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

Application of an absolute supply chain model does not invalidate the possibility of few defective items in a supplied lot, therefore it becomes essential to conduct an inspection process for segregating the defective items, subsequently such segregated items are sold at discounted price. Shortages mainly occur with sudden demand or erratic production capacity, and player’s decisions are influenced by it. In this paper, the shortage is considered as a seller’s decision variable and demand is receptive to selling price and marketing expenditure of the buyer. Player’s interaction will be reviewed and determined as non-cooperative Stackelberg game. Further, a supply chain model is endured to substantiate the interaction and democracy among buyer and seller in the supply chain and is pitched by non-cooperative game theoretical approaches. The Stackelberg game approach is used in the non-cooperative method where one player acts as leader and another as follower. Hereafter, unanimous numerical examples along with sensitivity analysis are exhibited to compare amidst two different models with and without shortages to demonstrate the significance of the paper.