An inventory model and supply chain coordination for ameliorating items allowing for shortages under non-instantaneous replenishment

This study constructs an ameliorating item supply chain consisted of a single supplier and a single retailer. The replenishment from the supplier to the retailer takes a while to complete. The retailer is allowed to run out of stock. We analyse the order cycle, the profit of the supply chain system and the profit for each member under the cooperative and the non-cooperative decision-making conditions respectively. The results show that the profit of the supply chain system per unit time is higher under the cooperative decision making than under the non-cooperative decision making. However, compared with the latter, the former will lead to a decrease in the supplier's profit per unit time. To make up for the supplier's loss, a revenue-sharing contract is designed to coordinate the ameliorating item supply chain. The equilibrium solution is given by using the Nash bargaining theory. A numerical example is used to verify the main conclusions.