A three-level servicing contract with an integrated maintenance plan, warranty policy, technology level, and pricing model that considers the time value of money

Document Type : Article


Department of Industrial Engineering, Faculty of Engineering, University of Qom, Qom, Iran


A common way to address customer concerns in the post-warranty period is to provide an extended warranty. Although sometimes the manufacturer is reluctant to offer an extended warranty, an agent takes on this task to maintain market share. In this regard, a three-level-servicing-contract among manufacture, agent and customer is presented in which both warranty period and useful life of the product are considered as function of age and usage. The proposed model considers two approaches to control the number of product failures and reduce cost: (1) the technology level used in manufacturing as an effective factor in product reliability; and (2) non-periodic maintenance activities to maintain the product reliability at an acceptable level. In addition, in this study, to calculate the costs imposed on each side of the contract more accurately, the time-value-of-money is considered in the calculation of financial flows. To illustrate the effectiveness of the proposed approach, three comparative studies are provided. The first comparative study shows the impact of the provision of an extended warranty, while the second comparative study proves the importance of preventive maintenance to reduce costs. The results of the last one show the effect of considering the time-value-of-money in calculating cash flows.


1. Singpurwalla, N.D. and Wilson, S. "The warranty problem: Its statistical and game-theoretic aspects", SIAM Review, 35, pp. 17-42 (1993).
2. Huang, Y.S., Gau, W.Y., and Ho, J.W. "Cost analysis of two-dimensional warranty for products with periodic preventive maintenance", Reliability Engineering & System Safety, 134, pp. 51-58 (2015).
3. Tong, P., Liu, Z., Menet, F., et al. "Designing and pricing of two-dimensional extended warranty contracts based on usage rate", International Journal of Production Research, 52, pp. 6362-6380 (2014).
4. Ye, Z.S. and Murthy, D.P. "Warranty menu design for a two-dimensional warranty", Reliability Engineering & System Safety, 155, pp. 21-2 (2016).
5. Gertsbakh, I.B. and Kordonsky, K.B. "Parallel time scales and two-dimensional manufacturer and individual customer warranties", IIE Transactions, 30, p. 1181 (1998).
6. Chun, Y.H. and Tang, K. "Cost analysis of warranty policies based on the product usage rate", IEEE Transactions on Engineering Management, 46, pp. 201-209 (1999).
7. Baik, J., Murthy, D.N.P., and Jack, N. "Twodimensional failure modeling with minimal repair", Naval Research Logistics (NRL), 51, pp. 345-362 (2004).
8. Wu, S. and Longhurst, P. "Optimizing agereplacement and extended non-renewing warranty policies in lifecycle costing", International Journal of Production Economics, 130, pp. 262-267 (2011).
9. Esmaeili, M., Gamchi, N.S., and Asgharizadeh, E. "Three-level warranty service contract among manufacturer, agent and customer: A game-theoretical approach", European Journal of Operational Research, 239, pp. 177-186 (2014).
10. Asgharizadeh, E. and Murthy, D.D. "Service contracts: A stochastic model", Mathematical and Computer Modelling, 31, pp. 11-20 (2000).
11. Bouguerra, S., Chelbi, A., and Rezg, N. "A decision model for adopting an extended warranty under different maintenance policies", International Journal of Production Economics, 135, pp. 840-849 (2012).
12. Chang, W.L., and Lin, J.H. "Optimal maintenance policy and length of extended warranty within the life cycle of products", Computers & Mathematics with Applications, 63, pp. 144-150 (2012).
13. Lam, Y. and Lam, P.K.W. "An extended warranty policy with options open to consumers", European Journal of Operational Research, 131, pp. 514-529 (2001).
14. Hartman, J.C. and Laksana, K. "Designing and pricing menus of extended warranty contracts", Naval Research Logistics (NRL), 56, pp. 199-214 (2009).
15. Salmasnia, A. and Yazdekhasti, A. "A bi-objective model to optimize periodic preventive maintenance strategy during warranty period by considering customer satisfaction", International Journal of System Assurance Engineering and Management, 8, pp. 770- 781 (2017).
16. Kim, C.S., Djamaludin, I., and Murthy, D.N.P. "Warranty and discrete preventive maintenance", Reliability Engineering & System Safety, 84, pp. 301-309 (2004).
17. Park, M., Jung, K.M., and Park, D.H. "A generalized age replacement policy for systems under renewing repair-replacement warranty", IEEE Trans. Reliability, 65, pp. 604-612 (2016).
18. Su, C. and Wang, X. "Optimizing upgrade level and preventive maintenance policy for second-hand products sold with warranty", Proceedings of the Institution of Mechanical Engineers, Journal of Risk and Reliability, 228, pp. 518-528 (2014).
19. Huang, Y.S., Huang, C.D., and Ho, J.W. "A customized two-dimensional extended warranty with preventive maintenance", European Journal of Operational Research, 257(3), pp. 971-978 (2017).
20. Darghouth, M.N., Ait-Kadi, D., and Chelbi, A. "Joint optimization of design, warranty and price for products sold with maintenance service contracts", Reliability Engineering & System Safety, 165, pp. 197-208 (2017).
21. DeCroix, G.A. "Optimal warranties, reliabilities and prices for durable goods in an oligopoly", European Journal of Operational Research, 112, pp. 554-569 (1999).
22. Luciano, E. and Peccati, L. "Capital structure and inventory management: The temporary sale price problem", International Journal of Production Economics,59, pp. 169-178 (1999). 
23. Van der Laan, E. "An NPV and AC analysis of a stochastic inventory system with joint manufacturing and remanufacturing", International Journal of Production Economics, 81, pp. 317-331 (2003).
24. Disney, S.M., Warburton, R.D., and Zhong, Q.C. "Net present value analysis of the economic production quantity", IMA Journal of Management Mathematics, 24, pp. 423-435 (2013).
25. Lin, J., Pulido, J., and Asplund, M. "Reliability analysis for preventive maintenance based on classical and Bayesian semi-parametric degradation approaches using locomotive wheel-sets as a case study", Reliability Engineering & System Safety, 134, pp. 143-156 (2015).
26. Teng, H.M. "Extended warranty pricing considering the time of money", Journal of Information and Optimization Sciences, 27, pp. 401-409 (2006).
27. Kijima, M., Morimura, H., and Suzuki, Y. "Periodical replacement problem without assuming minimal repair", European Journal of Operational Research, 37, pp. 194-203 (1988).
28. Kijima, M. "Some results for repairable systems with general repair", Journal of Applied Probability, 26, pp. 89-102 (1989).
29. Wright, T.P. "Factors affecting the cost of airplanes", Journal of Aeronautical Sciences, 3, pp. 122-128 (1936).
30. Salmasnia, A., Bashiri, M., and Salehi, M. "A robust interactive approach to optimize correlated multiple responses", The International Journal of Advanced Manufacturing Technology, 67(5-8), pp. 1923-1935 (2013).
31. Salmasnia, A., Kaveie, M., and Namdar, M. "An integrated production and maintenance planning model under VP-T2 Hotelling chart", Computers & Industrial Engineering, 118, pp. 89-103 (2018).
32. Salmasnia, A., Namdar, M., and Noroozi, M. "Robust design of a VP-NCS chart for joint monitoring mean and variability in series systems under maintenance policy", Computers & Industrial Engineering, 124, pp. 220-236 (2018).
33. Foumani, M., Razeghi, A., and Smith-Miles, K. "Stochastic optimization of two-machine flow shop robotic cells with controllable inspection times: From theory toward practice", Robotics and Computer- Integrated Manufacturing, 61, p. 101822 (2020).
34. Chen, J.A. and Chien, Y.H. "Renewing warranty and preventive maintenance for products with failure penalty post-warranty", Quality and Reliability Engineering International, 23, pp. 107-121 (2007).
35. Chien, Y.H. "Optimal age-replacement policy under an imperfect renewing free-replacement warranty", IEEE Transactions on Reliability, 57, pp. 125-133 (2008). 
36. Jack, N., Iskandar, B.P., and Murthy, D.P. "A repairreplace strategy based on usage rate for items sold with a two-dimensional warranty", Reliability Engineering & System Safety, 94, pp. 611-617 (2009).
37. Shafiee, M. and Chukova, S. "Maintenance models in warranty: A literature review", European Journal of Operational Research, 229, pp. 561-572 (2013).
38. Wang, J., Zhou, Z., and Peng, H. "Flexible decision models for a two-dimensional warranty policy with periodic preventive maintenance", Reliability Engineering & System Safety, 162, pp. 14-27 (2017).