The document discusses inventory management and risk pooling strategies. It begins with an overview of General Motors' supply chain in 1984 and goals of effective inventory management. It then covers topics such as inventory levels, functions of inventory, factors affecting inventory policy, economic order quantity modeling, and single period inventory models with and without initial inventory. The document concludes by discussing risk pooling strategies for reducing demand variability and inventory levels through approaches like location pooling, product pooling, lead time pooling and capacity pooling.

1. Inventory Management
&
Risk Pooling

2. Introduction
General Motors in 1984:
 Logistic network consisted of 20,000 supplier plants, 133
parts plants, 31 assembly plants, and 11,000 dealers.
 Freight transportation costs were about $4.1 billion, of
which 60 percent for material shipments.
 GM inventory was valued at $7.4 billion, of which 70
percent was WIP and the rest was finished vehicles.
Response:-
Inventory Management in Supply Chain

3. Goals of Inventory Management
 By effectively managing inventory:
 GM has reduced parts inventory and transportation costs
by 26% annually
 Xerox eliminated $700 million inventory from its supply
chain
 Wal-Mart became the largest retail company utilizing
efficient inventory management
Reduce Cost, Improve Service
Inventory Levels Financial
Investment
Operational
Need

4. Inventory
 Where do we hold inventory?
 Suppliers and manufacturers
 warehouses and distribution centers
 retailers
 Types of Inventory: General classification
 WIP
 raw materials
 finished goods

5. Functions of Inventory
 To meet anticipated demand
 To smooth production requirements
 To decouple operations
 To protect against stock-outs
 To take advantage of order cycles
 To help hedge against price increases
 To take advantage of quantity discounts

6. Factors Affecting Inventory Policy
 Demand Characteristics: known in advance or random
 Lead Time
 Number of Different Products Stored in the Warehouse
 Economies of scale offered by suppliers & transport
companies
 Length of Planning Horizon
 Service level desired

7. 1000 2000 3000 4000 5000 6000
0
50
100
150
200
250
300
350
Ordering (Acquisition)Costs
Holding or Carrying Costs
Total Costs
Economic Order Quantity
Economic Order Quantity Model
Assuming demand certainty
Trade-offs between setup costs and inventory holding costs,
but ignores issues such as demand uncertainty and forecasting.

8. Single Period Model
Without Initial Inventory

9. Case: Swimsuit Production
■ A company designs, produces, and sells summer fashion
items such as swinsuits.
■ The company has to commit itself six months before summer
to specific production quantities for all its products
– predicting demand for each product.
■ The trade-offs are clear: overestimating customer demand
will result in unsold inventory while underestimating
customer demand will lead to inventory stockouts and
loss of potential customers.

10. Demand forecast
forecast averages about 13,000
■The marketing department uses historical data from the last
five years, current economic conditions, and other factors to
construct a probabilistic forecast of the demand.
11% 11%
28%
22%
18%
10%
0%
5%
10%
15%
20%
25%
30%
8000 10000 12000 14000 16000 18000
Unit sales

11. Swimsuit 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

12. Swimsuit Two 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

13. Swimsuit Best Questions ?
 Find order quantity that maximizes
weighted average profit?
 Will this quantity be less than, equal to, or
greater than average demand?

14. How much to Make?
 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

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

16. Swimsuit : 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
 9000 and 16000 units lead to about the same average
profit, so which do we prefer?

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

18. Case: Swimsuit Production
 But Need to understand risk associated with certain
decisions.
 A frequency histogram provides information about
potential profit for the two given production
quantities, 9,000 units and 16,000 units. The
possible risk and possible reward increases as we
increase the production size.

19. Probability of Outcomes
0 0 0 0 0
0.11
0.89
0 0
0
0.11 0.11
0 0
0.28
0
0.22
0
0.28
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
-3E+05
-2E+05
-1E+05
0
10000
20000
30000
40000
50000
60000
Cost
Probability
Q =9000
Q =16000

20. Key Points from this Case
 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

21. Single Period Model With
Initial Inventory

22. 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 the company do? What should
they do if there are 10,000 remaining?

23. Initial Inventory and Profit
0
100000
200000
300000
400000
500000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
Production Quantity
Profit
The case motivates a powerful (s,S) inventory policy (or a min max
policy): s is the reorder point and S is the order-up-to-level

24. Multi-Order Opportunities
under Uncertainties

25. Inventory Policies
 Continuous review policy
 in which inventory is reviewed every day and a
decision is made about whether and how much to
order.
 Periodic review policy
 in which the inventory level is reviewed at regular
intervals and an appropriate quantity is ordered
after each review.

26. Variable Demand with a Fixed ROP
Reorder
point, R
Q
LT
Time
LT
Inventory
level
0
Result of
uncertainty

27. Reorder Point with a Safety Stock
Reorder
point, R
Q
LT
Time
LT
Inventory
level
0
Safety Stock
The amount of safety stock needed is based on the degree of
uncertainty in the lead time demand and desired customer service level

28. Determinants of the Reorder Point
 The rate of demand
 The lead time
 Demand and/or lead time variability
 Stockout risk (safety stock)

29. Continuous Review Policy
AVG = Average daily demand faced
STD = Standard deviation of daily demand faced
L = Replenishment lead time
h = Cost of holding one unit of the product per unit time
α = service level (the probability of stocking out is 1 – α)
h
p
p
+
=
α
p =shortage cost

30. Continuous Review Policy
 The inventory position at any point in time is the actual
inventory at the warehouse plus items ordered by the
distributor that have not yet arrived minus items that are
backordered.
 The reorder level, R consists of two components: the
average inventory during lead time, which is the product of
average daily demand and the lead time; and the safety
stock, which is the amount of inventory that the distributor
needs to keep at the warehouse and in the pipeline to protect
against deviations from average demand during lead time.

31. Continuous Review Policy –
Variable demand & fixed lead time
 Average demand during lead time is exactly
 Safety stock is
where z is a constant, referred to as the safety factor.
This constant is associated with the service level.
 The reorder level is
 Economic lot size is
L
STD
z ×
×
AVG
L×
L
STD
z
AVG
L ×
×
+
×
h
AVG
K
Q
×
=
2

32. Continuous Review Policy –
Variable demand & fixed lead time
■ The expected level of inventory before receiving the order
is (lowest level i.e. Safety Stock)
■ The expected level of inventory immediately after receiving
the order is (highest level)
■ The average inventory level is the average of these two
values
L
STD
z
Q ×
×
+
L
STD
z
Q
×
×
+
2
L
STD
z ×
×

33.  In many situation, the lead time to the warehouse must be
assumed to be normally distributed with average lead time
denoted by AVGL and standard deviation denoted by STDL.
In this case, the reorder point is calculated as
where AVG x AVGL represents average demand during lead
time, &
is the standard deviation of demand during lead time. The
amount of safety stock that has to be kept is equal to
2
2
2
STDL
AVG
STD
AVGL
z ×
+
×
2
2
2
STDL
AVG
STD
AVGL ×
+
×
Continuous Review Policy –
Variable demand & lead time

34. Periodic Review Policy
 Inventory level is reviewed periodically at regular
intervals and an appropriate quantity so as to arrive at
base stock level is ordered after each review .
 Since inventory levels are reviewed at a periodic interval, the fixed
cost of placing an order is a sunk cost and hence can be ignored.
 This level of the inventory position should be enough to
protect the warehouse against shortages until the next order
arrives, that is to cover demand during a period of r + L
days, with r being the length of review period and L being
the lead time.

35. Periodic Review Policy
 Thus, the base-stock level should include two
components: average demand during an interval of r + L
days, which is equal to
 and the safety stock, which is calculated as
where z is a safety factor.
AVG
L
r ×
+ )
(
L
r
STD
z +
×
×

36. Periodic Review Policy
■ Maximum inventory level is achieved immediately after
receiving an order, while the minimum level of inventory
is achieved just before receiving an order.
■ It is easy to see that the expected level of inventory after
receiving an order is
while the expected level of inventory before an order
arrives is just the safety stock
■ Hence, the average inventory level is the average of these
two values
L
r
STD
z
AVG
r +
×
×
+
×
L
r
STD
z +
×
×
L
r
STD
z
AVG
r
+
×
×
+
×
2

37. RISK POOLING

38. Risk Pooling
 Consider these two systems:
Market Two
Supplier
Warehouse One
Warehouse Two
Market One
Market Two
Supplier Warehouse
Market One
Questions:
Q1: For the same service level, which system will require more inventory?
Q2: For the same total inventory level, which system will have better service?

39. What is Risk Pooling?
The idea behind risk pooling is to redesign the supply chain,
the production process, or the product to either reduce the
uncertainty the firm faces or to hedge uncertainty so that
the firm is in a better position to mitigate the consequence
of uncertainty.
• Location pooling
• Product pooling
• Lead Time pooling
• Capacity pooling

40. Lead Time Pooling
Store 1
Supplier
Store 100
8-week lead time

41. Lead Time Pooling
Store 1
Supplier
Store 100
8-week lead time
Retail DC
1-week lead time

42. Capacity Pooling
3 Links – no flexibility

43. Capacity Pooling
9 Links – Total Flexibility

44. Advantages / Disadvantages
large costs to have flexibility
accommodate demand uncertainty
Capacity Pooling
reduce inventory investment
additional transportation costs
keep inventory closer to customer
extra costs of operating distribution center
decrease lead time
Lead Time Pooling
better performance in terms of
matching supply and demand
potentially degrades product functionality
reduction in demand variability
Product Pooling
reduce expected inventory
investment needed to achieve a
target service level
creates distance between inventory and
customers
reduce demand variability
Location Pooling
Disadvantages
Advantages

45. Summary Risk Pooling
 Risk-pooling strategies are most effective when demands
are negatively correlated because then the uncertainty
with total demand is much less than the uncertainty
with any individual item/location
 Risk-pooling strategies do not help reduce pipeline
inventory
 Risk-pooling strategies can be used to reduce inventory
while maintaining the same service or they can be used
to increase service while holding the same inventory

46. Example
Decentralized system:
total SS = 47.88
total avg. invent. = 179
Safety Stock SS = z ·STD · L
Reorder Point R = AVG·L + SS
Order Quantity Q = sqrt(2*C0*AVG/h)
Order-up-to-level R + Q
Average Inventory ≈ SS + Q/2
AVG STD SS R Q
Order-
up-to Level
Average
Inventory
Warehouse 1 39.3 13.2 25.08 65 132 197 91
Warehouse 2 38.6 12.0 22.8 62 131 193 88
Centralized
Warehouse
77.9 20.7 39.35 118 186 304 132
Service Level:97% k=1.88
Lead Time= 1 week
Q/2+SS

47. Risk Pooling – Effect of Correlation
 The benefits of risk pooling depend on the
behavior of demand from one market relative
to the demand from another market.

48. Warehouse
Market 1
Market 2
D1+D2: (µ, σ2
)
Calculating demand variability
of centralized system
Warehouse 1
Warehouse 2
Market 1
Market 2
D1: (µ1, σ1
2
)
D2: (µ2, σ2
2
)
σ2
= σ1
2
+ σ2
2
+ 2ρσ1σ2,
where -1 ≤ ρ ≤ 1
ρ: correlation coefficient of D1, D2
σ≤ σ1+ σ2
Conclusions:
1. Stdev of aggregated demand is
less than the sum of stdev of individual
demands
2. If demands are independent or
negatively correlated, the std of
aggregated demand is much less
1. If D1, D2 positively correlated, ρ > 0
2. If D1, D2 are independent, ρ = 0
3. If D1, D2 negatively correlated, ρ < 0
µ = µ1 + µ2
σ = ??
σ
ρ
σ1+σ2
1
0
-1
2
2
2
1 σ
σ +
P.C.
N.C. Ind.
As (safety) stock is based on standard deviation
Square Root Law:
Square Root Law: stock for combined demands
usually less than the combined stocks

49. Risk Pooling –
Effect of Coefficient of Variation
 The higher the C.V. of demand observed in one market,
the greater the benefit from risk pooling
 COV= Standard deviation/Avg. demand

50. Decentralized
Centralized
Inbound transportation cost
(from factories to warehouses)
Facility/Labor cost
Outbound transportation cost
(from warehouses to retailers)
Safety Stock
Responsiveness to customers
(lead time)
Centralized vs. Decentralized
Overhead
Costs
Service Level

51. Case Study
 # below stage = processing time
 # in white box = CST
 In this solution, inventory is held of finished
product and its raw materials
PART 1
DALLAS ($260)
15
7
8
PART 2
CHARLESTON ($7)
14
PART 4
BALTIMORE ($220)
5
PART 3
AUSTIN ($2)
14
6
8
5
PART 5
CHICAGO ($155)
45
PART 7
CHARLESTON ($30)
14
PART 6
CHARLESTON ($2)
32
8
0
14
55
14
45
14
32
(Adapted from Simchi-Levi, Chen, and Bramel,
The Logic of Logistics, Springer, 2004)

52. A Pure Pull System
 Produce to order
 Long CST to customer
 No inventory held in system
PART 1
DALLAS ($260)
15
7
8
PART 2
CHARLESTON ($7)
14
PART 4
BALTIMORE ($220)
5
PART 3
AUSTIN ($2)
14
6
8
5
PART 5
CHICAGO ($155)
45
PART 7
CHARLESTON ($30)
14
PART 6
CHARLESTON ($2)
32
8
77
14
55
14
45
14
32

53. A Pure Push System
 Produce to forecast
 Zero CST to customer
 Hold lots of finished goods inventory
PART 1
DALLAS ($260)
15
7
8
PART 2
CHARLESTON ($7)
14
PART 4
BALTIMORE ($220)
5
PART 3
AUSTIN ($2)
14
6
8
5
PART 5
CHICAGO ($155)
45
PART 7
CHARLESTON ($30)
14
PART 6
CHARLESTON ($2)
32
8
0
14
55
14
45
14
32

54. A Hybrid Push-Pull System
 Part of system operated produce-to-
stock, part produce-to-order
 Moderate lead time to customer
PART 1
DALLAS ($260)
15
7
8
PART 2
CHARLESTON ($7)
14
PART 4
BALTIMORE ($220)
5
PART 3
AUSTIN ($2)
14
6
8
5
PART 5
CHICAGO ($155)
45
PART 7
CHARLESTON ($30)
14
PART 6
CHARLESTON ($2)
32
8
30
7
8
9
45
14
32
push/pull boundary

55. CST vs. Inventory Cost
$0
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
0 10 20 30 40 50 60 70 80
Committed Lead Time to Customer (days)
Inventory
Cost
($/year)
Push System
Pull System
Push-Pull System

56. Echelon Inventory System
Supplier
Warehouse
Retailers
Warehouse
echelon
inventory
Warehouse
echelon lead
time

57. Managing Inventory in the Supply
Chain
 How should the reorder point associated with the warehouse
echelon inventory position be calculated? The reorder point
is
where Le
= echelon lead time, defined as the lead time between the
retailers and the warehouse plus the lead time between the
warehouse and its supplier
AVG = average demand across all retailers (i.e., the
average of the aggregate demand)
STD = standard deviation of (aggregate) demand across
all retailers
e
e
L
STD
z
AVG
L
s ×
+
×
=

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

59. THANKYOU