On an optimal replenishment policy for inventory models for non-instantaneous deteriorating items with stock dependent demand and partial backlogging

Abstract

This paper proposes a procedure for determining the optimal replenishment policy for the simple inventory model with stock-dependent demand items, non-instantaneous deteriorating items and partial backlogging. The optimal policy is shown to be of a threshold form. That is, (i) if the time of the onset of deterioration is greater than or equal to the time at which partial-backlogging begins in the basic model (with no deterioration), then the optimal policy is determined by the parameters of the basic model, else (ii) The optimal policy corresponds to the unique critical point of the objective function for the model with non-instantaneous deterioration. Moreover, a simple test for deciding in favor of the former model is given. The procedure obtained is simpler and easier to implement than those existing in the literature. Numerical examples are presented for illustration.