Inventory Management and Risk
Pooling (2)
Designing & Managing the Supply Chain
Chapter 3
Byung-Hyun Ha
bhha@pusan.ac.kr
Outline
 Introduction to Inventory Management
 The Effect of Demand Uncertainty




(s,S) Policy
Supply Contracts
Periodic Review Policy
Risk Pooling
 Centralized vs. Decentralized Systems
 Practical Issues in Inventory Management
Supply Contracts
 Assumptions for Swimsuit production
 In-house manufacturing
 Usually, manufactures and retailers
 Supply contracts





Pricing and volume discounts
Minimum and maximum purchase quantities
Delivery lead times
Product or material quality
Product return policies
Supply Contracts
 Condition
Fixed Production Cost =$100,000
Variable Production Cost=$35
Wholesale Price =$80
Selling Price=$125
Salvage Value=$20
Manufacturer
Manufacturer DC
Retail DC
Stores
Demand Scenario and Retailer Profit
30%
25%
20%
15%
10%
5%
0%
80
00
10
00
0
12
00
0
14
00
0
16
00
0
18
00
0
Probability
Demand Scenarios
Sales
Expected Profit
500000
400000
300000
200000
100000
0
6000
8000
10000
12000
14000
Order Quantity
16000
18000
20000
Demand Scenario and Retailer Profit
 Sequential supply chain




Retailer optimal order quantity is 12,000 units
Retailer expected profit is $470,700
Manufacturer profit is $440,000
Supply Chain Profit is $910,700
 Is there anything that the distributor and
manufacturer can do to increase the profit of both?
 Global optimization?
Buy-Back Contracts
 Buy back=$55
$513,800
500,000
400,000
300,000
200,000
100,000
0
retailer
600,000
500,000
$471,900
400,000
300,000
200,000
100,000
0
60
00
70
00
80
00
90
00
10
00
0
11
00
0
12
00
0
13
00
0
14
00
0
15
00
0
16
00
0
17
00
0
18
00
0
Order Quantity
Manufacturer Profit
60
00
70
00
80
00
90
00
10
00
0
11
00
0
12
00
0
13
00
0
14
00
0
15
00
0
16
00
0
17
00
0
18
00
0
Retailer Profit
600,000
Production Quantity
manufacturer
Buy-Back Contracts
 Sequential supply chain




Retailer optimal order quantity is 12,000 units
Retailer expected profit is $470,700
Manufacturer profit is $440,000
Supply Chain Profit is $910,700
 With buy-back contracts




Retailer optimal order quantity is 14,000 units
Retailer expected profit is $513,800
Manufacturer expected profit is $471,900
Supply Chain Profit is $985,700
 Manufacture sharing some of risk!
Revenue-Sharing Contracts
 Wholesale Price from $80 to $60, RS 15%
$504,325
500,000
400,000
Supply Chain Profit is
$985,700
300,000
200,000
100,000
0
60
00
70
00
80
00
90
00
10
00
0
11
00
0
12
00
0
13
00
0
14
00
0
15
00
0
16
00
0
Manufacturer Profit
17
00
0
18
00
0
700,000
Order Quantity
retailer
600,000
500,000
$481,375
400,000
300,000
200,000
100,000
0
60
00
70
00
80
00
90
00
10
00
0
11
00
0
12
00
0
13
00
0
14
00
0
15
00
0
16
00
0
17
00
0
18
00
0
Retailer Profit
600,000
Production Quantity
manufacturer
Other Types of Supply Contracts
 Quantity-flexibility contracts
 Supplier providing full refund for returned (unsold) items up to a
certain quantity
 Sales rebate contracts
 Direct incentive to retailer by supplier for any item sold above a
certain quantity
 …
 Consult Cachon 2002
Global Optimization
 What is the most profit both the supplier and the
buyer can hope to achieve?
 Assume an unbiased decision maker
 Transfer of money between the parties is ignored
 Allowing the parties to share the risk!
 Marginal profit=$90, marginal loss=$15
 Optimal production quantity=16,000
1,000,000
$1,014,500
800,000
600,000
400,000
200,000
0
60
00
70
00
80
00
90
00
10
00
0
11
00
0
12
00
0
13
00
0
14
00
0
15
00
0
16
00
0
17
00
0
18
00
0
 Decision-making power
 Allocating profit
Supply Chain Profit
 Drawbacks
1,200,000
Production Quantity
Global Optimization
 Revised buy-back contracts
 Wholesale price=$75, buy-back price=$65
 Global optimum
 Equilibrium point!
 No partner can improve his profit by deciding to deviate from the
optimal decision
 Consult Ch14 of Winston, “Game theory”
 Key Insights
 Effective supply contracts allow supply chain partners to replace
sequential optimization by global optimization
 Buy Back and Revenue Sharing contracts achieve this objective
through risk sharing
Supply Contracts: Case Study
 Example: Demand for a movie newly released video
cassette typically starts high and decreases rapidly
 Peak demand last about 10 weeks
 Blockbuster purchases a copy from a studio for $65
and rent for $3
 Hence, retailer must rent the tape at least 22 times before
earning profit
 Retailers cannot justify purchasing enough to cover
the peak demand
 In 1998, 20% of surveyed customers reported that they could not
rent the movie they wanted
Supply Contracts: Case Study
 Starting in 1998 Blockbuster entered a revenuesharing agreement with the major studios
 Studio charges $8 per copy
 Blockbuster pays 30-45% of its rental income
 Even if Blockbuster keeps only half of the rental
income, the breakeven point is 6 rental per copy
 The impact of revenue sharing on Blockbuster was
dramatic
 Rentals increased by 75% in test markets
 Market share increased from 25% to 31% (The 2nd largest
retailer, Hollywood Entertainment Corp has 5% market share)
A Multi-Period Inventory Model
 Situation
 Often, there are multiple reorder opportunities
 A central distribution facility which orders from a manufacturer
and delivers to retailers
• The distributor periodically places orders to replenish its inventory
 Reasons why DC holds inventory
 Satisfy demand during lead time
 Protect against demand uncertainty
 Balance fixed costs and holding costs
Continuous Review Inventory Model
 Assumptions





Normally distributed random demand
Fixed order cost plus a cost proportional to amount ordered
Inventory cost is charged per item per unit time
If an order arrives and there is no inventory, the order is lost
The distributor has a required service level
• expressed as the likelihood that the distributor will not stock out
during lead time.
 Intuitively, how will the above assumptions effect our
policy?
 (s, S) Policy
 Whenever the inventory position drops below a certain level (s)
we order to raise the inventory position to level S
Reminder: The Normal Distribution
Standard Deviation = 5
Standard Deviation = 10
Average = 30
0
10
20
30
40
50
60
A View of (s, S) Policy
S
Inventory Level
Inventory Position
Lead
Time
s
0
Time
(s, S) Policy
 Notations






AVG = average daily demand
STD = standard deviation of daily demand
LT = replenishment lead time in days
h = holding cost of one unit for one day
K = fixed cost
SL = service level (for example, 95%)
• The probability of stocking out is 100% - SL (for example, 5%)
 Policy
 s = reorder point, S = order-up-to level
 Inventory Position
 Actual inventory + (items already ordered, but not yet delivered)
(s, S) Policy - Analysis
 The reorder point (s) has two components:
 To account for average demand during lead time:
LTAVG
 To account for deviations from average (we call this safety
stock)
zSTDLT
where z is chosen from statistical tables to ensure that the
probability of stock-outs during lead-time is 100% - SL.
 Since there is a fixed cost, we order more than up to
the reorder point:
Q=(2KAVG)/h
 The total order-up-to level is:
S=Q+s
(s, S) Policy - Example
 The distributor has historically observed weekly demand of:
AVG = 44.6
STD = 32.1
 Replenishment lead time is 2 weeks, and desired service level
SL = 97%
 Average demand during lead time is: 44.6  2 = 89.2
 Safety Stock is: 1.88  32.1  2 = 85.3
 Reorder point is thus 175, or about 3.9 weeks of supply at
warehouse and in the pipeline
 Weekly inventory holding cost: .87
 Therefore, Q=679
 Order-up-to level thus equals:
 Reorder Point + Q = 176+679 = 855
Periodic Review
 Periodic review model
 Suppose the distributor places orders every month
 What policy should the distributor use?
 What about the fixed cost?
 Base-Stock Policy
r
r
Inventory Level
Base-stock
Level
L
L
L
Inventory
Position
0
Time
Periodic Review
 Base-Stock Policy
 Each review echelon, inventory position is raised to the basestock level.
 The base-stock level includes two components:
• Average demand during r+L days (the time until the next order
arrives):
(r+L)*AVG
• Safety stock during that time:
z*STD* r+L
Risk Pooling
 Consider these two systems:
 For the same service level, which system will require more
inventory? Why?
 For the same total inventory level, which system will have better
service? Why?
 What are the factors that affect these answers?
Warehouse One
Market One
Warehouse Two
Market Two
Supplier
Market One
Supplier
Warehouse
Market Two
Risk Pooling Example
 Compare the two systems:





two products
maintain 97% service level
$60 order cost
$.27 weekly holding cost
$1.05 transportation cost per unit in decentralized system, $1.10
in centralized system
 1 week lead time
Week
1
2
3
4
5
6
7
8
Prod A,
Market 1
Prod A,
Market 2
Prod B,
Market 1
Product B,
Market 2
33
45
37
38
55
30
18
58
46
35
41
40
26
48
18
55
0
2
3
0
0
1
3
0
2
4
0
0
3
1
0
0
Risk Pooling Example
 Risk Pooling Performance
Warehouse Product AVG
STD CV
s
S
Market 1
A
39.3
13.2 .34
65
197
Avg.
%
Inven. Dec.
91
Market 2
A
38.6
12.0 .31
62
193
88
Market 1
B
1.125 1.36 1.21 4
29
14
Market 2
B
1.25
29
15
Cent.
Cent
A
B
77.9 20.7 .27
2.375 1.9 .81
1.58 1.26 5
118 304
6
39
132
20
36%
43%
Risk Pooling: Important Observations
 Centralizing inventory control reduces both safety
stock and average inventory level for the same
service level.
 This works best for
 High coefficient of variation, which increases required safety
stock.
 Negatively correlated demand. Why?
 What other kinds of risk pooling will we see?
Inventory in Supply Chain
 Centralized Distribution Systems
 How much inventory should
management keep at each location?
 A good strategy:
 The retailer raises inventory to level Sr
each period
 The supplier raises the sum of
inventory in the retailer and supplier
warehouses and in transit to Ss
 If there is not enough inventory in the
warehouse to meet all demands from
retailers, it is allocated so that the
service level at each of the retailers will
be equal.
Supplier
Warehouse
Retailers
Inventory Management
 Best Practice






Periodic inventory reviews
Tight management of usage rates, lead times and safety stock
ABC approach
Reduced safety stock levels
Shift more inventory, or inventory ownership, to suppliers
Quantitative approaches
Forecasting
 Recall the three rules
 Nevertheless, forecast is critical
 General Overview:




Judgment methods
Market research methods
Time Series methods
Causal methods
Judgment Methods
 Assemble the opinion of experts
 Sales-force composite combines salespeople’s
estimates
 Panels of experts – internal, external, both
 Delphi method
 Each member surveyed
 Opinions are compiled
 Each member is given the opportunity to change his opinion
Market Research Methods
 Particularly valuable for developing forecasts of
newly introduced products
 Market testing
 Focus groups assembled.
 Responses tested.
 Extrapolations to rest of market made.
 Market surveys
 Data gathered from potential customers
 Interviews, phone-surveys, written surveys, etc.
Time Series Methods
 Past data is used to estimate future data
 Examples include
 Moving averages – average of some previous demand points.
 Exponential Smoothing – more recent points receive more
weight
 Methods for data with trends:
• Regression analysis – fits line to data
• Holt’s method – combines exponential smoothing concepts with the
ability to follow a trend
 Methods for data with seasonality
• Seasonal decomposition methods (seasonal patterns removed)
• Winter’s method: advanced approach based on exponential
smoothing
 Complex methods (not clear that these work better)
Causal Methods
 Forecasts are generated based on data other than
the data being predicted
 Examples include:





Inflation rates
GNP
Unemployment rates
Weather
Sales of other products