Optimal design of sales and maintenance under the renewable warranty
RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 2, pp. 529-542.

This paper presents an integrated model to determine the optimal sales price, preventive maintenance (PM) interval and warranty period with the objective of maximizing the total profit. It is assumed that the sales growth can be featured by NHPP-Bass model over the time. Production cost, R&D cost and warranty cost involving product reliability are considered in this integrated profit model. Then, we consider a periodic PM policy, minimal repair and replacement policy in this paper and the product is deteriorated with the time goes. We also consider effects of the repair time of the repairable product. During the warranty period, manufacturer conducts the PM periodically, and if the repair time is beyond the limited repair time, the failure is replaced with a new product attached renewed warranty period. If not, the failed product is conducted with only minimal repair. Moreover, we give the numerical example and the sensitive analysis to provide insights into the influence of sales price, warranty period and PM interval.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2017077
Classification : 90B25, 90B50, 90C30
Mots clés : Sales price, preventive maintenance, warranty period, total profit, optimization
Jiao, Can 1 ; Zhu, Xiaoyan 1

1
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Jiao, Can; Zhu, Xiaoyan. Optimal design of sales and maintenance under the renewable warranty. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 2, pp. 529-542. doi : 10.1051/ro/2017077. http://archive.numdam.org/articles/10.1051/ro/2017077/

[1] F.M. Bass, A new product growth for model consumer durables. Manag. Sci. 15 (1969) 215–227 | DOI | Zbl

[2] W.R. Blischke, Mathematical models for analysis of warranty policies. Math. Comput. Model. 13 (1990) 1–16 | DOI | Zbl

[3] R. Canfield, Cost optimization of periodic preventive maintenance. IEEE Trans. Reliab. 35 (1986) 78–81 | DOI | Zbl

[4] C.C. Chou, C.Y. Huang and C.K. Huang, Optimal burn–in time and warranty length under fully renewing combination free replacement and pro–rata warranty. Reliability Eng. Syst. Safety. 92 (2007) 914–920 | DOI

[5] G.A. Decroix, Optimal warranties, reliabilities and prices for durable goods in an oligopoly. Eur. J. Oper. Res. 112 (1999) 554–569 | DOI | Zbl

[6] T.S. Glickman and P.D. Berger, Optimal price and protection period decisions for a product under warranty. Manag. Sci. 22 (1976) 1381–1390 | DOI

[7] H.Z. Huang, Z.J. Liu and D.N.P. Murthy, Optimal reliability, warranty and price for new products. IIE Trans. 39 (2007) 819–827 | DOI

[8] Y.S. Huang, W.Y. Gau and J.W. Ho, Cost analysis of two–dimensional warranty for products with periodic preventive maintenance. Reliability Eng. Syst. Safety. 134 (2015) 51–58 | DOI

[9] B. Jiang and X. Zhang, How does a retailers service plan affect a manufacturers warranty? Manag. Sci. 57 (2011) 727–40 | DOI | Zbl

[10] S.P. Ladany and H. Shore, Profit maximizing warranty period with sales expressed by a demand function. Quality Reliability Eng. Int. (2007) 291–301 | DOI

[11] H. Lee and J.H. Cha, New stochastic models for preventive maintenance and maintenance optimization, Eur. J. Oper. Res. 255 (2016) 80–90 | DOI | MR | Zbl

[12] B. Liu, J. Wu and M. Xie, Cost analysis for multi–component system with failure interaction under renewing free–replacement warranty. Eur. J. Oper. Res. 243 (2015) 874–882 | DOI | MR | Zbl

[13] A. Mettas, Reliability Allocation and Optimization for Complex Systems. Reliability & Maintainability Symposium. 30 (2000) 216–221

[14] A. Mitra and J.G. Patankar, Market share and warranty costs for renewable warranty programs. Int. J. Prod. Econ. 50 (1997) 155–168 | DOI

[15] A. Monga and M.J. Zuo, Optimal design of series–parallel systems considering maintenance and salvage value, Comput. Ind. Eng. 40 (2001) 323–337 | DOI

[16] D.N.P. Murthy and I. Djamaludin, New product warranty: A literature review. Int. J. Prod. Econ. 79 (2002) 231–260 | DOI

[17] T. Nakagawa, Sequential imperfect preventive maintenance policies. IEEE Trans. Reliab. 37 (1988) 295–298 | DOI | Zbl

[18] T. Nakagawa and S. Mizutani, A summary of maintenance policies for a finite interval. Reliability Eng. Syst. Safety 94 (2009) 89–96 | DOI

[19] S.C. Niu,A piecewise–diffusion model of new–product demands. Oper. Res. 54 (2006) 678–695 | DOI | MR | Zbl

[20] M. Park,K.M. Jung and D.H. Park, Optimal maintenance strategy under renewable warranty with repair time threshold. Appl. Math. Model. 43 (2017) 498–508 | DOI | MR | Zbl

[21] M. Park and H. Pham, Cost models for age replacement policies and block replacement policies under warranty. Appl. Math. Modell. 40 (2016) 5689–5702 | DOI | MR | Zbl

[22] M.S. Mehrabad, S. Chukova, S.T.A. Niaki and M. Shafiee, Two–dimensional warranty cost analysis for second–hand products. Commun. Stat. - Theor. Method 40 (2011) 684–701 | DOI | MR | Zbl

[23] C. Su and X. Wang, A two–stage preventive maintenance optimization model incorporating two–dimensional extended warranty. Reliability Eng. Syst. Safety 155 (2016) 169–178 | DOI

[24] Washington General Lemon Law. Available at: www.atg.wa.gov (2018)

[25] C.C. Wu, C.Y. Chou and C. Huang, Optimal burn–in time and warranty length under fully renewing combination free replacement and pro–rata warranty. Reliability Eng. Syst. Safety 92 (2007) 914–920 | DOI

[26] C.C. Wu, C.Y. Chou and C. Huang, Optimal price, warranty length and production rate for free replacement policy in the static demand market. Omega 37 (2009) 29–39 | DOI

[27] S. Wu, Warranty claim analysis considering human factors. Reliability Eng. Syst. Safety. 96 (2011) 131–138 | DOI

[28] W. Xie, H. Liao and X. Zhu, Estimation of gross profit for a new durable product considering warranty and post–warranty repairs. IIE Trans. 46 (2014) 87–105 | DOI

[29] L. Yang, X. Ma, R. Peng, Q. Zhai and Yu Zhao, A preventive maintenance policy based on dependent two–stage deterioration and external shocks. Reliability Eng. Syst. Safety 160 (2017) 201–211 | DOI

[30] Z.S. Ye, D.N.P. Murthy, M. Xie and L.C. Tang, Optimal burn–in for repairable products sold with a two–dimensional warranty. IIE Trans. 45 (2013) 164–176 | DOI

[31] X. Zhu and S. Cetinkaya, A stochastic inventory model for an immediate liquidation and price–promotion decision under price–dependent demand. Int. J. Prod. Res. 53 (2015) 3789–3809 | DOI

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