Note on inventory models with Weibull distribution deterioration

This article explores the inventory model with a general demand rate function in which both the Weibull distributed deterioration and partial backlogging are considered. The inventory model discussed here is based on the important finding by Wu [Wu, K.S., 2001. An EOQ inventory model for items with Weibull distribution deterioration, ramp type demand rate and partial backlogging. Production Planning and Control, 12, 787-793]. There are four parts in our research. First, we derive the analytical framework of the inventory model for a general demand rate function(1). Second, for the ramp type demand, we improve Wu's model to find the criterion to guarantee the existence and uniqueness of the optimal solution. Third, we develop a new model to compensate for the missing case in Wu's article. Fourth, we combine our results to show that our findings are applicable to the ramp type demand inventory model, so that the optimal solution is independent of the demand function. Finally, some numerical examples and graphs are provided to illustrate our discovery and demonstrate the application of our analytical framework.