A note on “optimal replenishment policies for non-instantaneous deteriorating items with price and stock sensitive demand under permissible delay in payment”

Soni 2013. Int. J. Prod. Econ., 146 (1), 259-268 proposed optimal replenishment policies for non-instantaneous deteriorating items (i.e., the product starts deteriorating after a period of no-deterioration) with price and stock sensitive demand. With a stock-dependent demand, it is desirable to have non-zero ending inventory due to potential profit resulting from the increased demand. However, Soni 2013. Int. J. Prod. Econ., 146 (1), 259-268 treated those ending inventory as fresh stocks to go through another period of non-deterioration again. Additionally, he assumed for simplicity that the replenishment cycle time T must be longer than the period of non-deterioration td(i.e., T>td). In reality, one should consider all possible replenishment cycle time to maximize the profit. In this note, we complement the shortcomings of his model by (i) selling those ending inventory as salvages, and (ii) considering all possible replenishment cycle time, which may be shorter than the period of non-deterioration. With these modifications the repeatability of the replenishment cycle is ensured and the applicability of Soni′s model is strengthened. The numerical examples indicate that the global optimal solution is indeed possible in the case of T≤td.