Question

a grocery store estimates that it will sell 100 pounds of its specially prepared potatoes salad in the next week. the demand distribution is normally distributed with a standard deviation of 20 pounds. the supermarket can sell the salad for $5.99 per pound. it pays $2.50 per pound for the ingredients. Since no preservatives are used, any unsold salad is given to charity at no cost. What would be the optimal stocking quantity?

Answer 1

Given values:

Average sales = 100 pounds

Standard deviation () = 20 pounds

Selling price (SP) = $5.99 per pound

Ingredients cost (C) = $2.50 per pound

Solution:

Profit = Selling price - Cost = $5.99 - $2.50 = $3.49

Loss = $2.50

Service level = Profit / (Profit + Loss)

Service level = $3.49 / ($3.49 + $2.50)

Service level = $3.49 / $5.99

Service level = 0.583

Using NORMSINV function in Excel, Value of Z can be computed.

Z-value = NORMSINV (Service level)

Z-value = NORMSINV (0.583)

Z-value = 0.21

Optimal stock quantity (Q):

Q = Average Sales + (Z-value x Standard deviation)

Q = 100 + (0.21 x 20)

Q = 104.2

Optimal stocking quantity = 104.2 pounds