To minimize the inventory costs of detecting demand change, an acceptance/rejection method （ threshold） is proposed. The proposed threshold can be identified by the newsvendor based on the excess cost, the shortage cost, the transitional probability of the demand change, and the magnitude of the demand change. Compared with the single exponential smoothing method, it is proved that the proposed method can save many more inventory costs when detecting a step change in demand. By analyzing the proposed method, it shows that as the magnitude of step change increases, the supply chain members turn to synchronously judge a step change, and as excess （ shortage） cost increases, a newsvendor tends to respond slowly （early） to an increase in demand and responds early （slowly） to a decrease in demand. Observations from this study suggest that supply chain members should pay careful attention to different profit-margin products and different magnitude demand changes in cooperating and sharing demand information with others.
To investigate the optimal retail price and service level in a supply chain under consumer returns, a consumer returns model under the retailer＇s service provision is built. The optimal decision results and optimal profits are obtained in the vertical integration game and the manufacturer Stackelberg game, respectively. Through comparing the optimal profits with service provision with those of no service provision, the boundary conditions that the retailer＇s service should be provided are derived. The results show that in the manufacturer Stackelberg game, the optimal profit of the retailer and the manufacturer with service is always superior to that of a no service provision. However, in the vertical integration game, the supply chain can only benefit from the service under certain conditions. Finally, through numerical examples, the impacts of the cost for providing services and the consumer return rate on the optimal decisions are analyzed.
A decision model to maximize the total profit of manufacturers in an imperfect production system is constructed.In this model the production reliability and the warranty length are jointly used as decision variables for the case that products are sold with a warranty i.e. the demand is dependent on the warranty length and sale price.Also all the non-conforming quality defective items in the production process are refurbished to conform to quality ones at a cost. The existence and uniqueness of the optimal values of production reliability and the warranty length are proved by using the Euler-Lagrange method in analyzing the model.A numerical example is also provided to illustrate the effectiveness of the decision model.The sensitivity analysis of the key parameters of the optimal solution and objective value is presented in addition.
