性能式质保政策设计与优化研究

doi:10.16381/j.cnki.issn1003-207x.2022.1350

摘要/Abstract

摘要：

性能式质保是近年来复杂产品售后服务领域出现的全新商业模式。在该模式下，制造商对产品性能进行保障以提升用户满意度。因此，追求高性能成为制造商与用户的共同目标。同时，新一代信息通信技术的飞速发展也为实时监控产品性能创造了条件。为进一步优化用户的使用体验，降低频繁维修给用户带来的停机损失，本文提出了一种考虑维修次数限制的性能式质保政策设计与优化方法。在所提出的性能式质保政策中，若产品关键性能退化到性能保证阈值时，制造商将根据产品的失效时间实施更换或非完美维修。若质保期内的维修次数超过规定限值，制造商还需对用户进行赔偿。基于此，本文首先建立了更换-维修策略下的关键性能退化过程，得出了期望质保成本。其次，以制造商利润最大化为目标，构建了性能式质保政策设计与优化模型，并利用Nelder-Mead方法得出最优产品价格、质保期长度与性能保证阈值。研究结果表明，与传统质保政策相比，性能式质保政策可协助制造商获取更高的利润。此外，通过对关键参数的分析发现，对于制造商而言，延缓产品退化速率、降低单次维修成本以及合理选择更换区间，对于提升利润起到了关键作用。

关键词: 质保政策设计, 性能退化, 维修策略, 质保成本

Abstract:

In recent years， performance-based warranty has become a new business model in the field of after-sales market for complex products. Under a performance-based warranty， manufacturers guarantee the product performance to enhance customer satisfaction. Therefore， the pursuit of high performance has become the common goal of manufacturers and users. At the same time， the rapid development of the new generation of information and communication technology has created conditions for real-time monitoring of product performance. In order to further optimize the user experience and reduce the downtime loss caused by frequent maintenance， a performance-based warranty policy design and optimization method is proposed with repair number limit. Under the proposed performance-based warranty policy， if the actual performance level hits the performance guarantee level， the manufacturer will implement replacement or imperfect repair according to the failure time of the product. Additionally， if the number of repairs exceeds the specified limit， the manufacturer is also required to compensate the user. Based on that， the critical performance degradation process is established with a replacement-maintenance strategy and the expected warranty cost is derived. Then， a performance-based warranty policy optimization model is constructed with the goal of maximizing the manufacturer’s profit. The Nelder-Mead method is used to obtain the optimal product price， warranty period length and performance guarantee level. The results show that the performance-based warranty policy can help the manufacturer to obtain higher profits compared with the traditional warranty policy. In addition， the analysis of the key parameters revealed that for manufacturers， slowing down the rate of product degradation， reducing the cost per repair and choosing a reasonable replacement interval play a key role in increasing profits.

Key words: warranty policy design, performance deterioration, maintenance strategy, warranty cost

中图分类号:

C934

戴安舒, 罗智, 孙桂莲, 王鑫. 性能式质保政策设计与优化研究[J]. 中国管理科学, 2025, 33(3): 186-195.

Anshu Dai, Zhi Luo, Guilian Sun, Xin Wang. Design and Optimization of a Performance-based Warranty Policy-Considering Limited Maintenance Number[J]. Chinese Journal of Management Science, 2025, 33(3): 186-195.

图/表 7

图 1

表1

M=2,3,4下的最优质保政策（利润单位：106元）"

$M$	$W *$	$l d *$ （%）	$S p *$	$П *$	$E C Ω$	$Q$
$M = 2$
性能式质保政策	$7.2$	$66.9$	$38468$	$331.23$	$1486$	$15069$
传统质保政策	$9.1$	$-$	$38430$	$326.43$	$1381$	$14945$
$M = 3$
性能式质保政策	$7.1$	$66.8$	$38317$	$321.47$	$1422$	$14681$
传统质保政策	$9.0$	$-$	$38177$	$315.77$	$1361$	$14474$
$M = 4$
性能式质保政策	6.9	67.4	$38245$	$315.17$	$1390$	$14421$
传统质保政策	8.6	-	$37645$	$308.88$	$1133$	$14358$

表1

表2

M=2下的最优质保政策（利润单位：106元）"

$μ$	$q$	性能式质保政策				传统质保政策
$μ$	$q$	$W *$	$l d *$ （%）	$S p *$	$П *$	$W *$	$l d *$	$S p *$	$П *$
$0.05$	$0.3$	$7.5$	$69.1$	$37844$	$345.64$	$10.6$	$-$	$38091$	$339.90$
	$0.6$	$8.5$	$67.6$	$38557$	$346.06$	$11.2$	$-$	$38683$	$340.51$
	$0.9$	$8.9$	$67.7$	$39044$	$346.84$	$11.3$	$-$	$38637$	$341.23$
$0.06$	$0.3$	$7.1$	$66.6$	$38359$	$330.98$	$8.9$	$-$	$38180$	$325.93$
	$0.6$	$7.2$	$66.9$	$38468$	$331.23$	$9.1$	$-$	$38430$	$326.43$
	$0.9$	$7.3$	$66.7$	$38542$	$331.62$	$9.5$	$-$	$38763$	$327.12$
$0.07$	$0.3$	$6.6$	$64.7$	$38664$	$317.65$	$7.5$	$-$	$37950$	$314.50$
	$0.6$	$6.7$	$65.0$	$38850$	$317.91$	$7.6$	$-$	$38033$	$314.72$
	$0.9$	$7.1$	$64.3$	$39037$	$318.14$	$8.1$	$-$	$38714$	$315.25$

表2

表3

M=3下的最优质保政策（利润单位：106元）"

$μ$	$q$	性能式质保政策				传统质保政策
$μ$	$q$	$W *$	$l d *$ (%)	$S p *$	$П *$	$W *$	$l d *$	$S p *$	$П *$
$0.05$	$0.3$	$7.6$	$69.3$	$38054$	$335.44$	$10.9$	$-$	$38302$	$328.50$
	$0.6$	$7.5$	$69.2$	$37964$	$335.46$	$10.9$	$-$	$38287$	$328.50$
	$0.9$	$7.4$	$69.2$	$37818$	$335.46$	$10.8$	$-$	$38227$	$328.54$
$0.06$	$0.3$	$7.0$	$67.2$	$38345$	$321.41$	$8.9$	$-$	$38065$	$315.75$
	$0.6$	$7.1$	$66.8$	$38317$	$321.47$	$9.0$	$-$	$38177$	$315.77$
	$0.9$	$7.0$	$67.4$	$38391$	$321.49$	$9.2$	$-$	$38479$	$315.70$
$0.07$	$0.3$	$6.4$	$65.7$	$38759$	$308.81$	$7.6$	$-$	$38096$	$305.15$
	$0.6$	$6.4$	$65.6$	$38625$	$308.82$	$7.4$	$-$	$37784$	$305.14$
	$0.9$	$6.5$	$65.5$	$38698$	$308.90$	$7.5$	$-$	$37945$	$305.18$

表3

表4

M=4下的最优质保政策（利润单位：106元）"

$μ$	$q$	性能式质保政策				传统质保政策
$μ$	$q$	$W *$	$l d *$ （%）	$S p *$	$П *$	$W *$	$l d *$	$S p *$	$П *$
$0.05$	$0.3$	$7.4$	$69.5$	$37869$	$328.70$	$10.6$	$-$	$37986$	$320.83$
	$0.6$	$7.4$	$69.7$	$37903$	$328.68$	$10.3$	$-$	$37664$	$320.79$
	$0.9$	$7.3$	$69.9$	$37865$	$328.65$	$10.9$	$-$	$37639$	$320.74$
$0.06$	$0.3$	$6.7$	$68.0$	$38236$	$315.14$	$8.8$	$-$	$37645$	$308.88$
	$0.6$	$6.7$	$67.6$	$38083$	$315.12$	$8.8$	$-$	$37888$	$308.89$
	$0.9$	$6.9$	$67.4$	$38275$	$315.16$	$9.1$	$-$	$37948$	$308.89$
$0.07$	$0.3$	$6.2$	$65.6$	$38331$	$303.03$	$7.6$	$-$	$37929$	$298.96$
	$0.6$	$6.1$	$66.0$	$38379$	$303.00$	$7.7$	$-$	$37809$	$298.99$
	$0.9$	$6.2$	$65.8$	$38480$	$303.05$	$7.5$	$-$	$37644$	$298.96$

表4

表5

不同Dt下的最优质保政策（利润单位：106元）"

$D t$	$W *$				传统质保政策
$D t$	$W *$	$l d *$ (%)	$S p *$	$П *$	$W *$	$l d *$	$S p *$	$П *$
$0$	$6.6$	$69.0$	$38357$	$332.51$	$9.1$	$-$	$38337$	$326.46$
$2$	$6.4$	$69.7$	$38204$	$332.55$	$9.1$	$-$	$38276$	$326.49$
$4$	$7.2$	$66.9$	$38468$	$331.23$	$9.0$	$-$	$38430$	$326.43$
$6$	$9.0$	$61.6$	$39613$	$322.94$	$9.6$	$-$	$39546$	$322.57$

表5

表6

不同Cm和Cr下的最优质保政策（利润单位：106元）"

$C m$	$C r$	性能式质保政策				传统质保政策
$C m$	$C r$	$W *$	$l d *$ (%)	$S p *$	$П *$	$W *$	$l d *$	$S p *$	$П *$
$8000$	$20000$	$7.1$	$66.8$	$38468$	$331.23$	$9.0$	$-$	$38430$	$326.43$
	$25000$	$7.2$	$66.3$	$38386$	$330.57$	$9.0$	$-$	$38275$	$326.24$
	$30000$	$7.3$	$65.8$	$38386$	$330.03$	$8.9$	$-$	$38177$	$325.95$
$12000$	$20000$	$6.6$	$66.3$	$38097$	$326.88$	$8.4$	$-$	$38080$	$322.11$
	$25000$	$6.8$	$66.2$	$38350$	$326.38$	$8.1$	$-$	$37776$	$321.94$
	$30000$	$6.9$	$65.5$	$38290$	$325.95$	$8.1$	$-$	$37702$	$321.85$
$16000$	$20000$	$6.0$	$67.4$	$38043$	$323.70$	$7.8$	$-$	$37811$	$318.83$
	$25000$	$6.3$	$66.4$	$38090$	$323.18$	$7.6$	$-$	$37562$	$318.75$
	$30000$	$6.4$	$65.3$	$37736$	$322.65$	$7.5$	$-$	$37380$	$318.64$

表6

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