IEEM 341 Supply Chain Management
Week 11 Risk-Pooling
Dr. Lu
11-1
Impact of Aggregation on Safety Inventory
‹ Risk-pooling
–
–
–
–
–
–
effect
Models of aggregation
Information centralization
Specialization
Product substitution
Component commonality
Postponement
‹ Improved
forecast
‹ Quick response
11-2
Risk-Pooling
var Di    2 , i  1, 2, . . . , k
EDi   u, i  1, 2, . . . , k
var
k
 Di
 n 2
i1
var  ki1 Di
 ki1 EDi 

n
nu 
1   
u
n u
var Di 
 
u
EDi 
11-3
Safety Stock Level
W/O aggregation : ss  zCSLk L 
With Aggregation : ss  zCSL k L   zCSLk L 
zCSL  F1
S CSL
11-4
Impact of Aggregation (Example 11.7)
Car Dealer : 4 dealership locations (disaggregated)
D = 25 cars; σD = 5 cars; L = 2 weeks; desired CSL=0.90
What would the effect be on safety stock if the 4 outlets
are consolidated into 1 large outlet (aggregated)?
At each disaggregated outlet:
For L = 2 weeks, σL = 7.07 cars
ss = Fs-1(CSL) x σL = Fs-1(0.9) x 7.07 = 9.06
Each outlet must carry 9 cars as safety stock inventory, so
safety inventory for the 4 outlets in total is (4)(9) = 36
cars
11-5
Impact of Aggregation
(Example 11.7)
One outlet (aggregated option):
Expected demand per period for the aggregate demand =
D1 + D2 + D3 + D4 = 25+25+25+25 = 100 cars/wk
σC = Sqrt(52 + 52 + 52 + 52) = 10
σLC = σDC Sqrt(L) = (10)Sqrt(2) = (10)(1.414) = 14.14
ss = Fs-1(CSL) x σLC = Fs-1(0.9) x 14.14 =18.12
or about 18 cars
11-6
Risk-Pooling
var Di    2i , i  1, 2, . . . , k
EDi   u i , i  1, 2, . . . , k
var
k
 Di
k

i1
  2i  2  covDi, Dj 
i1
ij
k

  2i  2   ij  i j
i1
When  ij  0, var
ij
k
 Di
i1
k
  2i
i1
k

  2i
i1
k

 i
i1
11-7
Safety Inventory W and W/O Aggregation
W/O aggregation : ss  zCSL L
k
 i
i1
With Aggregation : ss  zCSL L
k
  2i  2   ij  i j
i1
Independent : ss  zCSL L
k
  2i
i1
ij
 zCSL L
k
 i
i1
zCSL  F1
S CSL
11-8
Table 11.3
‹
Benefits of aggregation can be affected by:
– coefficient of variation of demand (higher cv yields greater reduction in
safety inventory from centralization)
– If ρ does not equal 0 (demand is not completely independent), the impact
of aggregation is not as great (Table 11.3)
– value of item (high value items provide more benefits from centralization)
ρ
0
Safety inventory w/o Safety stock with
aggregation
aggreation
36.24
18.12
0.2
0.4
36.24
36.24
22.92
26.88
0.6
0.8
36.24
36.24
30.32
33.41
1.0t
36.24
36.24
11-9
Discussion of Risk Pooling
‹ In
case of independent stocking locations, we have
square root law
– By aggregation, the safety stock can be reduced by square
root of n
‹ Many
e-commerce retailers attempt to take
advantage of aggregation (Amazon)
‹ Aggregation has two major disadvantages:
– Increase in response time to customer order
– Increase in transportation cost to customer
– Some e-commerce firms (such as Amazon) have reduced
aggregation to mitigate these disadvantages
11-10
Information Centralization
‹ Virtual
aggregation
‹ Information system that allows access to current
inventory records in all warehouses from each
warehouse
– Most orders are filled from closest warehouse
– In case of a stockout, another warehouse can fill the order
– Better responsiveness, lower transportation cost, higher
product availability with reduced safety inventory
‹ Examples:
McMaster-Carr, Gap, Wal-Mart
11-11
Specialization
‹ Stock
all items in each location or stock different
items at different locations?
– Different products may have different demands in different
locations (e.g., snow shovels)
– Centralize slow-moving products which typically have a
high coefficient of variation (why) to achieve largest
benefit of aggregation
– Leave fast-moving, low-value products closer to customers
to provide faster service and save delivery cost
11-12
Value of Aggregation at Grainger
(Table 11.4)
Motors
Mean demand 20
SD of demand 40
Disaggregate cv 2
Value/Unit
$500
Disaggregate ss $105,600,000
Aggregate cv
0.05
Aggregate ss
$2,632,000
Holding Cost
$25,742,000
Saving
Saving / Unit
$7.74
Cleaner
1,000
100
0.1
$30
$15,792,000
0.0025
$394,770
$3,849,308
$0.046
11-13
Product Substitution
‹ Substitution:
use of one product to satisfy the
demand for another product
– Manufacturer-driven one-way substitution
– Customer-driven two-way substitution
– If the cost difference is small, one should carry more
higher-value components to substitute the shortage of
lower-value product
– Joint management of inventories across substitutable
products
11-14
Component Commonality
‹ Using
common components in a variety of
different products
‹ Can be an effective approach to exploit
aggregation and reduce component inventories
11-15
Example 11.9
‹
‹
Evaluate the safety stock requirement for the following
example.
Suppose Dell is to produce 27 different PCs with three distinct
components: processor, memory and hard drive. Monthly
demands for each computer is independent and normally
distributed variable with mean 5000, and standard deviation
3000. Suppose Dell is targeting 95% CSL
– Case 1: if Dell designs specific components for each PC resulting
3*27=81 components
– Common components: 3 processors, 3 memory and 3 hard drives to
create 27 kinds of computers
11-16
Example 11.9: Value of Component
Commonality
450000
400000
350000
300000
250000
SS
200000
150000
100000
50000
0
1
2
3
4
5
6
7
8
9
11-17
Postponement
‹ The
ability of a supply chain to delay product
differentiation or customization until closer to the
time the product is sold
‹ Goal is to have common components in the supply
chain for most of the push phase and move
product differentiation as close to the pull phase
as possible
‹ Examples: Dell, Benetton
11-18
Postponement
‹
‹
‹
‹
‹
Delay of product differentiation until closer to the time of the
sale of the product
All activities prior to product differentiation require aggregate
forecasts more accurate than individual product forecasts
Individual product forecasts are needed close to the time of sale
– demand is known with better accuracy (lower uncertainty)
Results in a better match of supply and demand
Higher profits, better match of supply and demand
11-19
Value of Postponement: Benetton
‹ For
each color
– Mean demand = 1,000; SD = 500
‹ For
–
–
–
–
each garment
Sale price = $50
Salvage value = $10
Production cost using Option 1 (long lead time) = $20
Production cost using Option 2 (uncolored thread) = $22
‹ What
is the value of postponement?
– Expected profit increases from $94,576 to $98,092
11-20
Value of Postponement
with Dominant Product
‹ Color
with dominant demand: Mean = 3,100, SD = 800
‹ Other three colors: Mean = 300, SD = 200
‹ Expected profit without postponement = $102,205
‹ Expected profit with postponement = $99,872
11-21
Tailored Postponement: Benetton
‹ Produce
Q1 units for each color using Option 1 and QA
units (aggregate) using Option 2
‹ Results:
– Q1 = 800
– QA = 1,550
– Profit = $104,603
‹ Tailored
postponement allows a firm to increase
profits by postponing differentiation only for products
with the most uncertain demand; products with more
predictable demand are produced at lower cost
without postponement
11-22
Tailored Sourcing
‹A
firm uses a combination of two supply sources
‹ One is lower cost but is unable to deal with
uncertainty well
‹ The other is more flexible, and can therefore deal
with uncertainty, but is higher cost
‹ The two sources must focus on different capabilities
‹ Depends on being able to have one source that faces
very low uncertainty and can therefore reduce costs
‹ Increase profits, better match supply and demand
11-23
Tailored Sourcing
‹ Sourcing
alternatives
– Low cost, long lead time supplier
» Cost = $245, Lead time = 9 weeks
– High cost, short lead time supplier
» Cost = $250, Lead time = 1 week
11-24
Tailored Sourcing Strategies
Fraction of demand from
overseas supplier
0%
Annual Profit
$37,250
50%
$51,613
60%
$53,027
100%
$48,875
11-25
Tailored Sourcing: Multiple Sourcing
Sites
Characteristic
Primary Site
Manufacturing High
Cost
Flexibility
High
(Volume/Mix)
Responsiveness High
Secondary Site
Low
Low
Low
11-26
Managerial Levers to Improve Supply Chain
Profitability
‹ “Obvious”
actions
– Increase salvage value of each unit
– Decrease the margin lost from a stockout
‹ Postponement
‹ Tailored
sourcing
‹ Improved forecasting
‹ Quick response
11-27
Improved Forecasts
‹ Improved
forecasts result in reduced uncertainty
‹ Less uncertainty (lower σR) results in either:
– Lower levels of safety inventory (and costs) for the same
level of product availability, or
– Higher product availability for the same level of safety
inventory, or
– Both lower levels of safety inventory and higher levels of
product availability
11-28
Impact of Improving Forecasts
(Example)
Demand: Normally distributed with a mean of R =
350 and standard deviation of σR = 100
Purchase price = $100
Retail price = $250
Disposal value = $85
Holding cost for season = $5
How many units should be ordered as σR changes?
11-29
Impact of Improving Forecasts
O* Expected Expected Expected
σR
Overstock Understock Profit
186.7
8.6
$47,469
150
526
120
491
149.3
6.9
$48,476
90
456
112.0
5.2
$49,482
60
420
74.7
3.5
$50,488
30
385
37.3
1.7
$51,494
0
350
0
0
$52,500
11-30
Quick Response
‹
‹
Set of actions taken by managers to reduce lead time
Reduced lead time results in improved forecasts
– Typical example of quick response is multiple orders in one
season for retail items (such as fashion clothing)
– For example, a buyer can usually make very accurate forecasts
after the first week or two in a season
– Multiple orders are only possible if the lead time is reduced –
otherwise there wouldn’t be enough time to get the later orders
before the season ends
‹
Benefits:
– Lower order quantities Æ less inventory, same product
availability
– Less overstock
– Higher profits
11-31
Quick Response: Multiple
Orders Per Season
‹ Ordering
–
–
–
–
–
shawls at a department store
Selling season = 14 weeks
Cost per handbag = $40
Sale price = $150
Disposal price = $30
Holding cost = $2 per week
‹ Expected
weekly demand = 20
‹ SD of weekly demand = 15
11-32
Impact of Quick Response
Single Order
Two Orders in Season
Service Order Ending Expect. Initial OUL
Level
Size Invent. Profit
Order for 2nd
Order
0.96
378
97
$23,624 209
209
Average Ending Expect.
Total
Invent. Profit
Order
349
69
$26,590
0.94
367
86
$24,034 201
201
342
60
$27,085
0.91
355
73
$24,617 193
193
332
52
$27,154
0.87
343
66
$24,386 184
184
319
43
$26,944
0.81
329
55
$24,609 174
174
313
36
$27,413
0.75
317
41
$25,205 166
166
302
32
$26,916
11-33
Forecast Improves for Second Order
(SD=3 Instead of 15)
Single Order
Two Orders in Season
Service Order Ending Expect. Initial OUL
Level
Size Invent. Profit
Order for 2nd
Order
0.96
378
96
$23,707 209
153
Average Ending Expect.
Total
Invent. Profit
Order
292
19
$27,007
0.94
367
84
$24,303 201
152
293
18
$27,371
0.91
355
76
$24,154 193
150
288
17
$26,946
0.87
343
63
$24,807 184
148
288
14
$27,583
0.81
329
52
$24,998 174
146
283
14
$27,162
0.75
317
44
$24,887 166
145
282
14
$27,268
11-34
Summary
‹ Risk
pooling effect is discussed to reduce the safety
inventory
– Several application is discussed, information centralized,
substitution, common components, postponement, tailored
sourcing
‹ Improved
forecast
‹ Quick response
11-35