Journal of Applied Mathematics and Decision Sciences
Volume 2009 (2009), Article ID 414507, 14 pages
Research Article

Warranty Optimization in a Dynamic Environment

1Department of Mechanical Engineering, University of Texas at Austin, 1 University Station C2200, Austin, TX 78712, USA
2School of Mathematics, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand

Received 9 November 2008; Accepted 4 March 2009

Academic Editor: John E. Bell

Copyright © 2009 Nedialko B. Dimitrov and Stefanka Chukova. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A product warranty is an agreement offered by a producer to a consumer to replace or repair a faulty item, or to partially or fully reimburse the consumer in the event of a failure. Warranties are very widespread and serve many purposes, including protection for producer, seller, and consumer. They are used as signals of quality and as elements of marketing strategies. In this study we review the notion of an online convex optimization algorithm and its variations, and apply it in warranty context. We introduce a class of profit functions, which are functions of warranty, and use it to formulate the problem of maximizing the company's profit over time as an online convex optimization problem. We use this formulation to present an approach to setting the warranty based on an online algorithm with low regret. Under a dynamic environment, this algorithm provides a warranty strategy for the company that maximises its profit over time.