Optimal pricing and two-dimensional warranty policies for a new product

Abstract

For commercial products, pricing and warranty are two crucial marketing strategies, which are used to promote the potential market share. The warranty policy adopted by most of the capital-intensive products, such as machines and automobiles, usually has two dimensions, i.e. warranty age and warranty usage. In this paper, we propose to investigate the profit-maximisation problem, in which the revenue and costs will be affected by the product price and the area of warranty region, for a new product sold under two-dimensional warranty. We assume that the product sales can be captured by a stochastic Bass model based on the nonhomogeneous Poisson process. The product follows a two-dimensional failure process and is covered by a non-renewable free minimal-repair warranty, with age and usage limits. We focus on three revenue/cost components, i.e. sales revenue, warranty cost and production cost, that will significantly affect a firm’s total profit. The profit is maximised by jointly optimising three decision variables, i.e. product price, warranty age limit and warranty usage limit. Numerical experiments are conducted to illustrate the effects of some key parameters, including product reliability, price elasticity, warranty elasticity and learning effect factor, on the optimal settings of the price and warranty region.

Keywords:

• pricing
• two-dimensional warranty
• reliability
• stochastic Bass model
• Gumbel’s bivariate distribution

Acknowledgements

The author would like to thank the Associate Editor and two anonymous reviewers for their valuable comments and suggestions that helped considerably improve the quality of the manuscript.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the Fundamental Research Funds for the Central Universities [grant number 2017MS115]; Guangdong Natural Science Funds for Distinguished Young Scholar [grant number 2015A030306007]; Guangdong Natural Science Foundation [grant number 2016A030310415], [grant number 2015A070705001]; National Natural Science Foundation of China [grant number 71601079], [grant number 71501075], [grant number 71520107001].