An economic lot-size model with non-linear holding cost hinging on time and quantity

This paper develops an economic lot size inventory model where the demand rate depends on the stock level and the cumulative holding cost is non-linear on both the quantity and the time they are stored. More concretely, it is supposed that the demand rate is a concave potential function of the inventory level and the holding cost is potential on both time and quantity. Moreover, shortages are not allowed. A general procedure to determine the optimal lot size and the maximum inventory profit is developed. Also, some results about the profitability of the inventory system are presented. This work extends several inventory models previously considered in the literature. Finally, numerical examples, which help us to understand the theoretical results, are also given.