A Study on Extended Warranty Models. Prof. Dr. Alagar Rangan Vahid.H Khiabani Department of Industrial Engineering Eastern Mediterranean University North Cyprus. Outline. Introduction Extended Warranty Model Extended Warranty Model based on Total Sales Volume
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A Study on Extended Warranty Models Prof. Dr. Alagar Rangan Vahid.H Khiabani Department of Industrial Engineering Eastern Mediterranean University North Cyprus
Outline • Introduction • Extended Warranty Model • Extended Warranty Model based on Total Sales Volume • Extended Warranty Model based on Total Sales Volume and Customer Satisfaction • Conclusions
Introduction • A warranty is a contractual obligation that assures the buyer that the product will perform its intended function at a specified level under the stated conditions for a specified period of time. If it fails to do so, the manufacturer will repair/replace the product at no cost or at a reduced cost to the buyer as the case may be depending on the warranty terms.
Introduction • The manufacturer uses warranty as a tool of advertisement in competition to other products.
Introduction • Presently a large number of products are being sold in the market with long term or extended warranty policies. This is mainly due to fierce competition in the market share and customer demand. An extended warranty is the extension of the base warranty and is an obligation on the part of the manufacturer for further service to the consumer beyond the free replacement period W.
Introduction • On average 27% of the new car buyer’s purchased extended warranty. • Sears Roebuck reported a revenue generation of nearly US $1 billion from the sale of extended warranties. • The annual sale of extended warranties in UK alone is more than US $1 billion.
Literature Review • Blishke and Murthy (1994), Anisur and Chattopadhyay (2006), and Thomas and Rao (1999) • Nguyen and Murthy (1984 and 1986) • Mamer (1982) • Sahin and Polatoglu (1996) • AmitMonga and Ming J.Zuo (1998)
Literature Review • Mitra and Patnakar (1997) • Lutz and Padmanabhan (1998) • Hollis (1999) • Yeh Lam and Peggo Kwok Wai Lam (2001)
The Model • A repairable product is purchased at time t=0 which is subject to failures. The times between successive failures are independently and identically distributed with distribution function F (·). Failures are classified as type I and type II failures with probabilities q and p respectively.
The Model • Type I failures are minor in nature and can be minimally repaired (Barlow and Proschan, 1965) restoring the product to its original condition just prior to failure. If a product is minimally repaired at time t, then its failure rate after minimal repair is given by
The Model • Also it is well-known that if product failures are maintained by minimal repairs only, then the failures are governed by a non-homogeneous Poisson process with intensity function r (t). A type II failure is major and necessitates product replacement.
The Model • Major Repair • Minimal Repair :Major failure 0 t+x t 0 :Minor failure 0 t t+x
The Model • The customer at the time of the purchase buys the product along with FRW with an option for an extended warranty policy at the expiry of FRW for an additional cost. The manufacturer while agreeing to replace items on failure of any type during the FRW period W offers the following extended warranty policies:
Policy 1 (Tm) 0 w
Policy 2 (Tk) 0 w <k 0 w kth
Policy 3 (T) 0 w <T 0 w W+T
Numerical Illustration • The reason for writing LAP in the above form is to separate the cost parameters under the control of the manufacturer and the parameters associated with product lifetime. • For the specific choice of the cost parameters not shown here in our case, the long run average profits under different policies are given by:
Optimization Based on Total Sales Volume • We wish to determine the optimal product price and warranty periods based on the total sales volume. The motivation for choosing such an objective is that sales volume is directly affected by these variables.
Optimization Based on Total Sales Volume • We assume the expected forecast sales volume q for the product to be a function of product price , warranty period W and the extended warranty period Yi and is assumed to follow the displaced log linear function
Optimization Based on Total Sales Volume • The manufacturer’s total long run average profit under the assumed demand function is seen to be
Optimization Based on Total Sales Volume • In our analysis the extended warranty period is fixed once the model parameters are known. Thus, we treat , the extended warranty period for policy i, as fixed and merge it with the amplitude factor so that the total long run average profit is
Optimization Based on Total Sales Volume Policy 1 Policy 3 Policy 2
EXT Warranty based on T.S.V and Customer Satisfaction • Each dissatisfied customer can impact future sales in several ways and this has serious cost implications for the manufacturer. • Though customer satisfaction with a purchased product is influenced by several reasons including product price and after sale service, the main factor that attracts (detracts) a customer to return to buy the product again is its performance over the warranty and extended warranty periods.
EXT Warranty based on T.S.V and Customer Satisfaction • Existing warranty models in the literature mainly focus on minimizing total warranty cost to optimize for warranty period and maintenance strategies; however they fail to take into consideration the penalty cost of customer’s non return in computing their objective functions as such a penalty seems to play a major rule. Lasser et al. (1998), Jack and Murthy (2004)
EXT Warranty based on T.S.V and Customer Satisfaction • We assume that the customer satisfaction of the product depends on the number of major failures during the warranty and extended warranty periods. It is tacitly assumed that the customer’s satisfaction is not influenced by minor failures.
EXT Warranty based on T.S.V and Customer Satisfaction If W is the FRW and T is the extended warranty period, the customer satisfaction depends on N2(W+T), the number major failures in W+T. We assume that the conditional probability function of customer return given N2(W+T) = k is specified as follows:
EXT Warranty based on T.S.V and Customer Satisfaction • Other forms for the customer dissatisfaction depending on the product could be chosen. For instance when the customer is highly sensitive to failures of the product, one can choose to be:
EXT Warranty based on T.S.V and Customer Satisfaction • Let be the probability of exactly k major failures during the warranty and extended warranty period for our extended warranty model. Then the probability Pr of the customer making a repurchase of the product is given by:
EXT Warranty based on T.S.V and Customer Satisfaction • Let Cp be the penalty cost to the manufacturer for a dissatisfied customer not returning to repurchase the product, then the manufacturer’s total profit function given in previous section can be rewritten as:
Policy 1 Policy 2 Policy 3
Conclusion • The present work develops a new extended warranty model with different options for the consumer. • Several extensions and generalizations are possible from here on, and in the following we will spell out a few of them:
Different types of failures • p and q functions of the time • General repair • Alternate forms of demand function • Optimal burn in period • Preventive maintenances • Other factors that influence the product sales
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