ISITECH B-SCHOOLHyderabad

Kishore

Bullwhip effect Key concept for understanding the SCMProcter & 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.

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.

Why the bullwhip effect occurs?２． Lead timeWith 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.

Why the bullwhip effect occurs? ３． Batch OrderingWhen 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.

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.

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

Quantifying the Bullwhip EffectOne stage model

Customer Retailer

Demand D[t]Inventory I[t]

For each period t=1,2…, let

Ordering quantity q[t]

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

3) Forecast demand F[t+1]4) Order q[t]

１） Arrive the items ordered in period t-L-1

Arrive the itemsin period t+L+1 （ L=3)

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

ttt DdD 1

)11( ),2,1( tt

An example of demand process d=80,ρ=0.5,ε[t]=[-10,10]

0

50

100

150

200

250

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41

t期 D(t)=d+需要量

ρ *D(t- 1)+ε1 802 146.43491073 166.24902534 181.9468235 200.65612556 210.03596447 202.09400068 200.39716979 193.98555510 194.6002961

=80+0.5*B2+(RAND()*(-20)+10)

Ordering quantity q[t]Forecasting （ pp period moving average ）

　　　Ordering quantity q[t] of period t is: q[t]=D[t]+L (F[t+1]-F[t]) ,t=1,2,…

p

D

d

p

jjt

t

1ˆ

ly.respective ,][ and ][by and ˆ denote We tDtFDd tt

Inventory I[t] Inventory flow conservation equation:

Final inventory (period t)=Final inventory (period t-1)-Demand ＋Arrival Volume

I[0]=A Safety Stock LevelI[t] =I[t-1] –D[t] +q[t-L-1],t=1,2,…

Excel Simulation (bull.xls)

t期 D(t)=d+需要量

ρ *D(t- 1)+ε移動平均法による

F(t):p=4予測

リードタイム中の需要量予測F(t)*:L, L=2

目標在庫レベルy(t)= F[t]*L+ z*σ

発注量q(t)=y(t)- y(t-

1)+D(t- 1)

在庫量I(t)=I(t- 1)-D(t)+q(t- 3)

1 80 80 02 127.81847 80 03 144.8770316 80 04 152.9420471 80 3005 157.4258033 126.4093872 252.8187744 254.8187744 196.138705 222.57419676 151.3785902 145.765838 291.5316761 293.5316761 163.1586503 151.19560647 161.1899679 151.6558681 303.3117361 305.3117361 169.3464361 70.005638518 158.4760476 155.7341022 311.4682043 313.4682043 161.2430479 107.66829599 164.937867 157.1176023 314.2352046 316.2352046 168.6938988 105.889079210 156.4019926 158.9956182 317.9912364 319.9912364 158.9136938 118.8335227

=(B5+B4+B3+B2)/4

=C6*2=D6+1

=E7-E6+B6

=G5-B6+F3

Demand, ordering quantity, and demand processes

- 100

- 50

0

50

100

150

200

250

300

350

1 5 9 13 17 21 25 29 33 37 41

D(t)=d+e*D(t-需要量1)+epsilon

q(t)=y(t)- y(t-発注量1)+D(t- 1)

I(t)=I(t- 1)-在庫量D(t)+q(t- 3)

Asymptotic analysis: expectation,variance, and Covariance)

2

2

1])[(

tDVar

1])[(

dtDE

2

2

1])[],[(

p

ptDtDCov

By solving E[D]=d+ρE[D]

By solving Var[D]=ρ2 Var[D]+σ2

Expansion of ordering quantity

p

jtDL

ptDp

LtD

p

Lp

jtDL

tD

tLFtLFtDtqp

j

p

j

11

][

][][)1(

]1[

][

][]1[][][

Variance of ordering quantity

])[()1(22

1

])[],[())(1(2

])[()(])[()1(])[(

22

2

22

tDVarp

L

p

L

ptDtDCovp

L

p

L

ptDVarp

LtDVar

p

LtqVar

22

2

)1(22

1])[(

])[(

p

L

p

L

tDVar

tqVar

Observations2

2

2

)1(22

1])[(

])[(

p

L

p

L

tDVar

tqVar

• 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.

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 replenishmentVMI （ Vender Managed Inventory: VMI ）

Coping with the Bullwhip Effect２． Lead time Lead time reductionInformation lead time can be reduced ujsing

EDI （ Electric Data Interchange ） or CAO （ Computer Assisted Ordering ） .

QR （ Quick Response ） in apparel industry

Coping with the Bullwhip Effect３． Batch orderingReduction of fixed ordering cost using EDI

and CAO 3PL （ Third Party Logistics ）VMI

Coping with the Bullwhip Effect４． Variability of PriceEDLP: Every Day Low Price （ P&G ）Remark that the same strategy does not work

well in Japan.

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 ）