Question

Slick sam knows that daily demand for the new iu sweatshirt is normally distributed with a mean of sixty sweatshirts and a standard deviation of two sweatshirts. He also knows the lead time is nine days. If the reorder point is 549 sweatshirts, what is the implied service level?.

Answer 1

The implied service level when Slick Sam knows that daily demand for the new iu sweatshirt is normally distributed is 93.32%.

What is the service level?

Daily demand (d) = 60 sweatshirts

Standard deviation (sigma d) = 2 sweatshirts

Lead time (L) = 9 days

Reorder point (ROP) = 549 sweatshirts

From the given information, we can observe that the daily demand for the sweatshirt is variable, while the lead time is constant. In such case, reorder point is calculated using the below formula,

ROP = (d x L) + [Z-value x Sigma (d) x SQRT(L)]

Putting the given values in the above formula, we get,

549 = (60 x 9) + [Z-value x 2 x SQRT(9)]

549 = 540 + (Z-value x 2 x 3)

(6 x Z-value) = 549 - 540

(6 x Z-value) = 9

Z-value = 1.5

Now, from the standard normal table, the service level can be determined,

For Z-value = 1.5, service level = 0.93319

Alternatively, Excel's NORMSDIST function can also be used to determine the service level,

Service level = NORMSDIST (Z-value)

Service level = NORMSDIST (1.5)

Service level = 0.93319

Service level = 93.32%

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