Managing Inventory Of Items with Replacement Warranty Vidyadhar Kulkarni * Joint Work with Wei Huang ** , Jayashankar Swaminathan * * University of North Carolina at Chapel Hill **SAS Inc. Cary, NC
Managing Inventory Of Items with Replacement Warranty Vidyadhar Kulkarni * Joint Work with Wei Huang **, Jayashankar Swaminathan * * University of North.
Jan 13, 2016
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Managing Inventory Of Items with Replacement Warranty
Vidyadhar Kulkarni*
Joint Work with Wei Huang**, Jayashankar Swaminathan*
* University of North Carolina at Chapel Hill**SAS Inc. Cary, NC
Warranty?!
Motivation• Digital projector company:
electrical, mechanical and optical parts.
New Demand
0
2000
4000
6000
8000
10000
12000
month
un
it
Demand fromNew Customer
Demand for Warranty Repairs
0
50
100
150
200
250
300
350
400
Oct-
02
Dec-0
2
Feb-0
3
Apr-0
3
Jun-
03
Aug-0
3
Oct-
03
Dec-0
3
month
un
it
Demand forWarranty Repair
•The demand for warranty repairs is significant compared to the new demand. (More than 15% in some periods.)
Current Policy
• The inventory replenishment strategy of the digital projector company: make inventory control policy depending on the new demand alone, and satisfy the warranty repair demand by inventory left on hand.– Suffers the high penalty cost for unsatisfied
demand of warranty repair, which directly causes shortage of inventory for new product demand as well.
• Manage the complex service parts challenges with a costly, “just order more parts” strategy.
Research Questions
• Develop an integrated inventory policy to simultaneously account for new and warranty parts
• Discounted cost and long-run average cost• Backlogging and emergency supply• Benefits of tracking the age of items under
warranty• Evaluate the cost benefits of such approaches
Model Settings
warranty expiration ratio warranty duration K
backlogs emergency supply backlogs emergency supply
finite discounted
infinite discounted
long-run average
finite discounted
finite discounted
infinite discounted
long-run average
finite discounted
age-independent failure age-dependent failure
Problem Structure
Manufacturer(w,x)
CustomerCustomer
Customer
Customer
Customernew product
Out of warranty
demand for new productdemand for warranty repairproduct warranty expires
? how much to order
failed product
product out of warranty
Model Parameters
Model Description and Assumptions
Proportional Model with Discounting (Finite Horizon)
Proportional Model with Discounting (Finite Horizon)
Proportional Model with Discounting (Finite Horizon)
Proportional Model with Discounting (Finite Horizon)
Proportional Model with Discounting (Finite Horizon)
Special Case: i.i.d Demand
Proportional Model with Discounting (Infinite Horizon)
Proportional Model Average Cost
Proportional Model with Emergency Supply
Proportional Model with Emergency Supply
Extensions: Pro-rata Policy
Extensions: Warranty Expiration Model
Extensions: Warranty Expiration Model
Computational Study: Cost Improvement
c=2, h=0.05, N=100, N=1000
C_standard
edC_integratC_standard
Cost Improvement for Different Failure Rate
0
10
20
30
40
50
60
70
80
0.01 0.05 0.1 0.15 0.2 0.25 0.3
Failure Rate
Per
cen
tag
e o
f C
ost
Im
pro
vem
ent
p=8
p=10
p=12
Computational Study: Cost Improvement
Cost Improvement with Stock-Out Penalty Cost
0
10
20
30
40
50
60
70
80
8 10 12 15 20 25 30
Stock-Out Penalty Cost
Per
cent
age
of C
ost I
mpr
ovem
ent
beta=0.01
beta=0.05
beta=0.1
Computational Study: Value of Information• Integrated policy VS. Approximate policy
• Approximate policy: base stock policy with base stock level
• Maximum improvement: 12.3%; Average improvement: 3%
Computational Study: Value of Information
Computational Study: Value of Information
Computational Study: Value of Information
Computational Study: Value of Information
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