Exam 2 Bullwhip Effect

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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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Estimates
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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)2.19Rate of Sales at Full Price
  65.66Rate of Sales at Full Price is the revenue
  you make above just salvaging
• (50 40)3.46 Rate of Sales at Full Price
  34.55Rate of Sales at Full Price is all you get
  from 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)2.19Rate of Sales at Full Price
• 65.66Rate of Sales at Full Price lt
• (50 40)(1Lift)Rate of Sales at Full Price
• 65.66 lt 10(1Lift)
• 6.566 lt (1 Lift)
• 5.566 lt 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 lt Q
• The next item costs you 400 if
• D lt Q so with probability P
• The next item saves you 200 if
• D gt Q so with probability (1-P)
• Want these to be equal
• 400P 200(1-P)
• P 1/3
• Thats the probability D lt 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
• 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(31002 192320.2862) 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 ?(TL)s2D D2 s2L
• Sqrt((23)1002 192320.2862) 593
• Safety Stock is about 1186 vs 1152, a little
  larger

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Question 4
Sqrt(N) rule is a bad fit. Widely different
customers
Assuming independence, variances add
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Question 4

• Pipeline
• 4 weeks at 361,000/52 6942 per week
• Thats 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 2standard deviation in demand during TL
• 2?(TL)s2D D2 s2L
• 2Sqrt(514822) 2Sqrt(5)1482 6,626

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Question 4

• Safety
• A 2standard deviation in demand during TL
• 2?(TL)s2D D2 s2L
• 2Sqrt(514822) 2Sqrt(5)1482 6,626
• B Shanghai Singapore
• Shanghai 2standard deviation in demand during
  TL
• 2?(TL)s2D D2 s2L
• 2Sqrt(514302) 2Sqrt(5)1430 6,396
• Singapore 2standard deviation in demand during
  TL
• 2?(TL)s2D D2 s2L
• 2Sqrt(53872) 2Sqrt(5)387 1,730
• Total 8,126

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Performance
Average 80
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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
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Consumer demand
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Retailer's Orders to Distributor
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Retailer Order
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Illustration
Retailer's Orders to Distributor
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Retailer Order
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Distributor's Orders to PG
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Distributor Order
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Illustration
Distributors Orders to PG
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Even worse at superabsorber suppliers like Degussa
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Distributor Order
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PG's Orders with 3M
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PG Order
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Illustration
Consumer Sales at Retailer
1000
900
800
700
600
Consumer demand
500
400
300
200
100
0
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PG's Orders with 3M
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PG Order
400
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The Causes

• 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

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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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