Estimation of gross profit for a new durable product considering warranty and post-warranty repairs

Wei Xie, Haitao Liao, Xiaoyan Zhu

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


This article presents an integrated model to estimate the gross profit for a new durable product to be sold in a fixed sales period at a fixed price. It is assumed that the sales over time can be characterized by a stochastic Bass model in the form of a nonhomogeneous Poisson process and the production system is a make-to-order type of system. An approximate yet accurate approach is developed to quantify the expected total cost of production involving a learning effect. Moreover, a non-renewable free minimal-repair warranty and non-free post-warranty service are considered for the repair service offered by the manufacturer. To quantify the related costs and profit, the fact that customers may not always request warranty and/or post-warranty repairs is explicitly addressed and modeled. A numerical example is provided to illustrate the effects of some key parameters, including the product reliability, price elasticity, and warranty period elasticity, on the optimal settings of the price, warranty period, and post-warranty charge. The saturation effect of sales process on achieving the optimal gross profit is also discussed.

Original languageEnglish (US)
Pages (from-to)87-105
Number of pages19
JournalIIE Transactions (Institute of Industrial Engineers)
Issue number2
StatePublished - 2014
Externally publishedYes


  • Learning effect
  • New product
  • Post-warranty
  • Stochastic Bass model
  • Warranty

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering


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