An Inventory Model for New Product When Demand Follows Dynamic Innovation Process having Dynamic Potential Market Size

1. Introduction

The dynamic behaviour of the inventory system forces the inventory planner to manage and control the inventories in such a way that optimum inventory policy is maintained because the effective inventory management is the backbone of any business operations and it becomes more crucial when the parameters associated with the demand function are of dynamic nature. The dynamic behaviour of the system makes the people more cautious while taking decisions of economic ordering policies. The first and foremost task of any organization is to maintain optimum inventory level which is necessary to meet its requirement and avoid over or under inventory that can impact the financial figures. The dynamic behaviour of the system is generally observed when there is introduction of new products in the market. The management of such inventories becomes an important and critical function because these inventory resources besides being as assets of the organization and have economic value its contribution in the determination of financial health of the organization cannot be ignored. Now, the decision regarding optimum inventory level without developing mathematical models brings the decision maker in a confused state and does not support the fruitful decision for a complex system which ultimately tends towards gambling. Because mathematical models are the primary tools for studying the behaviour of the system by incorporating all the components of the inventory system and gives a scientific way of solving decision making problems arising in a large and complex systems. The mathematical models have been proved to be useful for understanding the structure and functioning of the system, predicting future events and prescribing the best course of action. It also exhibits relationship between the parameters (quantitative variables) under a definite set of assumptions which describe the system clearly and appropriately. Therefore, it is not advisable to take decisions based on established theories, intuition and experience always for a complex inventory system and a wise decision is to make analysis for economic ordering policies based on mathematical models. This article uses mathematical model based on innovation diffusion criterion. The theory of innovation diffusion is highly desired for attentive management of the new products in order to minimize the total cost and maximize benefits. To make the business fascinating and demanding the importance of innovations in business and industry is highly significant. Rogers (1962) had observed that when a new innovation is introduced in the market consumers show variable buying behaviour and categorize them according to their time to purchase. Here, the demand function used to develop mathematical framework is based on the Fourt and Woodlock (1960). The coefficient of innovation and the potential market size incorporated in the demand model have been considered to be dynamic over time.

The approach of this paper is to focus on the effect of innovation factor on adoption behavior of consumers under the condition that both potential market size as well as coefficient of innovation are dynamic dependent on time to minimize the total average cost. The article is divided into the following sections: literature survey to provide a theoretical background, model development, special cases and numerical examples with observations to know the behaviour of the model. Finally, the article concludes with a discussion on the application, extension and limitations of the model.