An Integrated Production System Model for Multi Supplier Single Buyer with Non-conforming Item and Product Warranty

This paper develops a multi supplier single buyer integrated production system model. Several suppliers transform raw materials into semi-finished goods or components with constant production rates in order to supply a single buyer. The buyer processes components from the suppliers into finished products with a constant production rate. Non-conforming item and product warranty are also considered in this study. There are non-conforming items in the supplier production lot, in which the number of non-conforming items for each lot is probabilistic and the non-conforming items are reprocessed before they are delivered to the buyer. The result is that a buyer does not bear the cost of non-conforming item. Supplier provides component warranty to the buyer while finished product warranty to the customer is provided by the buyer. Component warranty period from the supplier (Wi) is shorter than finished product warranty period from the buyer (W), which is given and fixed. If a finished product is experiencing a failure in the end customer within the warranty period, a minimal repair will be done. If failure occurs after Wi, the supplier does not bear any warranty cost, but the buyer does, which covers the customer transportation cost and the repair cost. If failure occurs before Wi, the supplier should pay the repair cost and the transportation cost to the buyer while buyer only pays the customer transportation cost. A mathematical model is proposed to determine optimal number of delivery lots in order to minimize the integrated total relevant costs of both buyer and supplier. The cost of the supplier covers the setup cost, holding cost, rework cost, and the product warranty cost, while the buyer cost covers order cost, holding cost and product warranty cost. Approaches to solve the model are also being proposed in this paper, altogether with a numerical example.