Extended warranty policies with consumer’s options

1. Extended warranty policies with consumer’s options Prof. Dr. AlagarRangan Vahid.H Khiabani Department of Industrial Engineering Eastern Mediterranean University North Cyprus

2. Outline • Introduction to warranty policies • Cost Analysis of Warranty Policies by Nguyen and Murthy • An extended warranty policy with options open to consumers by Yeh Lam and Peggo Kwok Wai Lam • Extended warranty policies with consumers options ongoing work • Some remarks

3. Introduction What is the Warranty? • A warranty is a contractual obligation incurred by a manufacturer in connection with the sale of a product. • It is a item replacement or free item repair when the product fails to perform its intended function under normal use. • On the other hand , product warranty is the degree of willingness that the manufacturer will be responsible for any unexpected failure of their products. • From the consumer’s point of view ,product warranty is a compensation or remedy from the manufacturer, in the form of money-back guarantee. • Extensive warranties may increase the sale of the product.

4. FRW & PRW: • In practice , two broad classes of policies have been studied so far . • Free replacement warranty (FRW) provides product replacement or repair by the manufacturer , at no cost to the consumer for a limited period of time from the time of initial purchase. • Under a Pro-rata warranty (PRW) , the defective product is not replaced free of charge but a cost proportional to the working age of the product.

5. Free replacement warranty (FRW) w • Pro-rata warranty (PRW) w purchase failure

6. It seems that FRW is favorable to consumer at the expense of manufacturer while PRW protects manufacturer from full liability to replace free of charge near the end of the warranty period. • Therefore, a composite policy consisting of FRW for the period initially , followed by an extended period of under PRW was suggested by Nguyen and Murthy(“Cost Analysis of Warranty Policies,” Naval Research Logistics Quarterly, VOl. 31, pp. 525-541(1984)) .

7. Analysis of Policy І The warranty is renewed only after each purchase (failure outside the free replacement period) w w+T Y purchase :failure

8. The warranty is renewed after each failure Analysis of Policy ІІ w w w w w+T purchase :failure

9. The extended warranty model • An extended warranty policy with options open to consumers was suggested by Yeh Lam and Peggo Kwok Wai Lam I (“An extended warranty policy with options open to consumers was suggested,” European Journal of Operational Research, 131 , (2001) , 514-529)

10. The extended warranty model • In practice , many products , especially the home appliances, are sold with an extended warranty policy for which some options are available for the consumers at the expiry time W of the FRW. • Two cost criteria will be considered in turn : the expected discounted cost and long-run average cost per unit time.

11. The extended warranty model • Assumption 1. A repairable item is purchased at time 0 with an FRW on time period .Let X1 be operating time before the first failure and Xi , i=2,3,…, denote the operating times of the item after completion of the (i – 1)th repair. Then the total operating time of the item just before the nth failure given by , with . They assume that the repair is perfect , after repair the item is “as good as new” and the repair time is negligible. X2 Xi X1 S(i -1) 0 S1 S2 S(i)

12. The extended warranty model • The distribution function of X1 is denoted by F . The distribution function of is denoted by . Furthermore it is the number of failures of the item in the interval . Since forms a renewal process , we can define the renewal function .

13. The extended warranty model • Assumption 2. Under the extended warranty policy , the manufacturer agrees to repair a failed item free of charge in the period . At time W , the manufacturer offers a consumer one of the two options: 1. A renewal cost CN of the warranty contract is payable to the manufacturer at time W , in return the manufacturer repairs the failed item at no cost to the consumer for an extended warranty period L , so the consumer can renew the warranty at time W+L again by paying the same renewal cost CN and so on. CR CN CN CN W+2L 0 W W+L

14. The extended warranty model 2.The warranty expires at time W . Manufacturer claims no responsibility to repair the item after time W. Moreover , repair cost CP will be paid by consumer each time the item fails and is repaired by manufacturer. CR CP CP CP 0 W :failure

15. The extended warranty model • Assumption 3. A consumer will have the following possible policies: 1. K-renewal policy : renew the warranty contract at time W for an extended period L and then renew the warranty contract at time W+iL for another period of length L , i=1,….,k-1 . Then , replace the item by an identical new one at the time W+ kL . Replace 0 W W+L W+2L W+(k-1)L W+kL

16. The extended warranty model 2. K-repair policy : do not renew the warranty , but repair for k times and then replace the item by an identical new one at the time of the (k+1)th failure after the warranty period W. Assume that at once a consumer chooses a policy , she/he will take the same policy forever , and a replacement is finished instantaneously. Repair Replace 0 W 1 2 3 K K+1

17. The extended warranty model • Assumption 4.(Costs) • The initial purchase price or the replacement cost to the consumer is CR. • The production cost per item to manufacturer is Cr. • Let the repair cost incurred by the manufacturer be Cp ,it includes shipping , labor , administrative cost etc. • The cost for renewal of warranty contract is denoted by CN. • The repair cost paid by the consumer when the warranty is not renewed is CP , which is paid every time the item fails and is repaired.

18. The extended warranty model In practice , regardless of the terms of any warranty , the production cost Cr should be cheaper than the purchase price CR , the repair cost Cp incurred by the manufacturer should be lower than the repair cost CP paid by the consumer. On the other hand , the cost CN due to renewal of the warranty or the repair cost CP should not be larger than the initial purchase price CR. The reason behind this is trivial . Otherwise , the consumer will simply buy a new item or even choose an updated one when the item fails.

19. Table 1 Consumer’s optimal policy – Average cost case conditions consumer’s optimal policy Minimum consumer’s AV cost

20. Sincefrom Wald’s equationO2D2 is the line Figure 1 The discounted cost is given by Table 2 conditions consumer’s optimal policy Minimum consumer’s AV cost

21. Figure 2 Table 3 conditions consumer’s optimal policy Manufacturer’s average cost

22. Some remarks • First, they point out that the results for both cost criteria are comparable.(0-repair, -renewal, -repair). • In practice, Cr, CR, W, L are fairly fixed in the market by competitive force among the manufacturers. However, the manufacturer can choose the parameters CP, CN flexibly. As the consumers are intelligent, we should assume that they will apply the optimal policy. Then the manufacturer can make the optimal decision in choosing the values of CP and CN based on this assumption. Of course, this is a conservative but more reasonable assumption. Otherwise, if a consumer does not use the optimal policy, the manufacturer will incur a smaller cost and gain higher profits.

23. Some remarks If lies on a common boundaries, it will be indifferent for a consumer to apply two policies, but the according costs to the manufacturer are different . At the critical point Di, i=1,2, a consumer even has three indifferent policies. Therefore, an -optimal policy for the manufacturer is then introduced. It is interesting that an optimal policy or an -optimal policy for the manufacturer is always around the critical point Di, i=1,2. • One important result is that the optimal manufacturer’s policy may not exist. This is due to the existence of the common boundaries OiDi, DiEi and DiFi, i=1,2, in Figs. 1 and 2.

24. Extended warranty policies with consumers options • Major Repair • Minimal Repair :Major failure 0 t+x t 0 :Minor failure 0 t t+x

25. Type I failure Minor with probability q • Type II failure Major with probability p    0 t1 t2 t3 t     X

26. Policy I • Without warranty 0 x  

28. Policy II • Fixed warranty 0 w

29. Policy III Policy a • With warranty options 0   w   Policy b kth 0   w   Policy c 0   w  

30. Cost analysis policy a 0   w  

32. Cost analysis policy b kth 0   w  

34. Cost analysis policy c 0   w  

36. Profit • Average profit per unit time for manufacturer is given by : P3 P2 P1

37. Some remarks • We have considered two type of repairs.we can also consider different kinds of repairs, like general repair so that consumer can have greater flexibility. (Alagar Rangan and Timothy I. Matis(“Optimal Price and Pro-Rata Decisions for combined Warranty Policies with Different Repair Options” IIE transactions, (2008)) . • Most of the literature deal only with a fixed type of warranty where as our work enables consumers new options of warranty at the end of warranty period. • Policies like this will put the consumer in a better condition, because at the end of the fixed warranty consumer can decide which policy is better or not.

38. Thank you for your time and attention