An inventory decision model for new products when demand depends on dynamic advertising expenditure

The new product acceptance theory which is well recognised in the marketing literature plays a pivotal role in determining the procurement schedule of the products which are newly introduced in the market for the models developed in the inventory management field. The diffusion of new products are made mainly through the advertisements in different media and the word‐of‐mouth which are popularly known as external and internal influences respectively. The external influences in the form of advertising greatly influence the innovators, that is, those persons who are to purchase the product as new one. This paper develops an inventory model where demand of the product is assumed to be dynamic over time and influenced by level of advertising expenditure in an innovation diffusion environment based on Horsky and Simon (1983). The paper derives the profit functions for different situations and conditions and jointly optimises the level of initial advertising expenditure with the cycle length. A simple solution procedure in the form of algorithm has been developed to obtain the optimal solution. The numerical example followed by comprehensive sensitivity analysis with respect to different parameters has been performed to know the behaviour and effectiveness of the model.