Deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand

In this paper, we extend the inventory lot-size models to allow for inflation and fluctuating demand (which is more general than constant, increasing, decreasing, and log-concave demand patterns). We prove that the optimal replenishment schedule not only exists but is also unique. Furthermore, we show that the total cost associated with the inventory system is a convex function of the number of replenishments. Hence, the search for the optimal number of replenishments is simplified to finding a local minimum. Finally, several numerical examples are provided to illustrate the results.