Two Echelon Supply Chain Integrated Inventory Model for Similar Products: A Case Study

The purpose of this paper is to develop a mathematical model towards minimization of total cost across echelons in a multi-product supply chain environment. The scenario under consideration is a two-echelon supply chain system with one manufacturer, one retailer and M products. The retailer faces independent Poisson demand for each product. The retailer and the manufacturer are closely coupled in the sense that the information about any depletion in the inventory of a product at a retailer’s end is immediately available to the manufacturer. Further, stock-out is backordered at the retailer’s end. Thus the costs incurred at the retailer’s end are the holding costs and the backorder costs. The manufacturer has only one processor which is time shared among the M products. Production changeover from one product to another entails a fixed setup cost and a fixed set up time. Each unit of a product has a production time. Considering the cost components, and assuming transportation time and cost to be negligible, the objective of the study is to minimize the expected total cost considering both the manufacturer and retailer. In the process two aspects are to be defined. Firstly, every time a product is taken up for production, how much of it (production batch size, q) should be produced. Considering a large value of q favors the manufacturer while a small value of q suits the retailers. Secondly, for a given batch size q, at what level of retailer’s inventory (production queuing point), the batch size S of a product be taken up for production by the manufacturer. A higher value of S incurs more holding cost whereas a lower value of S increases the chance of backorder. A tradeoff between the holding and backorder cost must be taken into consideration while choosing an optimal value of S. It may be noted that due to multiple products and single processor, a product ‘taken’ up for production may not get the processor immediately, and may have to wait in a queue. The ‘S’ should factor in the probability of waiting time in the queue. © 2016, The Institution of Engineers (India).