Over the past 10 weeks, demand for gears at Michael’s Metals has been 140, 230, 100, 175, 165, 220, 200, and 178. Michael has placed weekly orders of 140, 250, 90, 190, 140, 240, 190, and 168 units.
The sample variance of a data set can be found by using the VAR.S function in Excel or by plugging each value (x) of the data set into the formula:

Question

Variance = [latex]\frac{\sum{(x - \bar{x})^2}{(n - 1)}[/latex], where x is the mean of the data set and n is the number of values in the set. Using Equation (S11-2), calculate the bullwhip measure for Michael’s Metals over the 10-week period.

Bullwhip = [latex]\frac{Variance of orders}{Variance of demand} = \frac{\sigma^2_{orders}}{\sigma^2_{demand}}[/latex] (S11-2)

Accepted Answer

Mean demand = (140 + 230 + 100 + 175 + 165 + 220 + 200 + 178)/8 = 1,408/8 = 176

Variance of demand

[latex]= \frac{(140 - 176)^2 + (230 - 176)^2 + (100 - 176)^2 + (175 - 176)^2 + (165 - 176)^2 + (220 - 176)^2 + (200 - 176)^2 + (178 - 176)^2}{(8 - 1)} = \frac{36^2 + 54^2 + 76^2 + 1^2 + 11^2 + 44^2 + 24^2 + 2^2}{7} = \frac{1,296 + 2,916 + 5,776 + 1 + 121 + 1,936 + 576 + 4}{7} = \frac{12,626}{7} = 1,804[/latex]

Mean orders = (140 + 250 + 90 + 190 + 140 + 240 + 190 + 168)/8 = 1,408/8 = 176

Variance of orders

[latex]= \frac{(140 - 176)^2 + (250 - 176)^2 + (90 - 176)^2 + (190 - 176)^2 + (140 - 176)^2 + (240 - 176)^2 + (190 - 176)^2 + (168 - 176)^2}{(8 - 1)} = \frac{36^2 + 74^2 + 86^2 + 14^2 + 36^2 + 64^2 + 14^2 + 8^2}{7} = \frac{1,296 + 5,476 + 7,396 + 196 + 1,296 + 4,096 + 196 + 64}{7} = \frac{20,016}{7} = 2,859[/latex]

From Equation (S11-2), the bullwhip measure = 2,859/1,804 = 1.58.
Since 1.58 > 1, Michael’s Metals is contributing to the bullwhip effect in its supply chain.

Question 11.S11.2: Over the past 10 weeks, demand for gears at Michael’s Metals...

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