Stackelberg models in a two-level supply chain with imperfect quality items and allowable shortage

Abstract

Given that the application of an absolute supply chain model does not invalidate the possibility of few defective items in a supplied lot, it is essential to conduct an inspection to segregate defective items so as to sell such segregated items at a discount. Shortage mainly occurs with sudden rise of demand or erratic production capacity affecting a player's decisions. In this paper, shortage is considered as the seller's decision variable, and demand is receptive to the selling price and marketing expenditure of the buyer. The interaction of players will in turn be reviewed and determined as a non-cooperative Stackelberg game. Further, a supply chain model is proposed to substantiate the interaction between buyer and seller in the supply chain, and it is pitched by non-cooperative game theoretical approaches. The Stackelberg game approach is used as an extension of the non-cooperative method according to which one player acts as the leader and the other as a follower. Hereafter, unanimous numerical examples along with sensitivity analysis will be given to compare the two different models in the absence and presence of shortages to highlight the significance of this study.