the manufacturer's holding cost is less than that of the retailer, most of the inventory is held in the manufacturer and is delivered to the retailer in low quantities with more shipments. It was also obtained that if the dual-channel supply chain reshapes to single one, the total cost of the supply chain would be minimized and the maximum value of total cost of the supply chain would be happened when the demand is distributed equally between two channels.