This document discusses inventory management, supply contracts, and risk pooling. It addresses issues like inventory management policies, demand uncertainty, centralized vs decentralized systems, and practical inventory management challenges. It provides an example of calculating optimal order quantity using the economic order quantity model and discusses how demand uncertainty, initial inventory levels, and supply contracts can impact profits. Supply contracts that include a buy-back agreement can increase profits for both manufacturers and distributors by better managing risks from demand uncertainty.

1. Inventory Management,
Supply Contracts and Risk
Pooling
Phil Kaminsky
February 1, 2007
kaminsky@ieor.berkeley.edu

2. Issues
• Inventory Management
• The Effect of Demand Uncertainty
– (s,S) Policy
– Periodic Review Policy
– Supply Contracts
– Risk Pooling
• Centralized vs. Decentralized Systems
• Practical Issues in Inventory Management

3. Customers,
Field demand
Sources: Regional Warehouses: centers
plants Warehouses: stocking sinks
vendors stocking points
ports points
Supply
Inventory &
warehousing
costs
Production/
purchase Transportation Transportation
costs costs costs
Inventory &
warehousing
costs

4. Inventory
• Where do we hold inventory?
– Suppliers and manufacturers
– warehouses and distribution centers
– retailers
• Types of Inventory
– WIP
– raw materials
– finished goods
• Why do we hold inventory?
– Economies of scale
– Uncertainty in supply and demand
– Lead Time, Capacity limitations

5. Goals:
Reduce Cost, Improve Service
• By effectively managing inventory:
– Xerox eliminated $700 million inventory from
its supply chain
– Wal-Mart became the largest retail company
utilizing efficient inventory management
– GM has reduced parts inventory and
transportation costs by 26% annually

6. Goals:
Reduce Cost, Improve Service
• By not managing inventory successfully
– In 1994, “IBM continues to struggle with shortages in
their ThinkPad line” (WSJ, Oct 7, 1994)
– In 1993, “Liz Claiborne said its unexpected earning
decline is the consequence of higher than anticipated
excess inventory” (WSJ, July 15, 1993)
– In 1993, “Dell Computers predicts a loss; Stock
plunges. Dell acknowledged that the company was
sharply off in its forecast of demand, resulting in
inventory write downs” (WSJ, August 1993)

7. Understanding Inventory
• The inventory policy is affected by:
– Demand Characteristics
– Lead Time
– Number of Products
– Objectives
• Service level
• Minimize costs
– Cost Structure

8. Cost Structure
• Order costs
– Fixed
– Variable
• Holding Costs
– Insurance
– Maintenance and Handling
– Taxes
– Opportunity Costs
– Obsolescence

9. EOQ: A Simple Model*
• Book Store Mug Sales
– Demand is constant, at 20 units a week
– Fixed order cost of $12.00, no lead time
– Holding cost of 25% of inventory value
annually
– Mugs cost $1.00, sell for $5.00
• Question
– How many, when to order?

10. EOQ: A View of Inventory*
Note:
• No Stockouts
• Order when no inventory
• Order Size determines policy
Inventory
Order
Size
Avg. Inven
Time

11. EOQ: Calculating Total Cost*
• Purchase Cost Constant
• Holding Cost: (Avg. Inven) * (Holding
Cost)
• Ordering (Setup Cost):
Number of Orders * Order Cost
• Goal: Find the Order Quantity that
Minimizes These Costs:

12. EOQ:Total Cost*
160
140
120 Total Cost
100
Cost
Holding Cost
80
60
40 Order Cost
20
0
0 500 1000 1500
Order Quantity

13. EOQ: Optimal Order Quantity*
• Optimal Quantity =
(2*Demand*Setup Cost)/holding cost
• So for our problem, the optimal quantity is
316

14. EOQ: Important Observations*
• Tradeoff between set-up costs and holding
costs when determining order quantity. In fact,
we order so that these costs are equal per unit
time
• Total Cost is not particularly sensitive to the
optimal order quantity
Order Quantity 50% 80% 90% 100% 110% 120% 150% 200%
Cost Increase 125% 103% 101% 100% 101% 102% 108% 125%

15. The Effect of
Demand Uncertainty
• Most companies treat the world as if it were
predictable:
– Production and inventory planning are based on
forecasts of demand made far in advance of the
selling season
– Companies are aware of demand uncertainty when
they create a forecast, but they design their planning
process as if the forecast truly represents reality
• Recent technological advances have increased
the level of demand uncertainty:
– Short product life cycles
– Increasing product variety

16. Demand Forecast
• The three principles of all forecasting
techniques:
– Forecasting is always wrong
– The longer the forecast horizon the worst is
the forecast
– Aggregate forecasts are more accurate

17. SnowTime Sporting Goods
• Fashion items have short life cycles, high variety
of competitors
• SnowTime Sporting Goods
– New designs are completed
– One production opportunity
– Based on past sales, knowledge of the industry, and
economic conditions, the marketing department has a
probabilistic forecast
– The forecast averages about 13,000, but there is a
chance that demand will be greater or less than this.

18. Supply Chain Time Lines
Jan 00 Jan 01 Jan 02
Design Production Retailing
Feb 00 Sep 00 Feb 01 Sep 01
Production

19. SnowTime Demand Scenarios
Demand Scenarios
Probability
30%
25%
20%
15%
10%
5%
0%
0
0
0
0
0
00
00
00
00
00
00
80
10
12
14
16
18
Sales

20. SnowTime Costs
• Production cost per unit (C): $80
• Selling price per unit (S): $125
• Salvage value per unit (V): $20
• Fixed production cost (F): $100,000
• Q is production quantity, D demand
• Profit =
Revenue - Variable Cost - Fixed Cost + Salvage

21. SnowTime Scenarios
• Scenario One:
– Suppose you make 12,000 jackets and demand ends
up being 13,000 jackets.
– Profit = 125(12,000) - 80(12,000) - 100,000 =
$440,000
• Scenario Two:
– Suppose you make 12,000 jackets and demand ends
up being 11,000 jackets.
– Profit = 125(11,000) - 80(12,000) - 100,000 +
20(1000) = $ 335,000

22. SnowTime Best Solution
• Find order quantity that maximizes
weighted average profit.
• Question: Will this quantity be less than,
equal to, or greater than average
demand?

23. What to Make?
• Question: Will this quantity be less than,
equal to, or greater than average
demand?
• Average demand is 13,100
• Look at marginal cost Vs. marginal profit
– if extra jacket sold, profit is 125-80 = 45
– if not sold, cost is 80-20 = 60
• So we will make less than average

24. SnowTime Expected Profit
Expected Profit
$400,000
$300,000
Profit
$200,000
$100,000
$0
8000 12000 16000 20000
Order Quantity

25. SnowTime Expected Profit
Expected Profit
$400,000
$300,000
Profit
$200,000
$100,000
$0
8000 12000 16000 20000
Order Quantity

26. SnowTime:
Important Observations
• Tradeoff between ordering enough to meet
demand and ordering too much
• Several quantities have the same average profit
• Average profit does not tell the whole story
• Question: 9000 and 16000 units
lead to about the same average
profit, so which do we prefer?

27. SnowTime Expected Profit
Expected Profit
$400,000
$300,000
Profit
$200,000
$100,000
$0
8000 12000 16000 20000
Order Quantity

28. Probability of Outcomes
100%
80%
Probability
60% Q=9000
40% Q=16000
20%
0%
0
0
00
00
00
00
00
00
00
00
00
00
10
30
50
-3
-1
Revenue

29. Key Insights from this Model
• The optimal order quantity is not necessarily
equal to average forecast demand
• The optimal quantity depends on the relationship
between marginal profit and marginal cost
• As order quantity increases, average profit first
increases and then decreases
• As production quantity increases, risk increases.
In other words, the probability of large gains and
of large losses increases

30. SnowTime Costs: Initial
Inventory
• Production cost per unit (C): $80
• Selling price per unit (S): $125
• Salvage value per unit (V): $20
• Fixed production cost (F): $100,000
• Q is production quantity, D demand
• Profit =
Revenue - Variable Cost - Fixed Cost +
Salvage

31. SnowTime Expected Profit
Expected Profit
$400,000
$300,000
Profit
$200,000
$100,000
$0
8000 12000 16000 20000
Order Quantity

32. Initial Inventory
• Suppose that one of the jacket designs is a
model produced last year.
• Some inventory is left from last year
• Assume the same demand pattern as before
• If only old inventory is sold, no setup cost
• Question: If there are 7000 units remaining, what
should SnowTime do? What should they do if
there are 10,000 remaining?

33. Initial Inventory and Profit
500000
400000
300000
Profit
200000
100000
0
00
00
00
00
0
0
0
0
00
00
50
50
50
65
80
95
11
12
14
15
Production Quantity

34. Initial Inventory and Profit
500000
400000
300000
Profit
200000
100000
0
00
00
00
00
0
0
0
0
00
00
50
50
50
65
80
95
11
12
14
15
Production Quantity

35. Initial Inventory and Profit
500000
400000
300000
Profit
200000
100000
0
00
00
00
00
0
0
0
0
00
00
50
50
50
65
80
95
11
12
14
15
Production Quantity

36. Initial Inventory and Profit
500000
400000
300000
Profit
200000
100000
0
6000
5000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
Production Quantity

37. Supply Contracts
Fixed Production Cost =$100,000
Variable Production Cost=$35
Wholesale Price =$80
Selling Price=$125
Salvage Value=$20
Manufacturer Manufacturer DC Retail DC
Stores

38. Demand Scenarios
Demand Scenarios
30%
Probability
25%
20%
15%
10%
5%
0%
00
0
0
0
0
0
00
00
00
00
00
80
10
18
12
14
16
Sales

39. Distributor Expected Profit
Expected Profit
500000
400000
300000
200000
100000
0
6000 8000 10000 12000 14000 16000 18000 20000
Order Quantity

40. Distributor Expected Profit
Expected Profit
500000
400000
300000
200000
100000
0
6000 8000 10000 12000 14000 16000 18000 20000
Order Quantity

41. Supply Contracts (cont.)
• Distributor optimal order quantity is 12,000
units
• Distributor expected profit is $470,000
• Manufacturer profit is $440,000
• Supply Chain Profit is $910,000
–Is there anything that the distributor and
manufacturer can do to increase the profit
of both?

42. Supply Contracts
Fixed Production Cost =$100,000
Variable Production Cost=$35
Wholesale Price =$80
Selling Price=$125
Salvage Value=$20
Manufacturer Manufacturer DC Retail DC
Stores

43. Retailer Profit
(Buy Back=$55)
600,000
500,000
Retailer Profit
400,000
300,000
200,000
100,000
0
00
00
00
00
0
0
0
0
0
0
0
0
0
00
00
00
00
00
00
00
00
00
60
80
90
70
11
12
13
14
17
18
10
15
16
Order Quantity

44. Retailer Profit
(Buy Back=$55)
600,000
$513,800
500,000
Retailer Profit
400,000
300,000
200,000
100,000
0
00
00
00
00
0
0
0
0
0
0
0
0
0
00
00
00
00
00
00
00
00
00
60
80
90
70
11
12
13
14
17
18
10
15
16
Order Quantity

45. Manufacturer Profit
(Buy Back=$55)
600,000
Manufacturer Profit
500,000
400,000
300,000
200,000
100,000
0
00
00
00
00
0
0
0
0
0
0
0
0
0
00
00
00
00
00
00
00
00
00
60
70
80
90
10
11
13
16
17
18
12
14
15
Production Quantity

46. Manufacturer Profit
(Buy Back=$55)
600,000
$471,900
Manufacturer Profit
500,000
400,000
300,000
200,000
100,000
0
00
00
00
00
0
0
0
0
0
0
0
0
0
00
00
00
00
00
00
00
00
00
60
70
80
90
10
11
13
16
17
18
12
14
15
Production Quantity

47. Supply Contracts
Fixed Production Cost =$100,000
Variable Production Cost=$35
Wholesale Price =$??
Selling Price=$125
Salvage Value=$20
Manufacturer Manufacturer DC Retail DC
Stores

48. Retailer Profit
(Wholesale Price $70, RS 15%)
600,000
500,000
Retailer Profit
400,000
300,000
200,000
100,000
0
00
00
0
00
00
0
0
0
0
0
0
0
0
00
00
00
00
00
00
00
00
00
70
60
80
90
10
14
15
17
18
11
12
13
16
Order Quantity

49. Retailer Profit
(Wholesale Price $70, RS 15%)
600,000
$504,325
500,000
Retailer Profit
400,000
300,000
200,000
100,000
0
00
00
0
00
00
0
0
0
0
0
0
0
0
00
00
00
00
00
00
00
00
00
70
60
80
90
10
14
15
17
18
11
12
13
16
Order Quantity

50. Manufacturer Profit
(Wholesale Price $70, RS 15%)
700,000
600,000
Manufacturer Profit
500,000
400,000
300,000
200,000
100,000
0
00
00
00
00
0
0
0
0
0
0
0
0
0
00
00
00
00
00
00
00
00
00
60
70
90
80
11
12
13
14
15
17
10
16
18
Production Quantity

51. Manufacturer Profit
(Wholesale Price $70, RS 15%)
700,000
600,000
Manufacturer Profit
500,000 $481,375
400,000
300,000
200,000
100,000
0
00
00
00
00
0
0
0
0
0
0
0
0
0
00
00
00
00
00
00
00
00
00
60
70
90
80
11
12
13
14
15
17
10
16
18
Production Quantity

52. Supply Contracts
Strategy Retailer Manufacturer Total
Sequential Optimization 470,700 440,000 910,700
Buyback 513,800 471,900 985,700
Revenue Sharing 504,325 481,375 985,700

53. Supply Contracts
Fixed Production Cost =$100,000
Variable Production Cost=$35
Wholesale Price =$80
Selling Price=$125
Salvage Value=$20
Manufacturer Manufacturer DC Retail DC
Stores

54. Supply Chain Profit
1,200,000
Supply Chain Profit
1,000,000
800,000
600,000
400,000
200,000
0
0
0
0
0
0
0
0
0
00
00
00
00
0
00
00
00
00
00
00
00
00
00
60
70
80
90
10
11
12
14
15
16
17
18
13
Production Quantity

55. Supply Chain Profit
1,200,000
$1,014,500
Supply Chain Profit
1,000,000
800,000
600,000
400,000
200,000
0
00
00
0
0
0
00
00
0
0
0
0
0
0
00
00
00
00
00
00
00
00
00
60
70
80
90
10
11
12
13
14
15
16
17
18
Production Quantity

56. Supply Contracts
Strategy Retailer Manufacturer Total
Sequential Optimization 470,700 440,000 910,700
Buyback 513,800 471,900 985,700
Revenue Sharing 504,325 481,375 985,700
Global Optimization 1,014,500

57. Supply Contracts: 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

58. Contracts and Supply Chain
Performance
• Contracts for Product Availability and
Supply Chain Profits
– Buyback Contracts
– Revenue-Sharing Contracts
– Quantity Flexibility Contracts
• Contracts to Coordinate Supply Chain
Costs
• Contracts to Increase Agent Effort
• Contracts to Induce Performance
Improvement

59. Contracts for Product Availability
and Supply Chain Profits
• Many shortcomings in supply chain performance occur
because the buyer and supplier are separate
organizations and each tries to optimize its own profit
• Total supply chain profits might therefore be lower than if
the supply chain coordinated actions to have a common
objective of maximizing total supply chain profits
• Double marginalization results in suboptimal order
quantity
• An approach to dealing with this problem is to design a
contract that encourages a buyer to purchase more and
increase the level of product availability
• The supplier must share in some of the buyer’s demand
uncertainty, however

60. Contracts for Product Availability and
Supply Chain Profits: Buyback Contracts
• Allows a retailer to return unsold inventory up to a
specified amount at an agreed upon price
• Increases the optimal order quantity for the retailer,
resulting in higher product availability and higher profits
for both the retailer and the supplier
• Most effective for products with low variable cost, such as
music, software, books, magazines, and newspapers
• Downside is that buyback contract results in surplus
inventory that must be disposed of, which increases
supply chain costs
• Can also increase information distortion through the
supply chain because the supply chain reacts to retail
orders, not actual customer demand

61. Contracts for Product Availability and Supply
Chain Profits: Revenue Sharing Contracts
• The buyer pays a minimal amount for each
unit purchased from the supplier but
shares a fraction of the revenue for each
unit sold
• Decreases the cost per unit charged to the
retailer, which effectively decreases the
cost of overstocking
• Can result in supply chain information
distortion, however, just as in the case of
buyback contracts

62. Contracts for Product Availability and
Supply Chain Profits: Quantity Flexibility
Contracts
• Allows the buyer to modify the order
(within limits) as demand visibility
increases closer to the point of sale
• Better matching of supply and demand
• Increased overall supply chain profits if the
supplier has flexible capacity
• Lower levels of information distortion than
either buyback contracts or revenue
sharing contracts

63. Contracts to Coordinate
Supply Chain Costs
• Differences in costs at the buyer and supplier
can lead to decisions that increase total supply
chain costs
• Example: Replenishment order size placed by
the buyer. The buyer’s EOQ does not take into
account the supplier’s costs.
• A quantity discount contract may encourage the
buyer to purchase a larger quantity (which would
be lower costs for the supplier), which would
result in lower total supply chain costs
• Quantity discounts lead to information distortion
because of order batching

64. Contracts to Increase Agent
Effort
• There are many instances in a supply chain
where an agent acts on the behalf of a principal
and the agent’s actions affect the reward for the
principal
• Example: A car dealer who sells the cars of a
manufacturer, as well as those of other
manufacturers
• Examples of contracts to increase agent effort
include two-part tariffs and threshold contracts
• Threshold contracts increase information
distortion, however

65. Contracts to Induce
Performance Improvement
• A buyer may want performance improvement
from a supplier who otherwise would have little
incentive to do so
• A shared savings contract provides the supplier
with
a fraction of the savings that result from the
performance improvement
• Particularly effective where the benefit from
improvement accrues primarily to the buyer, but
where the effort for the improvement comes
primarily from the supplier

66. 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

67. Supply Contracts: Case Study
• Starting in 1998 Blockbuster entered a revenue
sharing 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)

68. (s, S) Policies
• For some starting inventory levels, it is better to
not start production
• If we start, we always produce to the same level
• Thus, we use an (s,S) policy. If the inventory
level is below s, we produce up to S.
• s is the reorder point, and S is the order-up-to
level
• The difference between the two levels is driven
by the fixed costs associated with ordering,
transportation, or manufacturing

69. A Multi-Period Inventory Model
• Often, there are multiple reorder
opportunities
• Consider a central distribution facility
which orders from a manufacturer and
delivers to retailers. The distributor
periodically places orders to replenish its
inventory

70. Reminder:
The Normal Distribution
Standard Deviation = 5
Standard Deviation = 10
Average = 30
0 10 20 30 40 50 60

71. The DC holds inventory to:
• Satisfy demand during lead
time
• Protect against demand
uncertainty
• Balance fixed costs and
holding costs

72. The Multi-Period Continuous
Review Inventory Model
• 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. This
is expressed as the the likelihood that the
distributor will not stock out during lead time.
• Intuitively, how will this effect our policy?

73. A View of (s, S) Policy
S
Inventory Position
Inventory Level
Lead
Time
s
0
Time

74. The (s,S) Policy
• (s, S) Policy: Whenever the inventory
position drops below a certain level, s, we
order to raise the inventory position to
level S.
• The reorder point is a function of:
– The Lead Time
– Average demand
– Demand variability
– Service level

75. Notation
• 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%). This implies that
the probability of stocking out is 100%-SL (for example,
5%)
• Also, the Inventory Position at any time is the actual
inventory plus items already ordered, but not yet
delivered.

76. 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 stockouts during leadtime 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

77. 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 = (175/44.6)
weeks of supply at warehouse and in the pipeline

78. Example, Cont.
• Weekly inventory holding cost: 0.87=
(0.18x250/52)
– Therefore, Q=679
• Order-up-to level thus equals:
– Reorder Point + Q = 176+679 = 855

79. Periodic Review
• Suppose the distributor places
orders every month
• What policy should the distributor
use?
• What about the fixed cost?

80. Base-Stock Policy
r r
L L L
Base-stock
Level Inventory
Inventory Level
Position
0
Time

81. Periodic Review Policy
• Each review echelon, inventory position is
raised to the base-stock 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

82. Risk Pooling
• Consider these two systems:
Warehouse One Market One
Supplier
Warehouse Two Market Two
Market One
Supplier Warehouse
Market Two

83. Risk Pooling
• 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?

84. 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

85. Risk Pooling Example
Week 1 2 3 4 5 6 7 8
Prod A, 33 45 37 38 55 30 18 58
Market 1
Prod A, 46 35 41 40 26 48 18 55
Market 2
Prod B, 0 2 3 0 0 1 3 0
Market 1
Product B, 2 4 0 0 3 1 0 0
Market 2

86. Risk Pooling Example
Warehouse Product AVG STD CV
Market 1 A 39.3 13.2 .34
Market 2 A 38.6 12.0 .31
Market 1 B 1.125 1.36 1.21
Market 2 B 1.25 1.58 1.26

87. Risk Pooling Example
Warehouse Product AVG STD CV s S Avg. %
Inven. Dec.
Market 1 A 39.3 13.2 .34 65 197 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 1.58 1.26 5 29 15
Cent. A 77.9 20.7 .27 118 304 132 36%
Cent B 2.375 1.9 .81 6 39 20 43%

88. 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?

89. To Centralize or not to Centralize
• What is the effect on:
– Safety stock?
– Service level?
– Overhead?
– Lead time?
– Transportation Costs?

90. Centralized Systems*
Supplier
Warehouse
Retailers
• Centralized Decision

91. Centralized Distribution
Systems*
• Question: 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.

92. 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

93. Changes In Inventory Turnover
• Inventory turnover ratio =
annual sales/avg. inventory level
• Inventory turns increased by 30% from
1995 to 1998
• Inventory turns increased by 27% from
1998 to 2000
• Overall the increase is from 8.0 turns per
year to over 13 per year over a five year
period ending in year 2000.

94. Inventory Turnover Ratio
Industry Upper Median Lower
Quartile Quartile
Dairy Products 34.4 19.3 9.2
Electronic Component 9.8 5.7 3.7
Electronic Computers 9.4 5.3 3.5
Books: publishing 9.8 2.4 1.3
Household audio & 6.2 3.4 2.3
video equipment
Household electrical 8.0 5.0 3.8
appliances
Industrial chemical 10.3 6.6 4.4

95. Factors that Drive Reduction in
Inventory
• Top management emphasis on inventory
reduction (19%)
• Reduce the Number of SKUs in the warehouse
(10%)
• Improved forecasting (7%)
• Use of sophisticated inventory management
software (6%)
• Coordination among supply chain members
(6%)
• Others

96. Factors that Drive Inventory Turns
Increase
• Better software for inventory management
(16.2%)
• Reduced lead time (15%)
• Improved forecasting (10.7%)
• Application of SCM principals (9.6%)
• More attention to inventory management (6.6%)
• Reduction in SKU (5.1%)
• Others

97. Forecasting
• Recall the three rules
• Nevertheless, forecast is critical
• General Overview:
– Judgment methods
– Market research methods
– Time Series methods
– Causal methods

98. 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

99. 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.

100. 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)

101. 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

102. Selecting the Appropriate
Approach:
• What is the purpose of the forecast?
– Gross or detailed estimates?
• What are the dynamics of the system being forecast?
– Is it sensitive to economic data?
– Is it seasonal? Trending?
• How important is the past in estimating the future?
• Different approaches may be appropriate for different
stages of the product lifecycle:
– Testing and intro: market research methods, judgment methods
– Rapid growth: time series methods
– Mature: time series, causal methods (particularly for long-range
planning)
• It is typically effective to combine approaches.