Question

5.* choose z value that is closest to your target value

(A)

Ned's chain of natural food stores sells shelled peanuts by the pound. Historically, Ned has observed daily demand is normally distributed with a mean of 233 pounds and a standard deviation of 27 pounds. Lead time is 14 days.

If Ned wants a service level of 98.5%, what is the reorder point? (Note: Use two decimal place z-value.)

(B)

Ned's chain of natural food stores sells shelled peanuts by the pound. Historically, Ned has observed daily demand is normally distributed with a mean of 119 pounds and a standard deviation of 22 pounds. Lead time is 11 days.

If Ned can tolerate a 23% probability of stockout, what is the reorder point? (Note: Use two decimal place z-value.)

Answer 1

(a) Given values:

Daily demand (d) = 233 pounds

Standard deviation ( $\sigma$ d) = 27 pounds

Lead time (L) = 14 days

Service level = 98.5%

Solution:

Using NORMSINV function is Excel, Z-value corresponding to 98.5% service level is calculated as below:

NORMSINV (0.985) = 2.17

Z = 2.17

Reorder point (ROP) is calculated as,

ROP = (d x L) + [z x $\sigma$ d x SQRT (L)]

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

ROP = (233 x 14) + [2.17 x 27 x SQRT (14)]

ROP = 3,481.22 or 3,481 (Rounding off to the nearest whole number)

Reorder point = 3,481 units

(b) Given values:

Daily demand (d) = 119 pounds

Standard deviation ( $\sigma$ d) = 22 pounds

Lead time (L) = 11 days

Probability of stockout = 23% or 0.23

Service level = (1 - 0.23) = 77% or 0.77

Solution:

Using NORMSINV function is Excel, Z-value corresponding to 77% service level is calculated as below:

NORMSINV (0.77) = 0.74

Z = 0.74

Reorder point (ROP) is calculated as,

ROP = (d x L) + [z x $\sigma$ d x SQRT (L)]

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

ROP = (119 x 11) + [0.74 x 22 x SQRT (11)]

ROP = 1,362.99 or 1,363 (Rounding off to the nearest whole number)

Reorder point = 1,363 units