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This model illustrates an inventory model to obtain the retailers optimal replenishment policy for deteriorating items with fixed lifetime, shortages, and time- dependent backlogging rate. The backlogging rate is considered as non-increasing function of waiting time up to the next replenishment. Our intention is to minimize the total relevant cost of the system. Further, the necessary and sufficient conditions are derived for the existence and uniqueness of the optimal solution. Finally, some numerical examples, sensitivity analysis along with graphical representations are provided to illustrate the proposed model. From the numerical example, we prove more savings than Wu et al. (2006).

Optimal replenishment policy with variable deterioration for fixed lifetime products