Applying Game Theory to Competitive Production-Inventory Models with Vendor's Imperfect Production Processes and the Condition of Buyer's Exemption from Inspection

This study establishes the competitive production-inventory models with vendor’s imperfect production processes by using game theory. The imperfect production processes can be improved by capital investment which is shared out between the vendor and the buyer jointly. In addition, the inspection process is assumed to be imperfect and Type I and Type II inspection errors occur during product quality inspection. We first develop the total cost per unit time of the buyer and vendor, respectively and then seek the optimal buyer’s order quantity, vendor’s shipping times and defective rate of the product where the system achieves a Nash equilibrium. The necessary and sufficient conditions of the existence and uniqueness of the optimal solutions for the buyer and the vendor respectively are shown. Furthermore, we develop a algorithm to find the optimal solutions. Finally, an numerical example are presented to demonstrate the solution procedure.