JIA Yun-xian(賈云獻(xiàn)), LI Xin-yue(李欣玥)* , WANG Hong-mei(王紅梅)

1 Department of Management Engineering, Mechanical Engineering College, Shijiazhuang 050003, China 2 College of foreign languages, Hebei University of Economics and Business, Shijiazhuang 050003, China

Optimal Extended Warranty Policies under Different Maintenance Options

JIA Yun-xian(賈云獻(xiàn))1, LI Xin-yue(李欣玥)1*, WANG Hong-mei(王紅梅)2

1DepartmentofManagementEngineering,MechanicalEngineeringCollege,Shijiazhuang050003,China2Collegeofforeignlanguages,HebeiUniversityofEconomicsandBusiness,Shijiazhuang050003,China

Extended warranty has recently obtained increasing attention from both manufacturers and customers in China. In this paper, given the reality of China, two types of non-renewing extended warranty was proposed: one-dimensional extended warranty and two-dimensional extended warranty. And a combined warranty policy including pro-rata warranty policy and free-repair warranty policy was applied in these two types of warranty. Then the expected life-cycle cost models from the manufacturer and consumer’s perspectives were developed considering different maintenance options. The optimal warranty policy, maintenance options, and warranty price were adopted in terms of a win-win interval which was determined by the maximum extra cost the consumer should pay and the minimum price the manufacture should sell at the extended warranty. Finally, a case study were given to prove the effectiveness and validity of the model.

one-dimensionalextendedwarranty;two-dimensionalextendedwarranty;free-repairwarranty;pro-ratawarranty;preventivemaintenance(PM);win-wininterval

Introduction

A warranty is a contract in which the manufacturers are required to offer protection to customers against early product failures[1-2]. Blischke and Murthy[3]concluded that warranty could be divided into basic warranty and extended warranty. Extended warranty is the extension of the basic warranty with a given extra cost paid by the consumers. And the choice of whether providing or purchasing extended warranty exerts great influence on the total life cycle cost from the both perspectives of manufacturers and customers. In China, along with the fierce competition, the warranty service plays more important role in product choice. More and more manufactures are inclined to give customers a chance to buy extended warranty. However, although the Product Quality Law of China specified the manufacturer has responsibility to provide three guarantees (repair, replacement or compensation of faulty product) to customers in the extended warranty period, there’re still lots of problems when the manufacturers implement their obligation in the warranty period. As a result, the Complaint Department of China Association for Quality Promotion (CAQP) has been receiving successive complaints from the unsatisfied customers. The complaint statistical report in March of 2013 published by CAQP is shown in Fig.1[4].

Fig.1 Complaint report in March of 2013

The way to improve the embarrassing situation is that the manufacturers in China should provide suitable warranty contract to the customers. Obviously, it is urgent that the method of a finding suitable extended warranty policy should be developed considering both parties’ profit given the reality of Chinese industry. So in this paper, we mainly focus on the extended warranty policy, and consider two types of non-renewing extended warranty (one-dimensional extended warranty and two-dimensional extended warranty) with four different maintenance options. The combined warranty policy which includes free-repair warranty policy and pro-rata warranty policy is applied to developing the expected total cost models from the two perspectives to find the win-win cost interval. We use preventive maintenance (PM) to avoid product failure which can make the customer more satisfied. And the cost of PM actions is shared by the customer and the manufacturer which can incentivize the manufacturers.

1 Mathematical Model

1.1 Notation and hypothesis

(1)

Table 1 Number of PM actions over each interval

Note: ?*」means Integer part of a real number

(2)

1.2 The maximum extra extended warranty cost from the perspective of the consumer

(3)

(4)

Options III:

(5)

Option IV:

(6)

1.3 The minimum extended warranty price from the perspective of the manufacturer

Option I:

(7)

Option II:

(8)

Options III:

(9)

Options IV:

(10)

2 Numerical Example

We consider the same input data used by Bouguerraetal[8]. What must be stressed here is that we assume the effect of PM is reduction of the item’s age, so nine discrete levels of PM along with their corresponding costs are considered as shown in Table 2.

Table 2 Improving factor θ(m) and the corresponding cost Cm (RMB)

Andris gamma distributed withαandβas the shape and scale parameters whereα=4 andβ=3.33 (Huang and Yen[10]). Supposingr0=0.16 and Δ=0.33, select three typical levels of PM to analyze the models. The numeric results are shown in Table 3. A compromise pricing zone only exists for the extended warranty cost when the maximum buying extra cost for the consumer is higher than the minimum selling price for the manufacturer.

Table 3 Win-win intervals for extended warranty cost

(a) (b)

Obviously, the best compromise price of the extended warranty would be the middle of the win-win interval. The results shown in Table 3 are as follows (1) For Option I, the optimal price of the extended warranty is unique. (2) For Option II, the optimal price of the one-dimensional extended warranty is unique. However, the win-win interval for the two-dimensional extended warranty exists. So the two-dimensional extended warranty of Option II can provide more opportunities for the customers and the manufacturers to select/offer the extended warranty. And the value of the unique optimal extended cost as well as the win-win interval for the two-dimensional extended warranty cost becomes small as PM level increases. (3) For Option III, the win-win interval for the one-dimensional extended warranty can increase the interest of the customer and the manufacturer, but the win-win interval for the two-dimensional extended warranty doesn’t exist. And the one-dimensional win-win interval for the extended warranty cost becomes large as PM level increases. Figure 2 shows the one-dimensional and two-dimensional extended cost considering nine discrete levels of PM in the case of Option III. The costs of the consumer and the manufacturer are shown together in Fig.2(a). Figure 2(b) shows the two-dimensional extended cost considering nine discrete levels of PM of Option III. (4) In most situations, the one-dimensional win-win interval is higher than the two-dimensional win-win interval. However, the two-dimensional win-win interval in the case of Option IV is different. The two-dimensional win-win interval sometimes is higher than the one-dimensional win-win interval.

3 Conclusions

We focus on the research of extended warranty policies in regard to the present Chinese industry and the perspectives of both the consumers and the manufacturers. Two extended warranty policies with different maintenance options are presented and analyzed. The corresponding expected total cost models are presented to study the possibility provided by the extended warranty for the buyer as well as the manufactures. The conditions of the existence of a win-win interval are derived. The obtained numerical results show that many factors can affect the variation of the optimal price of the extended warranty.

[1] Shafiee M, Chukova S. Maintenance Models in Warranty: a Literature Review[J].EuropeanJournalofOperationalResearch, 2013, 229(3): 561-572.

[2] Shafiee M, Finkelstein M, Zuo M J. Optimal Burn-in and Preventive Maintenance Warranty Strategies with Time-Dependent Maintenance Costs[J].IIETransactions, 2013, 45(9): 1024-1033.

[3] Blischke W R, Murthy D N P. Product Warranty Management-I: a Taxonomy for Warranty Policies[J].EuropeanJournalofOperationalResearch, 1992, 62(2):127-148.

[4] Complaint Department of China Association for Quality Promotion. Manufacture Makes the Warranty Rules by Himself Ingnoring “Three Guarantees Law”-Complaint Report from the Complaint Department of China Association for Quality Promotion[R]. China: 1994-2014 China Academic Journal Electronic Publishing House, 2014: 26-27. (in Chinese)

[5] Ye Z S, Murthy D N P, Xie M,etal. Optimal Burn-in for Repairable Products Sold with a Two-Dimensional Warranty[J].IIETransactions, 2013, 45(2): 164-176.

[6] Blischke W R, Murthy D N P. Product Warranty Handbook[M]. New York: CRC Press, 1996: 305-308.

[7] Doyen L, Gaudoin O. Classes of Imperfect Repair Models Based on Reduction of Failure Intensity or Virtual Age[J].ReliabilityEngineeringandSystemSafety, 2004, 84(1): 45-56.

[8] Bouguerra S, Chelbi A, Rezg N. A Decision Model for Adopting an Extended Warranty under Different Maintenance Policies[J].InternationalProductionofProductionEconomics, 2012, 135(2): 840-849.

[9] Su C, Shen J Y. Analysis of Extended Warranty Policies with Different Repair Options[J].EngineeringFailureAnalysis, 2012, 25: 49-62.

[10] Huang Y S, Yen C. A Study of Two-Dimensional Warranty Policies with Preventive Maintenance[J].IIETransactions, 2009, 41(4): 299-308.

1672-5220(2014)06-0890-05

Received date: 2014-08-08

*Correspondence should be addressed to LI Xin-yue, E-mail: oeclxy@hotmail.com

CLC number: E92; F403.8 Document code: A