Bullwhip Effect and Risk Pooling

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Bullwhip Effect and Risk Pooling

• Tokyo University of
• Marine Science and Technology
• Mikio Kubo

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Bullwhip effect

• Key concept for understanding the SCM
• Procter Gamble noticed an interesting
  phenomenon that retail sales of the product were
  fairly uniform, but distributors orders placed
  to the factory fluctuated much more than retail
  sales.

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Why the bullwhip effect occurs?1.Demand
Forecasting

• One day, the manager of a retailer observed a
  larger demand (sales) than expected.
• He increased the inventory level because he
  expected more demand in the future (forecasting).
  
• The manager of his wholesaler observed more
  demand (some of which are not actual demand) than
  usual and increased his inventory.
• This caused more (non-real) demand to his maker
  the manager of the maker increased his inventory,
  and so on. This is the basic reason of the bull
  whip effect.

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Why the bullwhip effect occurs?2.Lead time

• With longer lead times, a small change in the
  estimate of demand variability implies a
  significant change in safety stock, reorder
  level, and thus in order quantities.
• Thus a longer lead time leads to an increase in
  variability and the bull whip effect.

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Why the bullwhip effect occurs? 3.Batch Ordering

• When using a min-max inventory policy, then the
  wholesaler will observe a large order, followed
  by several periods of no orders, followed by
  another large order, and so on.
• The wholesaler sees a distorted and highly
  variable pattern of orders.
• Thus, batch ordering increases the bull whip
  effect.

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Why the bullwhip effect occurs? 4.Variability of
Price

• Retailers (or wholesalers or makers) offer
  promotions and discounts at certain times or for
  certain quantities.
• Retailers (or customers) often attempt to stock
  up when prices are lower.
• It increases the variability of demands and the
  bull whip effect.

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Why the bullwhip effect occurs? 5.Lack of supply
and supply allocation

• When retailers suspect that a product will be in
  short supply, and therefore anticipate receiving
  supply proportional to the amount ordered (supply
  allocation).
• When the period of shortage is over, the retailer
  goes back to its standard orders, leading to all
  kinds of distortions and variations

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Quantifying the Bullwhip EffectOne stage model
For each period t1,2, let
Customer
Retailer
Ordering quantity qt
Demand Dt
Inventory It
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Discrete time model(Periodic ordering system)

• Lead time L Items ordered at the end of period
  t will arrive at the beginning of period tL1.

2) Demand Dt occurs
t
t1
t2
t3
t4
3) Forecast demand Ft14) Order qt
1) Arrive the items ordered in period t-L-1
Arrive the itemsin period tL1 (L3)
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Demand process

• d a constant term of the demand process
• ? a parameter that represents the correlation
  between two consecutive periods
• An error parameter in
  period t it has an independent distribution with
  mean 0 and standard deviation s
• Dt the demand in period t

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An example of demand process d80,?0.5,et-10
,10
800.5B2(RAND()(-20)10)
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Ordering quantity qt

• Forecasting (p period moving average)
• Ordering quantity qt of period t is
• qtDtL (Ft1-Ft) ,t1,2,

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Inventory It

• Inventory flow conservation equationFinal
  inventory (period t)Final inventory (period
  t-1)-DemandArrival VolumeI0A Safety Stock
  LevelIt It-1 Dt qt-L-1,t1,2,

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Excel Simulation (bull.xls)
E7-E6B6
(B5B4B3B2)/4
D61
G5-B6F3
C62
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Demand, ordering quantity, and demand processes
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Asymptotic analysis expectation,variance, and
Covariance)
By solving EDd?ED
By solving VarD?2 VarDs2
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Expansion of ordering quantity
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Variance of ordering quantity
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Observations

• When p is large, and L is small, the bullwhip
  effect due to forecasting error is negligible.
• The bullwhip effect is magnified as we increase
  the lead time and decrease p.
• A positive correlation DECRESES the bull whip
  effect.

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Coping with the Bullwhip Effect1.Demand
uncertainty

• Adjust the forecasting parameters, e.g., larger p
  for the moving average method.
• Centralizing demand information by providing
  each stage of the supply chain with complete
  information on actual customer demand (POS
  Point-Of-Sales data)
• Continuous replenishment
• VMI (Vender Managed Inventory VMI)

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Coping with the Bullwhip Effect2.Lead time

• Lead time reduction
• Information lead time can be reduced ujsing
  EDI(Electric Data Interchange) or CAO(Computer
  Assisted Ordering).
• QR(Quick Response) in apparel industry

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Coping with the Bullwhip Effect3.Batch ordering

• Reduction of fixed ordering cost using EDI and
  CAO
• 3PL(Third Party Logistics)
• VMI

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Coping with the Bullwhip Effect4. Variability of
Price

• EDLP Every Day Low Price (PG)
• Remark that the same strategy does not work well
  in Japan.

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Coping with the Bullwhip Effect5. Lack of supply
and supply allocation

• Allocate the lacking demand due to sales volume
  and/or market share instead of order volume.
  (General Motors,Saturn, Hewlett-Packard)
• Share the inventory and production information of
  makers with retailers and wholesalers.
  (Hewlett-Packard,Motorola)