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Optimal inventory policy for non-instantaneous items with stock-dependent holding cost function and shortage

The classical EOQ model considered the holding cost as constant, but the variability in the holding cost is an important practical issues in inventory operation. In this paper, an inventory model for non-instantaneous deteriorating items with complete backlogging is built. We treat the holding cost as a generalized function of the on-hand stock. Conditions are set when the total holding cost of the inventory system per cycle is a convex function of positive inventory level duration. The necessary and sufficient condition of the existence and uniqueness of the optimal solution is also presented when the total holding cost is convex. Numerical examples are used to illustrate our solution procedure and to reveal the effect of the holding cost function and the length of fresh product time on inventory policies.