A Game-Theoretic Approach for Determining the Economic Manufacturing Quantity and Mutual Inspection Policy under a Quality Contract

In this study, we deal with the optimal mutual inspection policies (OMIP) for a manufacturer and its downstream member (buyer) under a quality contract subject to the probability of non–conforming for each unit is transparent between the manufacturer and buyer. A game–theoretic framework is developed for both parties to determine their OMIP. Main difference between this study and related previous works is that in this research the full inspection policy will never be optimal for the manufacturer when a quality contract is considered. Based on this OMIP, we show how the OMIP is incorporated into the determination of optimal production lot size. To achieve an economical production under the defined contract, tradeoffs between manufacturing cost, inventory holding cost and quality related cost must be analyzed. Some properties for the optimal lot size are obtained. Numerical examples are performed to illustrate the optimal production lot size and OMIP.