Transcript Solution Key

Exam 2
Bullwhip Effect
John H. Vande Vate
Spring, 2006
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Question 1
• Consider a situation similar to the retail
game. You have 16 weeks to sell 2,000
units of an item. You must sell the item
at the full price of $100 for the first
week. After that you may discount by
10%, 20%, 30% or 50%, but once you
discount you cannot later raise the
price. You can salvage any items that
do not sell during the 16-week season
for $40 each.
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Estimates
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Price
100
100
90
90
90
90
80
80
80
80
70
70
70
50
50
50
Sales Inventory
68
1932
77
1855
94
1761
94
1667
99
1568
85
1483
129
1354
119
1235
127
1108
117
991
157
834
157
677
162
515
251
264
250
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14
0
Price
100
90
80
70
50
Avg
Weekly
Sales
72.50
93.00
123.00
158.67
250.50
Ratio
1.00
1.28
1.70
2.19
3.46
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Question A
• You are contemplating a pricing strategy for a new
item similar to the one illustrated above. Assuming
the new item enjoys essentially the same price
elasticity as the item above, would it make economic
sense to use a 50% discount for the new item?
• No. Only makes sense if you are otherwise going to
salvage. But in that case, a better strategy is to use
the 30% discount.
• ($70 – $40)*2.19*Rate of Sales at Full Price =
$65.66*Rate of Sales at Full Price is the revenue
you make above just salvaging
• ($50 – $40)*3.46* Rate of Sales at Full Price =
$34.55*Rate of Sales at Full Price is all you get from
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a 50% discount
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Question B
If your answer … explain how large the lift from
a discount of 50% would have to be for that
discount to make sense.
($70 – $40)*2.19*Rate of Sales at Full Price =
$65.66*Rate of Sales at Full Price <
($50 – $40)*(1+Lift)*Rate of Sales at Full Price
65.66 < 10*(1+Lift)
6.566 < (1 + Lift)
5.566 < Lift or 557%
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Question C
Decentralized: Allocate the inventory to the
stores and allow each store to optimize its
revenues using the pricing model.
Centralized: Allocate only a small amount of
inventory to the stores, optimize the pricing
using the model centrally, and then restock
the stores frequently from this central stock.
FOCUS YOUR ARGUMENTS ON
REVENUE RATHER THAN COST. BE
CERTAIN TO ADDRESS THE
ADVANTAGES OF EACH APPROACH IN
TERMS OF REVENUE.
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Question 2
• As the company prepares to make its final
scheduled shipment of the part to the Spartanburg
plant it recognizes that
• a. Current inventory position 1,000 units
• b. Remaining demand is uniformly distributed
between 500 and 2,500 units.
• c. Any suspension systems that have to be written
off cost the company $400 per unit.
• d. Sending additional suspension systems after the
last scheduled shipment costs the company $200
per unit.
• Based only on this information, how many units
would you recommend BMW include in its last
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shipment and why?
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Question 2
• Balance the risks:
• P = Probability Demand is <= Q
• The next item costs you $400 if
– D <= Q so with probability P
• The next item saves you $200 if
– D > Q so with probability (1-P)
• Want these to be equal
– 400P = 200(1-P)
– P = 1/3
• That’s the probability D <= Q.
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Question 2
•
•
•
•
Embarrassment from here on
What Q gives this probability?
1/3 of the way from 500 to 2500.
500 + 1/3 of the difference between the
two
• 500 + 2000/3  500 + 667 = 1167
• Net out the stock already sent
• 167 = 1167 – 1000
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Question 2
• 3.
A company relies on Continuous
Review policy to maintain its inventory of a
component with the following characteristics:
i. Annual Demand: 100,000 units per year
• ii. Std Dev in Weekly Demand: 100 units
• iii. Average Lead-time: 3 weeks
• iv. Std Dev in lead time: 2 days
• Carry about two standard deviations in leadtime demand as safety stock. HINT: BE
CAREFUL WITH UNITS HERE!
•
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Question A
• Question A: Assuming independence in the demand from
week to week and independence between the length of the
lead time and the rate of demand during that time, provide an
estimate of the standard deviation in lead time demand for this
product.
• Computing in terms of weeks or days
• L= 3 weeks or 21 days (or 15 days)
• D = 1923 (or 2000) per week or 274 (or 400) per day
• sD = 100 units per week or 37.78 = 100/sqrt(7) per week
• sL = 2/7 = 0.286 weeks (0.20 weeks)
• Should get something like 576 units as std. Dev in lead time
demand
sL = Ls2D + D2 s2L
• Sqrt(3*100^2 + 1923^2*0.286^2) = 576
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Question B
• Imagine that for the same cost you could
improve either the Standard Deviation in
Weekly Demand, the Standard Deviation in
Lead Time or the Average Lead Time by
10%. You only get to improve one of them.
Which will have the greatest impact on your
overall inventory?
• Improve Average Lead Time. This reduces
safety stock AND Pipeline inventory
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Question C
• If the company moves to a periodic review
policy for this product and orders every
two weeks. What safety stock will the
company need to carry to insure the same
98% in-stock performance per order cycle
as before? Is this more or less than the
safety stock required under the Continuous
Review Policy?
s = (T+L)s2D + D2 s2L
• Sqrt((2+3)*100^2 + 1923^2*0.286^2) = 593
• Safety Stock is about 1186 vs 1152, a little larger
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Sqrt(N) rule is a
bad fit. Widely
different
“customers”
Serve
Question 4
Annual
From
Demand ($)
Country
China
Shanghai
10,000
Korea
Shanghai
75,000
Japan
Shanghai
150,000
Sub Total
235,000
Indonesia Singapore
12,000
Malaysia Singapore
40,000
Thailand Singapore
30,000
Australia Singapore
24,000
India
Singapore
20,000
Sub Total
126,000
Total
361,000
Std. Dev.
In
Weekly
Demand
($)
256
243
1,386
1,430
148
124
138
129
277
387
1,482
Variance in
Weekly
Demand
65,536
59,049
1,920,996
2,045,581
21,904
15,376
19,044
16,641
76,729
149,694
2,195,275
Assuming
independence,
variances add
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Question 4
• Pipeline:
– 4 weeks at $361,000/52 = $6942 per week
– That’s $27,796 in the pipeline
– Same for both proposals
• Cycle:
– Shipments of $6942 in value
– Split between two locations or one, but same total
• Safety:
– A: 2*standard deviation in demand during T+L
2*(T+L)s2D + D2 s2L =
2*Sqrt(5*1482^2) = 2*Sqrt(5)*1482 = $6,626
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Question 4
• Safety:
– A: 2*standard deviation in demand during T+L
2*(T+L)s2D + D2 s2L =
2*Sqrt(5*1482^2) = 2*Sqrt(5)*1482 = $6,626
– B: Shanghai & Singapore
• Shanghai: 2*standard deviation in demand during T+L
2*(T+L)s2D + D2 s2L =
2*Sqrt(5*1430^2) = 2*Sqrt(5)*1430 = $6,396
• Singapore: 2*standard deviation in demand during T+L
2*(T+L)s2D + D2 s2L =
2*Sqrt(5*387^2) = 2*Sqrt(5)*387 = $1,730
Total: $8,126
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Performance
Average: 80
30
25
20
15
10
5
0
0-40
40-50
50-60
60-70
70-80
80-90
90-100
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Expectation
Expected
Average to be between 83 and 95
Question 1: 20 – 25 (Partial credit on C)
Question 2: 25
Question 3: 18 – 20 (B was tricky)
Question 4: 20 – 25
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The Bullwhip Effect
Be Sure To Read:
Chapter 4 of Simchi-Levi
“The Bullwhip Effect in Supply Chains”
By
Hau Lee, V. Padmanabhan &
Seungjin Whang
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What it is…
The Bullwhip Effect describes the
phenomenon in which order
variability is amplified as it moves up
the supply chain from end-consumers
through distribution and
manufacturing to raw material
suppliers.
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Example
Procter & Gamble: Pampers
• Smooth consumer demand
• Fluctuating sales at retail stores
• Highly variable demand on distributors
• Wild swings in demand on manufacturing
• Greatest swings in demand on suppliers
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Illustration
Consumer Sales at Retailer
Consumer demand
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Retailer's Orders to Distributor
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Retailer Order
900
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Illustration
Retailer's Orders to Distributor
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Retailer Order
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Distributor's Orders to P&G
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Distributor Order
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Illustration
Distributor’s Orders to P&G
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P&G's Orders with 3M
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P&G Order
Even worse at
superabsorber
suppliers like
Degussa
Distributor Order
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Illustration
Consumer Sales at Retailer
Consumer demand
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600
500
400
300
200
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P&G's Orders with 3M
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P&G Order
700
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The Causes
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•
•
•
•
Lead Times
Forecasting & Inventory Models
Pricing Strategies
Order batching
Uncertain Supply & Order Gaming
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Lead Times
• Long and Unreliable Lead Times make
forecasts worse and supply less reliable
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Forecasts
• Periodic Review Inventory Models
– Cost of Inventory
– Cost of Expediting or Backordering
– NO CONCERN FOR CHANGES IN ORDERS
• The Forecast is wrong, but we will chase it in and
drag our suppliers with us in futile attempt to
ensure our inventories are “smooth”
• BMW team on “Ship-to-Average” will talk more
about that Thursday
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Pricing Strategies
•
•
•
•
Promotions
Pre-announced price reductions
Volume discounts
Hockey stick effect
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Order Batching
• Driven by
– Pricing strategies
– Transportation rate structure (consolidate)
– Transportation infrastructure (weekly sailings)
• BMW team on Frequency will talk about
cures for this on Thursday
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Uncertain Supply & Order Gaming
• Lucent in 2000
Lucent Market Capitalization in Billions
$400
$350
$300
$250
$200
~2.5% of US GDP
$150
$100
$50
$0
6-Mar-96
19-Jul-97
1-Dec-98
14-Apr-00
27-Aug-01
9-Jan-03
23-May-04
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Reducing the Bullwhip
• Increase frequency
• Ship-to-Average
• Reduce variability
– Risk Pooling, Postponement, contracts,…
– Reduce lead time and lead time variability
• Strategic partnerships
• Less frequent financial reporting (?)
– Coca Cola
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