2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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
8. Quantifying the Bullwhip
Effect
One stage model
For each period t=1,2…, let
Retailer Customer
Ordering
quantity q[t] Inventory I[t] Demand D[t]
9. Discrete time model
(Periodic ordering system)
Lead time L
Items ordered at the end of period t will arrive at the
beginning of period t+L+1.
2)
Demand
D[t]
occurs
t t+1 t+2 t+3 t+4
1) Arrive the 3) Forecast demand F[t+1]
items ordered 4) Order q[t] Arrive the items
in period t-L-1 in period t+L+1 ( L=3)
10. Demand process
d: a constant term of the demand process
ρ: 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 σ
Dt: the demand in period t
ρ 1 < ρ < 1)
(−
ε t = 1,2,)
(t
Dt = d + ρDt −1 + ε t
12. Ordering quantity q[t]
Forecasting ( p period moving average )
p
∑D
j =1
t− j
ˆ
dt =
p
denote ˆ
We d t and Dt by F [t ] and D[t ], respectively.
Ordering quantity q[t] of period t is:
q[t]=D[t]+L (F[t+1]-F[t]) ,t=1,2,…
16. Asymptotic analysis: expectation,variance,
and Covariance)
d
E ( D[t ]) = By solving E[D]=d+ρE[D]
1− ρ
σ 2
Var ( D[t ]) = By solving
1− ρ 2 Var[D]=ρ2 Var[D]+σ2
ρ σ
p 2
Cov ( D[t ], D[t − p ]) =
1− ρ 2
17. Expansion of ordering quantity
q[t ] = D[t ] + LF [t + 1] − LF [t ]
p p
L ∑ D[t + 1 − j ] L ∑ D[t − j ]
j =1 j =1
= D[t ] + −
p p
L L
= (1 + ) D[t ] − D[t − p ]
p p
18. Variance of ordering quantity
L 2 L 2
Var ( q[t ]) = (1 + ) Var ( D[t ]) + ( ) Var ( D[t − p ])
p p
L L
− 2(1 + )( )Cov ( D[t ], D[t − p ])
p p
2 L 2 L2
= p + p 2 (1 − ρ ) Var ( D[t ])
1 +
2
Var ( q[t ]) 2 L 2 L2
=1+
p + 2 (1 − ρ ) 2
Var ( D[t ]) p
19. Observations
Var (q[t ]) 2 L 2 L2
= 1+ + 2 (1 − ρ ) 2
Var ( D[t ]) p p
• 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.
20. Coping with the Bullwhip Effect
1. 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 )
21. Coping with the Bullwhip Effect
2. 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
22. Coping with the Bullwhip Effect
3. Batch ordering
Reduction of fixed ordering cost using EDI and CAO
3PL ( Third Party Logistics )
VMI
23. Coping with the Bullwhip Effect
4. Variability of Price
EDLP: Every Day Low Price ( P&G )
Remark that the same strategy does not work well in
Japan.
24. Coping with the Bullwhip Effect
5. 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 )