Question

S11.9 Consider a three-firm supply chain consisting of a retailer, manufacturer,
and supplier. The retailer’s demand over an 8-week period was 100 units
each of the first 2 weeks, 200 units each of the second 2 weeks, 300
units each of the third 2 weeks, and 400 units each of the fourth 2 weeks.
The following table pre-sents the orders placed by each firm in the
supply chain. Notice, as is often the case in supply chains due to
economies of scale, that total units are the same in each case, but firms
further up the supply chain (away from the retailer) place larger, less
frequent, orders.
WEEK	RETAILER	MANUFACTURER	SUPPLIER
1	100	200	600
2	100
3	200	400
4	200
5	300	600	1400
6	300
7	400	800
8	400
Recall that the sample variance of a data set can be found by using the VAR.S function in Excel or by plugging each x value of
the data set into the formula: Variance=g(x-x)2(n-1), where x is
the mean of the data set and n is the number of values in the set.
a) What is the bullwhip measure for the retailer?
b) What is the bullwhip measure for the manufacturer?
c) What is the bullwhip measure for the supplier?
d) What conclusions can you draw regarding the impact that economies of scale may have on the bullwhip effect?

Answer 1

Let's find out mean and variance for Retailer, Manufacturer, and Supplier first:

mean of Retailer= (100+100+200+200+300+300+400+400)/8= 250

Variance of orders= [(250-100)² +(250-100)²+(250-200)² +(250-200)² +(300-250)² +(300-250)² +(400-250)² +(400-250)² ]/8-1

= 100,000/7= 14285.71= 14286

Similarly

mean of Manufacturer= 250

Variance of orders -Manufacturer=100000

mean of Supplier=250

Variance of orders-Supplier=260000

a) What is the bullwhip measure for the retailer?

bullwhip measure = Variance of orders/Variance of demand

variance of demand is equal to variance of orders as retailer use lot-for-lot production

so bullwhip measure= 1

b) What is the bullwhip measure for the manufacturer?

bullwhip measure = Variance of orders/Variance of demand

variance of orders=100000

variance of demand= variance of orders for retailer=14286

bullwhip measure = 100000/14286= 7

c) What is the bullwhip measure for the supplier?

bullwhip measure = Variance of orders/Variance of demand

variance of orders= 260000

variance of demand= variance of orders for manufacturer=100000

bullwhip measure = 260000/100000= 2.6

d) What conclusions can you draw regarding the impact that economies of scale may have on the bullwhip effect?

Economies of scale are the reason behind the bullwhip effect. Big orders which have low frequency can cause more variance as we move from retailers towards suppliers. This type of variance can be decreased through a proper supply chain process which determines lot sizes with help of channel coordination.