Question

Demand for walnut fudge ice cream at the Sweet Cream Dairy can be approximated by a normal distribution with a mean of 21 gallons per week and a standard deviation of 3.5 gallons per week.

The new manager desires a service level of 98 percent. Lead time is two days, and the dairy is open seven days a week. If an ROP model is used, what ROP would be consistent with the desired service level? ( Hint: Work in terms of weeks.)

Answer 1

Given Values:

Weekly demand (d) = 21 gallons per week

Standard deviation of demand (d) = 3.5 gallons per week

Service level = 98% or 0.98

Lead time (L) = 2 days or (2 / 7) = 0.2857 weeks

Solution:

In the given scenario, weekly demand is variable while lead time is constant. Therefore, Reorder point (ROP) will be calculated as,

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

where,

d = Weekly demand

L = Lead time (in weeks)

d = Standard deviation of demand

Using NORMSINV function in MS Excel, Z-value can be determined.

Z-value = NORMSINV (Service level)

Z-value = NORMSINV (0.98)

Z-value = 2.05

Putting the given values in the above formula,

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

ROP = (21 x 0.2857) + [2.05 x 3.5 x SQRT(0.2857)]

ROP = 5.9997 + 3.8351

Reorder Point (ROP) = 9.83 gallons