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A Study on Extended A Study on Extended Warranty ModelsWarranty Models

Prof. Dr. Alagar Rangan Prof. Dr. Alagar Rangan Vahid.H KhiabaniVahid.H Khiabani

Department of Industrial EngineeringDepartment of Industrial EngineeringEastern Mediterranean University Eastern Mediterranean University

North CyprusNorth Cyprus

OutlineOutline

IntroductionIntroduction Extended Warranty ModelExtended Warranty Model Extended Warranty Model based on Extended Warranty Model based on

Total Sales VolumeTotal Sales Volume Extended Warranty Model based on Extended Warranty Model based on

Total Sales Volume and Customer Total Sales Volume and Customer SatisfactionSatisfaction

Conclusions Conclusions 22

IntroductionIntroduction

A warranty is a contractual obligation that A warranty is a contractual obligation that assures the buyer that the product will assures the buyer that the product will perform its intended function at a perform its intended function at a specified level under the stated conditions specified level under the stated conditions for a specified period of time. If it fails to for a specified period of time. If it fails to do so, the manufacturer will do so, the manufacturer will repair/replace the product at no cost or at repair/replace the product at no cost or at a reduced cost to the buyer as the case a reduced cost to the buyer as the case may be depending on the warranty terms.may be depending on the warranty terms.

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IntroductionIntroduction

The manufacturer uses warranty as a The manufacturer uses warranty as a tool of advertisement in competition tool of advertisement in competition to other products.to other products.

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55A schematic diagram of various warranty policies

IntroductionIntroduction Presently a large number of products are Presently a large number of products are

being sold in the market with long term or being sold in the market with long term or extended warranty policies. This is mainly extended warranty policies. This is mainly due to fierce competition in the market due to fierce competition in the market share and customer demand. An extended share and customer demand. An extended warranty is the extension of the base warranty is the extension of the base warranty and is an obligation on the part of warranty and is an obligation on the part of the manufacturer for further service to the the manufacturer for further service to the consumer beyond the free replacement consumer beyond the free replacement period W.period W.

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IntroductionIntroduction

On average 27% of the new car buyer’s On average 27% of the new car buyer’s purchased extended warranty. purchased extended warranty.

Sears Roebuck reported a revenue Sears Roebuck reported a revenue generation of nearly US $1 billion from generation of nearly US $1 billion from the sale of extended warranties. the sale of extended warranties.

The annual sale of extended warranties The annual sale of extended warranties in UK alone is more than US $1 billion.in UK alone is more than US $1 billion.

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Literature ReviewLiterature Review

Blishke and Murthy (1994), Anisur and Blishke and Murthy (1994), Anisur and Chattopadhyay (2006), and Thomas and Rao Chattopadhyay (2006), and Thomas and Rao (1999)(1999)

Nguyen and Murthy (1984 and 1986)Nguyen and Murthy (1984 and 1986) Mamer (1982)Mamer (1982) Sahin and Polatoglu (1996) Sahin and Polatoglu (1996) Amit Monga and Ming J.Zuo (1998) Amit Monga and Ming J.Zuo (1998)

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Literature ReviewLiterature Review

Mitra and Patnakar (1997) Mitra and Patnakar (1997) Lutz and Padmanabhan (1998) Lutz and Padmanabhan (1998) Hollis (1999) Hollis (1999) Yeh Lam and Peggo Kwok Wai Lam Yeh Lam and Peggo Kwok Wai Lam

(2001)(2001)

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The ModelThe Model

A repairable product is purchased at A repairable product is purchased at time t=0 which is subject to failures. time t=0 which is subject to failures. The times between successive failures The times between successive failures are independently and identically are independently and identically distributed with distribution function F distributed with distribution function F (·). Failures are classified as type I and (·). Failures are classified as type I and type II failures with probabilities q and type II failures with probabilities q and p respectively. p respectively.

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The ModelThe Model

Type I failures are minor in nature Type I failures are minor in nature and can be minimally repaired and can be minimally repaired (Barlow and Proschan, 1965) (Barlow and Proschan, 1965) restoring the product to its original restoring the product to its original condition just prior to failure. If a condition just prior to failure. If a product is minimally repaired at time product is minimally repaired at time t, then its failure rate after minimal t, then its failure rate after minimal repair is given by repair is given by

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(t)F

f(t)r(t)

The ModelThe Model

Also it is well-known that if product Also it is well-known that if product failures are maintained by minimal failures are maintained by minimal repairs only, then the failures are repairs only, then the failures are governed by a non-homogeneous governed by a non-homogeneous Poisson process with intensity Poisson process with intensity function r (t). A type II failure is major function r (t). A type II failure is major and necessitates product and necessitates product replacement. replacement.

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The Model Major RepairMajor Repair

Minimal RepairMinimal Repair

0

0

t+xt

t t+x

0

:Minor failure

:Major failure

The ModelThe Model

The customer at the time of the The customer at the time of the purchase buys the product along with purchase buys the product along with FRW with an option for an extended FRW with an option for an extended warranty policy at the expiry of FRW for warranty policy at the expiry of FRW for an additional cost. The manufacturer an additional cost. The manufacturer while agreeing to replace items on while agreeing to replace items on failure of any type during the FRW failure of any type during the FRW period W offers the following extended period W offers the following extended warranty policies:warranty policies:

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Policy 1 (TPolicy 1 (Tmm))

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0 w

1Y

Policy 2 (TPolicy 2 (Tkk))

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0 w

2Y

12 ,min YTY k

0 w kth

2Y

<k

Policy 3 (T)Policy 3 (T)

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0 w

3Y

0 w W+T

3Y

<T

13 ,min YTY

Cost AnalysisCost Analysis

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Cost AnalysisCost Analysis

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Numerical IllustrationNumerical Illustration

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Numerical IllustrationNumerical Illustration

The reason for writing LAP in the above The reason for writing LAP in the above form is to separate the cost parameters form is to separate the cost parameters under the control of the manufacturer under the control of the manufacturer and the parameters associated with and the parameters associated with product lifetime. product lifetime.

For the specific choice of the cost For the specific choice of the cost parameters not shown here in our case, parameters not shown here in our case, the long run average profits under the long run average profits under different policies are given by:different policies are given by:

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Numerical IllustrationNumerical Illustration

2222

2323

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Optimization Based on Total Optimization Based on Total Sales VolumeSales Volume

We wish to determine the optimal We wish to determine the optimal product price and warranty periods product price and warranty periods based on the total sales volume. The based on the total sales volume. The motivation for choosing such an motivation for choosing such an objective is that sales volume is objective is that sales volume is directly affected by these variables. directly affected by these variables.

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Optimization Based on Total Optimization Based on Total Sales VolumeSales Volume

We assume the expected forecast We assume the expected forecast sales volume q for the product to be sales volume q for the product to be a function of product price , warranty a function of product price , warranty period W and the extended warranty period W and the extended warranty period Yperiod Yii and is assumed to follow and is assumed to follow the displaced log linear functionthe displaced log linear function

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Optimization Based on Total Optimization Based on Total Sales VolumeSales Volume

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Optimization Based on Total Optimization Based on Total Sales VolumeSales Volume

The manufacturer’s total long run The manufacturer’s total long run average profit under the assumed average profit under the assumed demand function is seen to bedemand function is seen to be

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Optimization Based on Total Optimization Based on Total Sales VolumeSales Volume

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In our analysis the extended In our analysis the extended warranty period is fixed once the warranty period is fixed once the model parameters are known. Thus, model parameters are known. Thus, we treat , the extended warranty we treat , the extended warranty period for policy i, as fixed and period for policy i, as fixed and merge it with the amplitude factor so merge it with the amplitude factor so that the total long run average profit that the total long run average profit is is

Optimization Based on Total Optimization Based on Total Sales VolumeSales Volume

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Policy 1

Policy 3Policy 2

EXT Warranty based on EXT Warranty based on T.S.V and Customer T.S.V and Customer

SatisfactionSatisfaction Each dissatisfied customer can impact future Each dissatisfied customer can impact future

sales in several ways and this has serious cost sales in several ways and this has serious cost implications for the manufacturer. implications for the manufacturer.

Though customer satisfaction with a Though customer satisfaction with a purchased product is influenced by several purchased product is influenced by several reasons including product price and after sale reasons including product price and after sale service, the main factor that attracts service, the main factor that attracts (detracts) a customer to return to buy the (detracts) a customer to return to buy the product again is its performance over the product again is its performance over the warranty and extended warranty periods.warranty and extended warranty periods.

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EXT Warranty based on EXT Warranty based on T.S.V and Customer T.S.V and Customer

SatisfactionSatisfaction Existing warranty models in the literature Existing warranty models in the literature

mainly focus on minimizing total warranty mainly focus on minimizing total warranty cost to optimize for warranty period and cost to optimize for warranty period and maintenance strategies; however they fail maintenance strategies; however they fail to take into consideration the penalty cost to take into consideration the penalty cost of customer’s non return in computing of customer’s non return in computing their objective functions as such a penalty their objective functions as such a penalty seems to play a major rule. seems to play a major rule. Lasser et alLasser et al. . (1998), (1998), Jack and MurthyJack and Murthy (2004) (2004)

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EXT Warranty based on EXT Warranty based on T.S.V and Customer T.S.V and Customer

SatisfactionSatisfaction We assume that the customer We assume that the customer

satisfaction of the product depends satisfaction of the product depends on the number of major failures on the number of major failures during the warranty and extended during the warranty and extended warranty periods. It is tacitly warranty periods. It is tacitly assumed that the customer’s assumed that the customer’s satisfaction is not influenced by satisfaction is not influenced by minor failures. minor failures.

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EXT Warranty based on EXT Warranty based on T.S.V and Customer T.S.V and Customer

SatisfactionSatisfaction If W is the FRW and T is the extended If W is the FRW and T is the extended

warranty period, the customer warranty period, the customer satisfaction depends on Nsatisfaction depends on N22(W+T), the (W+T), the number major failures in W+T. We number major failures in W+T. We assume that the conditional probability assume that the conditional probability function of customer return given function of customer return given NN22(W+T) = k is specified as follows:(W+T) = k is specified as follows:

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EXT Warranty based on EXT Warranty based on T.S.V and Customer T.S.V and Customer

SatisfactionSatisfaction

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Other forms for the customer Other forms for the customer dissatisfaction depending on the dissatisfaction depending on the product could be chosen. For product could be chosen. For instance when the customer is highly instance when the customer is highly sensitive to failures of the product, sensitive to failures of the product, one can choose to be:one can choose to be:

EXT Warranty based on EXT Warranty based on T.S.V and Customer T.S.V and Customer

SatisfactionSatisfaction Let be the probability of exactly k Let be the probability of exactly k

major failures during the warranty major failures during the warranty and extended warranty period for our and extended warranty period for our extended warranty model. Then the extended warranty model. Then the probability Pprobability Prr of the customer making of the customer making a repurchase of the product is given a repurchase of the product is given by: by:

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EXT Warranty based on EXT Warranty based on T.S.V and Customer T.S.V and Customer

SatisfactionSatisfaction

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Let CLet Cpp be the penalty cost to the be the penalty cost to the manufacturer for a dissatisfied manufacturer for a dissatisfied customer not returning to repurchase customer not returning to repurchase the product, then the manufacturer’s the product, then the manufacturer’s total profit function given in previous total profit function given in previous section can be rewritten as: section can be rewritten as:

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Policy 2

Policy 1

Policy 3

ConclusionConclusion

The present work develops a new The present work develops a new extended warranty model with extended warranty model with different options for the consumer.different options for the consumer.

Several extensions and Several extensions and generalizations are possible from generalizations are possible from here on, and in the following we will here on, and in the following we will spell out a few of them:spell out a few of them:

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Different types of failuresDifferent types of failures p and q functions of the time p and q functions of the time

General repairGeneral repair Alternate forms of demand functionAlternate forms of demand function Optimal burn in period Optimal burn in period Preventive maintenancesPreventive maintenances Other factors that influence the product Other factors that influence the product

sales sales 4141

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