Optimal policy for an inventory system with demand dependent on price, time and frequency of advertisement

Abstract This paper studies a new lot-size inventory problem for products whose demand pattern is dependent on price, advertising frequency and time. It is considered that the demand rate of an item multiplicatively combines the effects of a power function dependent on the frequency of advertisement and a function dependent on both selling price and time. This last function is additively separable in two power functions, one varies with the selling price and the other depends on the time since the last inventory replenishment. Moreover, it is assumed that the holding cost per unit of item is a non-linear function of time in stock. Shortages are not allowed. The aim consists of determining the frequency of advertisement, the selling price and the length of the stock period to maximize the average profit per unit time. This leads to a mixed integer non-linear inventory problem, which is solved by using an efficient algorithm previously developed. The inventory model considered here extends several inventory models previously proposed in the literature. Some numerical examples are solved to illustrate how the algorithm works to obtain optimal inventory policies. Finally, a sensitivity analysis for the optimal solution with respect to the parameters of the inventory system is presented.