Pricing and warranty for hi-tech products considering failures due to unknown faults and human errors (A game theory approach)

Document Type: Research Paper


Department of Industrial Engineering, Alzahra University, Tehran, Iran


Hi-tech warranty reports show that a considerable percent of product's failures are related to the unknown faults and human errors, respectively. In this paper, two joint price and warranty models in a supply chain are presented for Hi-tech products. The supply chain includes a retailer and a customer, regarding failures due to unknown faults and human errors, beside the production failures. In the first model, failures due to production defects and human errors are considered separable, and in the second model they are considered inseparable. For both models, the interaction between the retailer and the customer is considered by retailer-Stackelberg game. The optimal purchase time, price, and warranty length are determined by maximizing the profits of customer and the retailer. Finally, the numerical example and sensitivity analysis are presented to illustrate the working logic of the models.


Main Subjects

Anand, A., Shakshi, S., Panwar, S., &Singh, O. (2017). Optimal Price and Warranty Length for Profit Determination: An Evaluation Based on Preventive Maintenance. Quality, IT and Business Operations, 265-277.

‍‍Cao, K., &He, P. (2017). Price and warranty competition in a supply chain with a common retailer. INFOR: Information Systems and Operational Research, DOI:10.1080/03155986.2017.1363590.

Chen, X., Li, L., &Zhou, M. (2012). Manufacturer’s pricing strategy for supply chain with warranty period-dependent demand. Omega, 40,807-816.

Erkoyuncu, J.,  A,  SamirKhan,  Fazal  Hussain,  S. M., &Roy, R. (2016). A framework to estimate the cost of No-Fault Found events.  International Journal of Production Economics, 173,207-222.


Eskandari Dorabati, S., Zeinal Hamadani, A., &Fazlollahtabar, H. (2018). Investigating the effects of operators on warranty cost under sales delay conditions. Journal of Quality in Maintenance Engineering,

Esmaeili, M., Shamsi Gamchi, N., &Asgharizadeh, E. (2014). Three-level warranty service contract among manufacturer, agent and customer: A game-theoretical approach. European Journal of Operational Research, 239,177-186.

Huang, X., Choi, S. M., Ching, W. K., Siu, T. K., &Huang, M. (2011). On supply chain coordination for false failure returns: A quantity discount contract approach. International Journal of Production Economics, 133, 634-644.

Jones, J., &Hayes, J. (2001). Investigation of the occurrence of: no-faults-found in electronic equipment. IEEE Transactions on Reliability, 50(3), 289-292.

Khan, S., Farnsworth, M., &Erkoyuncu, J. (2017). A novel approach for No Fault Found decision-making. CIRP Journal of Manufacturing Science and Technology, 17,18-31.

Qi, H., Ganesan, S., &Pecht, M. (2008). No-fault-found and intermittent failures in electronic products. Microelectronics Reliability, 48, 663-674.

Raza, A., &Ulansky, V. (2015). Minimizing Total Lifecycle Expected Costs of Digital Avionics’ Maintenance. Procedia CIRP, 38, 118-123.

Shamsi Gamchi, N., Esmaeili, M., & Saniee Monfared, M. (2013). A stochastic model for tri-partite service contracts. International Journal of Reliability, Quality and Safety Engineering, 20(2), 1-21.


Taleizadeh, A., Hadadpour, Sh., Cardenas-Barron, LE., &Shaikh, A. (2017). Warranty and price optimization in a competitive duopoly supply chain with parallel importation.  International Journal of Production Economics,185, 76-88.

Tsao, Y. C., Teng, W. G., Chen, R. S., &Chou, W. Y. (2014). Pricing and inventory policies for Hi-tech products under replacement warranty. International Journal of System Science, 45, 1255-1267.

Wei, J., Zhao, J., &Li, Y. (2015). Price and warranty period decisions for complementary products with horizontal firms' cooperation/noncooperation strategies. Journal of Cleaner Production, 105, 86-102.

Wu, S. (2011). Warranty claim analysis considering human factors. Reliability Engineering and System Safety, 96, 131-138.

Wu, Sh. (2014). Warranty return policies for products with unknown claim cases and their optimization. International Journal of Production Economics, 156, 52-61.

Yang, P. C., Wee, H. M., Liu, B. S., &Fong, O. K. (2011). Mitigating Hi-tech products risks due to rapid technological innovation. Omega, 39, 456-463.

Yeh, Ch-W., &Fang, Ch-Ch. (2015). Optimal decision for warranty with consideration of marketing and production capacity. International Journal of  Production Research­, 53­(18), 5456-5471.

Zhou, Z., Li, Y., &Tang, K. (2009). Dynamic pricing and warranty policies for products with fixed lifetime. European  Journal of Operational Research, 196, 940-948.