An Inventory Discount Model under JIT

In this study, we focus on a multi-stage supply chain system that operates under a JIT (just-intime) delivery policy. Kanbans play an important role in the information and material flows in a supply chain system. Thus, a kanban mechanism is employed to assist in linking different production processes in a supply chain system to implement the scope of JIT philosophy. We develop an optimal model for a multistage supply chain system under just-in-time philosophy. In this mode, the significant features of developed model are: 1-We add a retailer to the multi-stage supply chain system. 2-Stage N offers quantity discounts to encourage the retailer to order more and the producer intends to discount the unit production cost if the amount of production is large. 3-We transform our developed model into a more concise version by applying an unequal demand rates for all stages. 4-The most important development of presented model is that the inventory cost of the semi -finished parts shipped to a plant from the preceding stage is considered. Finally the number of kanbans, the batch size, the number of batches and the total quantity over one period are determined optimally.