HC4 Value of information
Bullwhip effect
An increase in variability as we travel up in the supply chain is referred to as the bullwhip
effect.
There are a few causes of the bullwhip effect:
1. Demand forecasting
An important characteristic of all forecasting techniques is that as more data are
observed, the estimates of the mean and the standard deviation (or variability) of
customer demands are regularly modified. Since safety stock, as well as the base-
stock level, strongly depends on these estimates, the user is forced to change order
quantities, thus increasing variability.
2. Lead time
With longer lead times, a small change in the estimate of demand variability implies
a significant change in safety stock and base-stock level, leading to a significant
change in order quantities. This, of course, leads to an increase in variability. Zie HC2
voor de formule waarin lead time zit.
3. Batch ordering
If the retailer uses batch ordering then the wholesaler will observe a large order,
followed by several periods of no orders, followed by another large order, and so on.
4. Price fluctuation
If prices fluctuate, retailers often attempt to stock up when prices are lower. This is
accentuated by the prevailing practice in many industries of offering promotions and
discounts at certain times or for certain quantities. This practice, referred to as
forward buying, implies that retailers purchase large quantities during dis tributors'
and manufacturers' discount and promotion time and order relatively small
quantities at other time periods.
5. Inflated orders (order gaming)
Inflated orders placed by retailers during shortage periods tend to magnify the
bullwhip effect. Such orders are common when retailers and dis tributors suspect
that a product will be in short supply, and therefore anticipate receiving supply
proportional to the amount ordered. When the period of shortage is over, the
retailer goes back to its standard orders, leading to all kinds of dis tortions and
variations in demand estimates.
, The bullwhip effect also has behavioral causes:
1. Overreaction to backlogs
Panic ordering reactions after unmet demand
2. Decision-makers under-weight the supply line
Misperceptions of feedback and time delays
3. Lack of trust
Perceived risk of other players, because you don’t trust them
4. Bounded rationality
Inventory policies are misused
Quantifying the Bullwhip Effect
To quantify the increase in variability for a simple supply chain, consider a two-stage supply
chain with a retailer who observes customer demand and places an order to a
manufacturer. The base-stock level is, als r = 1 (zie HC2);
L∗AVG + z∗STD∗√ L
Specifically, the order-up-to point in period t , y t , is estimated from the observed demand as
y t = ^μt L+ z √ L S t
Where;
^μt =¿ the estimated average of daily customer demand at time t
St =¿ the estimated standard deviation of daily customer demand at time t
We kunnen kijken hoe deze berekend worden (simple moving average):
( )
t −1
∑ Di
i=t −p
^μt =
p
En
t −1
∑ ( Di−^μt )2
S2t = i=t− p
p−1
Where;
p=¿ number of previous periods
D i=¿ customer demand in period i
If the variance of the customer demand seen by the retailer is Var(D), then the variance of
the orders placed by that retailer to the manufacturer, Var(Q), relative to the variance of
customer demand satisfies (AANNAME):
VAR ( Q ) 2 L 2 L2
≥ 1+ + 2
VAR ( D ) 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.
VAR ( Q )
We can plot on the y-axis against p on the x-axis. We then get the lower bound on
VAR ( D )
the increase in variability for different lead times ( L).
