A modified economic order quantity of vendor – buyer non-cooperative supply chain model for imperfect quantity and inspection error using the nash equilibrium concept

Abstract

In this paper, the Economic Order Quantity (EOQ) of two-level supply-chain systems has been analyzed using the Nash Equilibrium concept. In this paper, a two-echelon supply chain consisting of a single vendor and a single buyer that both under the non-cooperative strategy. A mathematical analysis method, which according to appropriate literature, data and recent research result, is used to determine the mathematical formula of expected individual total cost both vendor and buyer, expected total cost of inventory system and also EOQ of decision variables. The non-cooperative strategy is used by the vendor and buyer to gain their optimal revenue. Thereby, game theoretical solution which is Nash equilibrium concept is used to determine the economic order quantity of this system. In this study, several assumptions are considered like the existence of the imperfect quality product in the manufacturing process and inspection error (Type I and Type II) in buyer’s place. To the best of authors’knowledge, this is the first paper that deals with a game theoretical solution, which is especially Nash equilibrium, in probabilistic supply chain under the imperfect condition and inspection error