![](bg2.png)
marketplace for products such as cell-phones, com-
puters, and projectors. Two-dimensional warranties
apply to products that display wear and tear, degra-
dation with usage. Automobiles, aircraft and heavy-
duty machinery are examples of products with 2-D
warranty policies. It is common to see car advertise-
ments stating coverage of 60 months, 120 000 kilo-
metres which ever occurs first.
Some basic warranty types are the Free replace-
ment (FRW), Pro-rata (PRW), and Rebate warranty.
1. Free replacement warranty (FRW): The manu-
facturer agrees to repair/replace a failed item du-
ring the warranty period at no charge to the custo-
mer. Example: small household appliances, elec-
tronics.
2. Pro-rata warranty (PRW): The customer covers
a proportion of the repair cost prorated to the age
of the item at failure. Example: Tires.
3. Rebate warranty: The seller agrees to refund
some proportion of the sale price to the buyer,
if the product fails during the warranty period.
The refund amount may be a linear or non-linear
function of the failure time. Example: Money
back Guarantee for electronic components such as
hard drives, computer screens, and storage devi-
ces.
A basic taxonomy of warranty policies is presen-
ted by (Blischke, 1993; Blischke, 1995). An in-
tegrated warranty-maintenance taxonomy based on
three categories ,i.e. product type, warranty policy,
and maintenance strategy, is proposed in (Shafiee and
Chukova, 2013).
Hybrid (combination) warranties are designed
to utilize the desirable characteristics of the pure
warranties and downplay some of their drawbacks
(Blischke, 1993; Blischke, 1995). The combination
warranty gives the buyer full protection against
full liability for later failures, where the buyer has
received nearly the full amount of service that was
guaranteed under the warranty. It has a significant
promotional value to the seller while at the same time
providing adequate control over costs for both buyer
and seller. An example for hybrid warranty is seen
in the FRW/PRW policy offered on Firestone tires.
During the first 2 years of service, the tire is replaced
free of charge. Beyond year 2, the replacement
price is pro-rated based on years of service from
the original purchase date. Some advantages of
combination warranties are improved protection
towards the product, customer satisfaction, higher
ownership lifetime for the buyers and higher sales
volume to increase profit to manufacturers.
Combination warranty is a good type of war-
ranty for second-hand products (SHPs) as its offers a
good protection to both manufacturers and consumers
(Chari, 2015). Two main problems faced by the con-
sumers acquiring SHPs are their uncertainty and du-
rability (Shafiee and Chukova, 2013) due to the lack
of past usage and maintenance history. In order to re-
duce the risk and impact of product malfunctioning,
dealers offer generous warranty policies. A review of
warranty models currently available in the literature
for SHPs show that there are very few of them and all
deal with the manufacturers perspective (Shafiee and
Chukova, 2013; Chari et al., 2016b; Su and Wang,
2016; Diallo et al., 2016). The goal of this article is to
address this shortcoming by proposing a warranty po-
licy and develop mathematical models from both the
manufacturer and consumer perspectives.
2 OPTIMAL COMBINATION
WARRANTY MODELS USING
SHPS
For most warranty policies, failed products are re-
paired or replaced with new components or products.
In the context of remanufacturing, second-hand pro-
ducts may be available and can therefore be re-used as
replacements when consumers return failed products
(Yeh et al., 2005; Yeh et al., 2011; Chari et al., 2016a).
In doing so, the manufacturers can lower their costs
and consumers can extend their ownership of the pro-
ducts. However, due to the lower reliability of SHP,
it is crucial to determine the optimal parameters of
the warranty policy to be offered to avoid higher costs
to the manufacturer and less than anticipated perfor-
mance/ownership time for the consumer. In this ar-
ticle, we will develop two mathematical models for
a combination rebate warranty policy using SHPs as
replacement products.
2.1 Proposed Warranty Policy
Under the proposed warranty policy, a brand new pro-
duct is sold with a total warranty coverage period of
length w. Under this policy, the seller will replace a
defective product with:
• A new product if the failure occurs before w
1
(Phase 0);
• A refurbished product of high quality if the failure
occurs between w
1
and w
2
(Phase 1);
• A refurbished product of normal quality if the fai-
lure occurs between w
2
and w
3
(Phase 2).
ICORES 2017 - 6th International Conference on Operations Research and Enterprise Systems
492