Optimizing inventory and marketing policy for non-instantaneous deteriorating items with generalized type deterioration and holding cost rates

This paper considers an inventory system with non-instantaneous deteriorating item in which demand rate is a function of advertisement of an item and selling price. This paper aids the retailer in maximizing the total profit by determining optimal inventory and marketing parameters. In contrast to previous inventory models, an arbitrary holding cost rate and arbitrary deterioration rate have been incorporated to provide general framework to the model. First, a mathematical model is formulated and then some useful theoretical results have been framed to characterize the optimal solutions. The necessary and sufficient conditions for the existence and uniqueness of the optimal solutions are also derived. An algorithm is designed to find the optimum solutions of the proposed model. Numerical examples are included to illustrate the algorithmic procedure and the effects of key parameters are studied to analyze the behavior of the model. ► The study considers the inventory model for non-instantaneous deteriorating item. ► Demand rate is linked to frequency of advertisement and the selling price. ► General-type of deterioration and holding cost rates are considered. ► Theoretical results have been framed to characterize the optimal solutions. ► The effect of key parameters is studied rigorously.