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A value-at-risk approach to optimisation of warranty policy

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  • Luo, Ming
  • Wu, Shaomin

Abstract

In the real world, a manufacturer may produce many products, which may have common components installed. Consequently, the frequencies of the warranty claims of those products are statistically dependent. Warranty policy optimisation in the existing research, however, has not considered such statistical dependence, which may increase bias in decision making. This paper is the first attempt to collectively optimises warranty policy for a set of different products, produced by one manufacturer, whose failures are statistically dependent, using tools borrowed from financial mathematics (i.e., value-at-risk theory and copula). We prove the existence of the optimal solutions for different scenarios. Numerical examples are used to validate the applicability of the proposed methods.

Suggested Citation

  • Luo, Ming & Wu, Shaomin, 2018. "A value-at-risk approach to optimisation of warranty policy," European Journal of Operational Research, Elsevier, vol. 267(2), pages 513-522.
    • Handle: RePEc:eee:ejores:v:267:y:2018:i:2:p:513-522
    DOI: 10.1016/j.ejor.2017.11.062
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    1. Babaei, Sadra & Sepehri, Mohammad Mehdi & Babaei, Edris, 2015. "Multi-objective portfolio optimization considering the dependence structure of asset returns," European Journal of Operational Research, Elsevier, vol. 244(2), pages 525-539.
    2. Bernard, Carole & Vanduffel, Steven, 2015. "A new approach to assessing model risk in high dimensions," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 166-178.
    3. Wu, Shaomin, 2014. "Construction of asymmetric copulas and its application in two-dimensional reliability modelling," European Journal of Operational Research, Elsevier, vol. 238(2), pages 476-485.
    4. Liu, Bin & Wu, Jun & Xie, Min, 2015. "Cost analysis for multi-component system with failure interaction under renewing free-replacement warranty," European Journal of Operational Research, Elsevier, vol. 243(3), pages 874-882.
    5. R. Ahmadi, 2016. "An optimal replacement policy for complex multi-component systems," International Journal of Production Research, Taylor & Francis Journals, vol. 54(17), pages 5303-5316, September.
    6. Bai, Jun & Pham, Hoang, 2006. "Cost analysis on renewable full-service warranties for multi-component systems," European Journal of Operational Research, Elsevier, vol. 168(2), pages 492-508, January.
    7. Wu, Shaomin, 2014. "Warranty return policies for products with unknown claim causes and their optimisation," International Journal of Production Economics, Elsevier, vol. 156(C), pages 52-61.
    8. Chen, Cheng-Kang & Lo, Chih-Chung & Weng, Tzu-Chun, 2017. "Optimal production run length and warranty period for an imperfect production system under selling price dependent on warranty period," European Journal of Operational Research, Elsevier, vol. 259(2), pages 401-412.
    9. Ye, Zhi-Sheng & Murthy, D.N. Pra, 2016. "Warranty menu design for a two-dimensional warranty," Reliability Engineering and System Safety, Elsevier, vol. 155(C), pages 21-29.
    10. Adkins, Roger & Paxson, Dean, 2017. "Replacement decisions with multiple stochastic values and depreciation," European Journal of Operational Research, Elsevier, vol. 257(1), pages 174-184.
    11. Wu, Chin-Chun & Chou, Chao-Yu & Huang, Chikong, 2009. "Optimal price, warranty length and production rate for free replacement policy in the static demand market," Omega, Elsevier, vol. 37(1), pages 29-39, February.
    12. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    13. Lei, Yong & Liu, Qian & Shum, Stephen, 2017. "Warranty pricing with consumer learning," European Journal of Operational Research, Elsevier, vol. 263(2), pages 596-610.
    14. Seyed Ahmad Yazdian & Kamran Shahanaghi & Ahmad Makui, 2016. "Joint optimisation of price, warranty and recovery planning in remanufacturing of used products under linear and non-linear demand, return and cost functions," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(5), pages 1155-1175, April.
    15. Boubaker, Heni & Sghaier, Nadia, 2013. "Portfolio optimization in the presence of dependent financial returns with long memory: A copula based approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 361-377.
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    Cited by:

    1. Park, Minjae & Jung, Ki Mun & Park, Dong Ho, 2020. "Warranty cost analysis for second-hand products under a two-stage repair-or-full refund policy," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    2. Deprez, Laurens & Antonio, Katrien & Boute, Robert, 2021. "Pricing service maintenance contracts using predictive analytics," European Journal of Operational Research, Elsevier, vol. 290(2), pages 530-545.
    3. Luo, Ming & Wu, Shaomin, 2019. "A comprehensive analysis of warranty claims and optimal policies," European Journal of Operational Research, Elsevier, vol. 276(1), pages 144-159.
    4. Liu, Xiang-dong & Pan, Fei & Cai, Wen-li & Peng, Rui, 2020. "Correlation and risk measurement modeling: A Markov-switching mixed Clayton copula approach," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    5. Yang, Li & Ye, Zhi-sheng & Lee, Chi-Guhn & Yang, Su-fen & Peng, Rui, 2019. "A two-phase preventive maintenance policy considering imperfect repair and postponed replacement," European Journal of Operational Research, Elsevier, vol. 274(3), pages 966-977.
    6. Lijun Shang & Guojun Shang & Yongjun Du & Qingan Qiu & Li Yang & Qinglai Dong, 2022. "Post-Warranty Replacement Models for the Product under a Hybrid Warranty," Mathematics, MDPI, vol. 10(10), pages 1-18, May.
    7. Yongjun Du & Lijun Shang & Qingan Qiu & Li Yang, 2022. "Optimum Post-Warranty Maintenance Policies for Products with Random Working Cycles," Mathematics, MDPI, vol. 10(10), pages 1-16, May.
    8. Deprez, Laurens & Antonio, Katrien & Boute, Robert, 2023. "Empirical risk assessment of maintenance costs under full-service contracts," European Journal of Operational Research, Elsevier, vol. 304(2), pages 476-493.
    9. Liu, Bin & Pandey, Mahesh D. & Wang, Xiaolin & Zhao, Xiujie, 2021. "A finite-horizon condition-based maintenance policy for a two-unit system with dependent degradation processes," European Journal of Operational Research, Elsevier, vol. 295(2), pages 705-717.
    10. Huang, Hongfu & Liu, Feng & Zhang, Peng, 2021. "To outsource or not to outsource? Warranty service provision strategies considering competition, costs and reliability," International Journal of Production Economics, Elsevier, vol. 242(C).
    11. Wang, Xiaolin & Li, Lishuai & Xie, Min, 2020. "An unpunctual preventive maintenance policy under two-dimensional warranty," European Journal of Operational Research, Elsevier, vol. 282(1), pages 304-318.
    12. Lu, Ziqiang & Zhu, Yuanguo & Li, Bo, 2019. "Critical value-based Asian option pricing model for uncertain financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 694-703.
    13. Lu, Zhen & Shang, Jennifer, 2019. "Warranty mechanism for pre-owned tech products: Collaboration between E-tailers and online warranty provider," International Journal of Production Economics, Elsevier, vol. 211(C), pages 119-131.

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