An integrated production-inventory model for ameliorating and deteriorating items taking account of time discounting

This study develops an integrated production-inventory model from the perspectives of both the manufacturer and the retailer. The model considered both ameliorating and deteriorating effects taking account of multiple deliveries, partial backordering and time discounting. The amelioration and deterioration are assumed to follow the Weibull distribution. The discounted cash flow and optimization technique are used to derive the optimal solution. A numerical example and the sensitivity analysis are given to illustrate the theory of the integrated production-inventory model. This model is particularly useful for items that ameliorate and deteriorate at the same time.