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Exam 2Bullwhip 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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EstimatesWeek Price Sales Inventory

1 100 68 19322 100 77 18553 90 94 17614 90 94 16675 90 99 15686 90 85 14837 80 129 13548 80 119 12359 80 127 1108

10 80 117 99111 70 157 83412 70 157 67713 70 162 51514 50 251 26415 50 250 1416 50 14 0

Price

Avg Weekly Sales Ratio

100 72.50 1.00 90 93.00 1.28 80 123.00 1.70 70 158.67 2.19 50 250.50 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 a 50% discount

 

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Question BIf 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 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

lead-time 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• D = 100 units per week or 37.78 = 100/sqrt(7) per

week • L = 2/7 = 0.286 weeks (0.20 weeks)• Should get something like 576 units as std. Dev in lead

time demand

L = L2D + D2 s2

L

• 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? = (T+L)2

D + 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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Question 4

CountryServe From

Annual Demand ($)

Std. Dev. In

Weekly Demand

($)

Variance in Weekly Demand

China Shanghai 10,000 256 65,536 Korea Shanghai 75,000 243 59,049 Japan Shanghai 150,000 1,386 1,920,996

Sub Total 235,000 1,430 2,045,581 Indonesia Singapore 12,000 148 21,904 Malaysia Singapore 40,000 124 15,376 Thailand Singapore 30,000 138 19,044 Australia Singapore 24,000 129 16,641 India Singapore 20,000 277 76,729

Sub Total 126,000 387 149,694 Total 361,000 1,482 2,195,275

Assuming independence, variances add

Sqrt(N) rule is a bad fit. Widely

different “customers”

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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)2D + D2 s2

L = 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)2D + D2 s2

L =

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)2D + D2 s2

L =

2*Sqrt(5*1430^2) = 2*Sqrt(5)*1430 = $6,396• Singapore: 2*standard deviation in demand during T+L

2*(T+L)2D + D2 s2

L =

2*Sqrt(5*387^2) = 2*Sqrt(5)*387 = $1,730

Total: $8,126

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Performance

Average: 80

0

5

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25

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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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IllustrationConsumer Sales at Retailer

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IllustrationRetailer's Orders to Distributor

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IllustrationDistributor’s Orders to P&G

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P&G's Orders with 3M

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Even worse at superabsorber suppliers like

Degussa

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IllustrationConsumer Sales at Retailer

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• Lead Times• Forecasting & Inventory Models• Pricing Strategies• Order batching• Uncertain Supply & Order Gaming

The Causes

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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

$0

$50

$100

$150

$200

$250

$300

$350

$400

6-Mar-96 19-Jul-97 1-Dec-98 14-Apr-00 27-Aug-01 9-Jan-03 23-May-04

~2.5% of US GDP

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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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