Optimal Dynamic Production and Sales Plans

Optimal Dynamic Sales Plans for Product Innovations in the Presence of Scarcity Effects

Rahul Patil

Assistant Professor, SJMSOM, IIT Bombay

Janat Shah

Professor, IIM Bangalore

Optimal Dynamic Sales Plans for Product Innovations in the Presence of Scarcity Effects

Abstract

In this paper, we develop a sales planning model for a firm that wants to sell a product innovation with a fixed market potential under a supply constraint. We consider a situation where a new product diffusion process depends upon word of mouth effects of waiting applicants in addition to adopters and innovators. This allows us to represent scarcity effects and its consequences namely hype and retarding effects. Some practitioners argue that firms intentionally delay sales to earn more profits. We identify situations where such a strategic sales delay can be optimal. In contrast, under a stylized situation, we show that a myopic sales plan that sells as much as possible is optimal when the hype effect exists. Under the retarding effect, a build up plan becomes dominant. Moreover, we find that the length of the build up period is not constant and depends upon the magnitude of the retarding effect. Finally, we investigate the capacity implications of the scarcity effects.

Key words: Innovation diffusion models; marketing- manufacturing interface; control theory; capacity planning.

1. Introduction

Several product innovations face capacity problems (New York Post 1999, Balachander et al. 2009). To incorporate supply constraint effects while developing optimal sales and production plans for the new products, researchers have suggested modifications to the original Bass model (Ho et al. 2002, Kumar and Swaminathan 2003), which assumed that only the customers who had successfully purchased the product and not the customers who had demanded the product controlled the future product growth. Their models thus have...