A complete proof on the solution procedure for non-instantaneous deteriorating items with permissible delay in payment

Ouyang et al. [Ouyang, L. Y., Wu, K. S., & Yang C. T. (2006). A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments. Computers & Industrial Engineering, 51, 637-651] present an inventory model for non-instantaneous deteriorating items with permissible delay in payments. They develop some theorems to characterize the optimal solutions and provide an easy-to-use method to find the optimal replenishment cycle time. Although, their inventory models are correct and interesting, processes of arguments to derive those theorems and the easy-to-use method to search for the optimal replenishment cycle time are not complete. So, the main purpose of this paper is to overcome those shortcomings and present complete proofs for Ouyang et al. (2006).