An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging

In this study, we consider a problme of determining the optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand. In the model, shortages are allowed and the backlogging rate is variable and dependent on the waiting time for the next replenishment. The necessary and sufficient conditions of the existence and uniqueness of the optimal solution are shown. As the special cases, the results for the models with instantaneous or non-instantaneous deterioration rate and with or without shortages are derived. Further, we analytically identify the best circumstance among these special cases based on the minimum total relevant cost per unit time. Sensitivity analysis of the optimal solution with respect to major parameters is carried out. Finally, four numerical examples are presented to demonstrate the developed model and the solution procedure.