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Optimal price, warranty length and production rate for free replacement policy in the static demand market

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  • Wu, Chin-Chun
  • Chou, Chao-Yu
  • Huang, Chikong

Abstract

In the present paper, a decision model is developed for producers in the static demand market to determine the optimal price, warranty length and production rate of a product to maximize profit based on the pre-determined life cycle. The free renewal warranty policy is considered under which failed products are renewed before the end of warranty length at no cost to consumers. The expected number of renewals based on warranty length is derived for Weibull life distributed products. The objective function includes both demand and cost functions, where production cost, warranty cost and inventory cost are involved. A solution approach using the maximum principle is described, and is applied to two specific cases of markets. The first case of market considers positive discount rate, and the second case of market considers zero discount rate. The economic sensitivity analysis is conducted to evaluate the effect of model parameters on the optimal solution. Some conclusions are drawn based on the sensitivity analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jomega:v:37:y:2009:i:1:p:29-39
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    2. Ateka Banu & Shyamal Kumar Mondal, 2018. "An integrated inventory model with warranty dependent credit period under two policies of a manufacturer," OPSEARCH, Springer;Operational Research Society of India, vol. 55(3), pages 677-702, November.
    3. Wei Xie, 2017. "Optimal pricing and two-dimensional warranty policies for a new product," International Journal of Production Research, Taylor & Francis Journals, vol. 55(22), pages 6857-6870, November.
    4. Adkins, Roger & Paxson, Dean, 2013. "Deterministic models for premature and postponed replacement," Omega, Elsevier, vol. 41(6), pages 1008-1019.
    5. Rezapour, Shabnam & Allen, Janet K. & Mistree, Farrokh, 2016. "Reliable flow in forward and after-sales supply chains considering propagated uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 93(C), pages 409-436.
    6. 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, Elsevier, vol. 239(1), pages 177-186.
    7. Prasanta Kumar Ghosh & Amalesh Kumar Manna & Jayanta Kumar Dey & Samarjit Kar, 2023. "Optimal production run in an imperfect production process with maintenance under warranty and product insurance," OPSEARCH, Springer;Operational Research Society of India, vol. 60(2), pages 720-752, June.
    8. Glock, Christoph H. & Grosse, Eric H., 2021. "The impact of controllable production rates on the performance of inventory systems: A systematic review of the literature," European Journal of Operational Research, Elsevier, vol. 288(3), pages 703-720.
    9. 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.
    10. Zhu, Xiaoyan & Jiao, Can & Yuan, Tao, 2019. "Optimal decisions on product reliability, sales and promotion under nonrenewable warranties," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
    11. Lo, Hui-Chiung & Yu, Rouh-Yun, 2013. "A study of quality management strategy for reused products," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 172-177.
    12. 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.
    13. Hooti, Fatemeh & Ahmadi, Jafar & Longobardi, Maria, 2020. "Optimal extended warranty length with limited number of repairs in the warranty period," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    14. Jianhua Ma & Xingzheng Ai & Wen Yang & Yanchun Pan, 2019. "Decentralization versus coordination in competing supply chains under retailers’ extended warranties," Annals of Operations Research, Springer, vol. 275(2), pages 485-510, April.
    15. Prashant M. Ambad & Makarand S. Kulkarni, 2017. "A goal programming approach for multi-objective warranty optimization," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(4), pages 842-861, December.
    16. 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.
    17. Luo, Ming & Wu, Shaomin, 2018. "A mean-variance optimisation approach to collectively pricing warranty policies," International Journal of Production Economics, Elsevier, vol. 196(C), pages 101-112.
    18. Kirkizoğlu, Zeynep & Karaer, Özgen, 2022. "After-sales service and warranty decisions of a durable goods manufacturer," Omega, Elsevier, vol. 113(C).
    19. Arda Yenipazarli, 2015. "A road map to new product success: warranty, advertisement and price," Annals of Operations Research, Springer, vol. 226(1), pages 669-694, March.
    20. Nazzal, Dima & Batarseh, Ola & Patzner, Joshua & Martin, Darren R., 2013. "Product servicing for lifespan extension and sustainable consumption: An optimization approach," International Journal of Production Economics, Elsevier, vol. 142(1), pages 105-114.
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