Optimal production-sales policies and entry time for successive generations of new products

This paper explores the optimal initial inventory at launch, sales plan, and introduction time for a new generation of a product. We propose a multi-generation demand model that accounts for supply constraints. A mathematical model of the supply-restricted multi-generation diffusion problem is then developed and the optimal sales policy is derived. Closed-form analytical expressions as well as numerical experiments are used to investigate the effect of consumers' backlogging, cost of production capacity, unit profit margin for the products, market expansion by the new generation, and cannibalization of older generations. Through consideration of supply restrictions and lost sales, we are able to generalize previous findings on market entry policy by showing that there is a continuous range of optimal introduction times. We show that the inter-dependence between production capacity and initial inventory varies based on the introduction time of the new generation. We also provide an application of the proposed model in the case of Sony's PlayStation®3 game console. The results suggest that the company introduced the product too late and overproduced inventory which, as supported by empirical evidence, had a negative impact on the product's performance. Limitations and considerations for the application of the model are also discussed.