Supply Chain Management
Lecture 22
Outline
• Today
– Finish Chapter 12
• Sections 1, 2, 3
– Section 2 up to and including Example 12.2
• Thursday
– Homework 5 due before class
– Start with Chapter 14
• Sections 1, 2, 3, 4, 6, 7, 8, 9
– Section 6 buyback and revenue sharing contracts only
• Next week
– Guest speaker: Paul Dodge
• SVP Supply Chain, ProBuild
Guest Lecture
• Date
– Tuesday April 13
• Speaker
– Paul Dodge (Senior Vice President – Supply
Chain)
• Subject
– Today’s Supply Chain
Semester Outline
•
•
•
•
•
•
•
•
Tuesday April 6
Thursday April 8
Tuesday April 13
Thursday April 15
Tuesday April 20
Thursday April 22
Tuesday April 27
Thursday April 29
Chap 12
Chap 14
Paul Dodge guest lecture
Chap 14, 15
Chap 15
Simulation Game briefing
Review, buffer
Simulation Game
The Newsboy/Newsvendor
Problem
The Newsboy/Newsvendor
Problem
• Order quantity (O)
• Uncertain demand (D)
• Cost of overstocking (Co = c – s)
– The loss incurred by a firm for each unsold unit at the end of the
selling season
• Cost of understocking (Cu = p – c)
– The margin lost by a firm for each lost sale because there is no
inventory on hand
• Includes the margin lost from current as well as future sales if the
customer does not return
O’Neill PsychoFreak 3347
• The “too much/too little problem”
– Order too much and inventory is left
over at the end of the season
– Order too little and sales are lost
Submit order to
Manufacturer
Nov
Dec
Jan
Selling seaon
Feb
Mar
Receive order from
Manufacturer
Apr
May
Jun
Jul
Aug
Discount leftovers
O’Neill PsychoFreak 3347
• Gather economic data
– Selling price (p = $180)
– Procurement cost (c = $110)
– Discount price (s = $90)
• Forecast demand
– Empirical demand distribution
– Normal demand distribution
• Order quantity (so as to maximize profits)
Example: Parkas at L.L. Bean
Demand
D_i
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
Prob
p_i
0.01
0.02
0.04
0.08
0.09
0.11
0.16
0.20
0.11
0.10
0.04
0.02
0.01
0.01
What is the expected demand?
Expected demand = ∑Dipi = 1,026 parkas
Example: Parkas at L.L. Bean
Demand
D_i
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
Prob
p_i
0.01
0.02
0.04
0.08
0.09
0.11
0.16
0.20
0.11
0.10
0.04
0.02
0.01
0.01
UnderOverstock
stock
0
600
0
500
0
400
0
300
0
200
0
100
0
0
100
0
200
0
300
0
400
0
500
0
600
0
700
0
What is the expected overstock?
What is the expected understock?
Expected understock = ∑Understockipi = 111 parkas
Expected overstock = ∑Overstockipi = 85 parkas
Example: Parkas at L.L. Bean
Demand
D_i
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
Prob
p_i
0.01
0.02
0.04
0.08
0.09
0.11
0.16
0.20
0.11
0.10
0.04
0.02
0.01
0.01
Sold
Unsold
units
units
400
600
500
500
600
400
700
300
800
200
900
100
1000
0
1000
0
1000
0
1000
0
1000
0
1000
0
1000
0
1000
0
Profit
19000
25000
31000
37000
43000
49000
55000
55000
55000
55000
55000
55000
55000
55000
Cost c = $45
Price p = $100
Salvage value s = $40
What is the expected profit?
Expected profit = ∑Profitipi = $49,900
Example: Parkas at L.L. Bean
Demand
D_i
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
Prob
p_i
0.01
0.02
0.04
0.08
0.09
0.11
0.16
0.20
0.11
0.10
0.04
0.02
0.01
0.01
CSL
0.01
0.03
0.07
0.15
0.24
0.35
0.51
0.71
0.82
0.92
0.96
0.98
0.99
1.00
1 - CSL
0.99
0.97
0.93
0.85
0.76
0.65
0.49
0.29
0.18
0.08
0.04
0.02
0.01
0.00
1100
1200
1300
1400
1500
1600
1700
Expected
Expected
Marg. benefit
Marg. cost
5500 x 0.49 = 2695 500 x 0.51 = 255
5500 x 0.29 = 1595 500 x 0.71 = 355
5500 x 0.18 = 990 500 x 0.82 = 410
5500 x 0.08 = 440 500 x 0.92 = 460
5500 x 0.04 = 220 500 x 0.96 = 480
5500 x 0.02 = 110 500 x 0.98 = 490
5500 x 0.01 = 55 500 x 0.99 = 495
(1 – CSL)(p – c)
CSL(c – s)
Expected
Marg. profit
2440
1240
580
-20
-260
-380
-440
Cost of understocking
p – c = $55
Cost of overstocking
c – s = $5
What is the optimal order quantity?
Example: Parkas at L.L. Bean
Demand
D_i
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
Prob
p_i
0.01
0.02
0.04
0.08
0.09
0.11
0.16
0.20
0.11
0.10
0.04
0.02
0.01
0.01
CSL
0.01
0.03
0.07
0.15
0.24
0.35
0.51
0.71
0.82
0.92
0.96
0.98
0.99
1.00
1 - CSL
0.99
0.97
0.93
0.85
0.76
0.65
0.49
0.29
0.18
0.08
0.04
0.02
0.01
0.00
1100
1200
1300
1400
1500
1600
1700
Expected
Expected
Marg. benefit
Marg. cost
5500 x 0.49 = 2695 500 x 0.51 = 255
5500 x 0.29 = 1595 500 x 0.71 = 355
5500 x 0.18 = 990 500 x 0.82 = 410
5500 x 0.08 = 440 500 x 0.92 = 460
5500 x 0.04 = 220 500 x 0.96 = 480
5500 x 0.02 = 110 500 x 0.98 = 490
5500 x 0.01 = 55 500 x 0.99 = 495
(1 – CSL)(p – c)
CSL(c – s)
Expected
Marg. profit
2440
1240
580
-20
-260
-380
-440
What is the safety stock?
Safety stock = Order quantity – Expected Demand
Optimal Level of Product
Availability
• Expected marginal contribution of raising the
order size from O* to O*+1
(1 – CSL*)(p – c) – CSL*(c – s)
CSL* = Prob(Demand  O*) =
p–c
p–s
=
Cu
Cu + Co
O* = F-1(CSL*, , ) = NORMINV(CSL*, , )
Example 12-1: Evaluating the optimal
service level for seasonal items
• The manager at Sportmart, a sporting goods store, has
to decide on the number of skis to purchase for the
winter season. Based on past demand data and weather
forecasts for the year, management has forecast
demand to be normally distributed, with a mean 350 and
a standard deviation of 100. Each pair of skis costs $100
and retails for $250. Any unsold skis at the end of the
season are disposed of for $85. Assume that it costs $5
to hold a pair of skis in inventory for the season. How
many skis should the manager order to maximize
expected profits?
Example 12-1: Evaluating the optimal
service level for seasonal items
Average demand (mean)
Standard deviation of
demand (stdev)
=
=
Material cost
c=
Price
p=
Salvage value
s=
Cost of understocking
Cu =
Cost of overstocking
Co =
Optimal cycle service level CSL* =
Optimal order size
O* =
350
100
$100
$250
85 – 5 = $80
p – c = 250 – 100 = $150
c – s = 100 – 80 = $20
Cu/(Cu + Co) = 150/170 =
0.88
NORMINV(CSL*, , ) =
468
When Demand is Normally Distributed
• Expected profits =
(p – s)Fs((O – )/) – (p – s)fs((O – )/)
– O(c – s)F(O, , ) + O(p – c)[1 – F(O, , )]
Expected overstock =
(O – )Fs((O – )/) + fs((O – )/)
• Expected understock =
( – O)[1 – Fs((O – )/)] + fs((O – )/)
Example 12-1: Evaluating the optimal
service level for seasonal items
• Expected profits =
(p – s)Fs((O – )/) – (p – s)fs((O – )/)
– O(c – s)F(O, , ) + O(p – c)(1 – F(O, , ))
59,500*NORMDIST(1.18,0,1,1) – 17,000*NORMDIST(1.18,0,1,0)
– 9,360*NORMDIST(468,350,100,1) + 70,200(1 – NORMDIST(468,350,100, 1))
= $49,146
• Expected overstock =
(O – )Fs((O – )/) + fs((O – )/) =
(450 – 350)*NORMDIST((450 – 350)/100,0,1,1)
+ 100*NORMDIST((450 – 350)/100,0,1,0) = 108
• Expected understock =
( – O)[1 – Fs((O – )/)] + fs((O – )/) =
(350 – 450)*[1 – NORMDIST(((450 – 350)/100,0,1,1)]
+ 100*NORMDIST((450 – 350)/100,0,1,0) = 8
Factors Affecting the Optimal Level
of Product Availability
Consider two products with the same margin. Any
leftover units of one product are worthless. Leftover
units of the other product can be sold to outlet stores.
Which product should have a higher level of product
availability?
Intermezzo
CSL*
1
Higher salvage
value leads to
lower Co
0
Co/Cu
Factors Affecting the Optimal Level
of Product Availability
Consider two products with the same margin. Any
leftover units of one product are worthless. Leftover
units of the other product can be sold to outlet stores.
Which product should have a higher level of product
availability?
Consider two products with the same cost but
different margins. Which product should have a
higher level of product availability?
Intermezzo
CSL*
1
Nordstrom
Discount store
0
Co/Cu
Maximizing Expected Profits
• Cost of over- and understocking have a direct
impact on both the optimal cycle service level
and profitability
How could one improve profitability?
Improving Supply Chain Profitability
•
Two obvious ways to improve profitability
1. Increase salvage value of each unit
•
•
Sport Obermeyer sells winter clothing in south America during the
summer.
Buyback contracts with manufacturer
2. Decrease the margin lost from a stock out
•
•
Arrange for backup sourcing or provide substitute product
Car part suppliers, McMaster-Carr and W.W.Grainger, are
competitors but they buy from each other to satisfy the customer
demand during a stockout
Improving Supply Chain Profitability
•
Another way to improve profitability
3. Reduce demand uncertainty
–
–
–
–
Improved forecasting: Use better market intelligence and
collaboration to reduce demand uncertainty
Quick response: Reduce replenishment lead time so that multiple
orders may be placed in a selling season
Postponement: In a multiproduct setting, postpone product
differentiation until closer to point of sale
Tailored sourcing: Use a low lead time, but perhaps an
expansive supplier as a backup for a low-cost, but perhaps long
lead time supplier
Example: Impact of Improved
Forecasting
• Demand is Normally distributed with a mean of
= 350 and standard deviation of  = 150
• Purchase price c = $100
• Retail price p = $250
• Salvage value s = $80
How many units should be ordered as  changes?
Example: Impact of Improved
Forecasting

150
120
90
60
30
0
O*
526
491
456
420
385
350
Expected Expected Expected
overstock understock
profit
186.7
8.6
$47,469
149.3
6.9
$48,476
112.0
5.2
$49,482
74.7
3.5
$50,488
37.3
1.7
$51,494
0
0
$52,500
Increase in forecast accuracy increases a firm’s profits
Impact of Improved Forecasting
• Better forecasts leads to reduced uncertainty
– Decreases both the overstocked and understocked
quantity
– Increases a firm’s profits
Impact of Quick Response
• Quick response is a set of actions a supply
chain takes to reduce replenishment lead time
Lead time
~30 weeks
Selling season
~14 weeks
Lead time
~14 weeks
Selling season
~14 weeks
Lead time
~4 weeks
Selling season
~14 weeks
Impact of Quick Response
• If quick response (reduction in replenishment lead
time) allows multiple orders in the season
– A buyer can usually improve forecast accuracy after
observing demand
– Less overstock, less understock
– Higher profits
Example: Impact of Quick
Response
• Mattel was hurt last year by inventory cutbacks at Toys
“R” Us, and officials are also eager to avoid a repeat of
the 1998 Thanksgiving weekend. Mattel had expected to
ship a lot of merchandise after the weekend, but
retailers, wary of excess inventory, stopped ordering
from Mattel. That led the company to report a $500
million sales shortfall in the last weeks of the year ...
For the crucial holiday selling season this year, Mattel
said it will require retailers to place their full orders
before Thanksgiving. And, for the first time, the
company will no longer take reorders in December, Ms.
Barad said. This will enable Mattel to tailor production
more closely to demand and avoid building inventory for
orders that don't come.
Wall Street Journal, Feb. 18, 1999
Mattel Inc. & Toys “R” Us
Did Mattel’s action help or hurt profitability at
Toys “R” Us?
• Decreasing replenishment lead times requires
tremendous effort from the manufacturer, yet
seems to benefit the retailer at the expense of
the manufacturer
• Hence, the benefits resulting from quick
response should be shared appropriately across
the supply chain
Impact of Postponement
• Postponement is delaying product differentiation
(customization) until closer to the time of the sale of the
product
– Delaying the commitment of the work-in-process inventory to a
particular product
• Examples
– Dell delivers customized PC in a few days after customer order
– HP printer places power supply modules, labels in appropriate
language on to printers after the demand is observed
– Motorola cell phones are customized for different service
providers after demand is materialized
– McDonalds assembles meal menus after customer order
Example: Impact of Postponement
• Benetton sells knit sweaters in four colors at a retail price
p = $50
– Option 1: (Long lead time) Dye the threat then knit the garment.
Results in manufacturing cost c = $20.
– Option 2: (Short lead time). Knit the garment then dye the
garment. Results in manufacturing cost c = $22
• Benetton disposes any unsold sweaters at the end of the
season in clearance for s = $10.
• For each color 20 weeks in advance demand forecast
– Normally distributed with a mean of  = 1000 and a standard
deviation of  = 500
Example: Impact of Postponement
 = 1000,  = 500
 = 4000,  = 1000
p = 50
c = 20
s = 10
p = 50
c = 22
s = 10
CSL CSL
= (p –
= c)/(c
0.75 – s)
CSL CSL
= (p –
= c)/(c
0.70 – s)
O* O*
= NORMINV(CSL*,,)
= 1,337*4 = 5,348
O* = NORMINV(CSL*,,)
O* = 4,524
Expected profits
$94,576
Expected profits
$98,092
Tailored Postponement
• By postponing all garment types, production cost of each
product goes up
– When this increase is substantial or a single product’s demand
dominates all other’s (causing limited uncertainty reduction via
aggregation), a partial postponement scheme is preferable to full
postponement.
• 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
Tailored (Dual) Sourcing
• Tailored sourcing is a business strategy where
a firm uses a combination of two supply sources
– The two sources must focus on different capabilities
Characteristic
Manufacturing cost
Flexibilility (volume/mix)
Responsiveness
Engineering support
Efficient
High
High
High
High
Flexible
Low
Low
Low
Low
Strategy
Volume based
Product based
Model based
Efficient
Predictable demand
Predictable demand
Older products
Flexible
Unpredictable demand
Unpredictable demand
Newer product