Question

A local bookstand believes that the demand for the Olympic edition of a sports magazine is normally distributed with a mean of 1,200 and a standard deviation of 200. Each of the

magazine costs the bookstand $1.50 per copy, and the bookstand will sell the issue for $5.00 Following the Olympic Games, there will be no demand for the magazine, and all leftover copies

will be recycled because they will have no salvage value. What is the optimal number of copies of the Olympic edition that the bookstand should order?

Answer 1

Solution:

Overage cost (Co) i.e. cost of over ordering is calculated as,

Co = Cost price - Salvage value

Co = $1.50 - $0 (No salvage value)

Co = $1.50

Underage cost (Cu) i.e. cost of under ordering is calculated as,

Cu = Selling price - Cost price

Cu = $5.00 - $1.50

Cu = $3.50

Service level = Cu / (Cu + Co)

Service level = $3.50 / ($3.50 + $1.50)

Service level = 0.7

Z-value can be determined using NORMSINV function in Excel.

Z-value = NORMSINV (Service level)

Z-value = NORMSINV (0.7)

Z-value = 0.52

Optimal Order Quantity (Q):

Q = Mean Demand + (Z-value x Standard deviation)

Q = 1,200 + (0.52 x 200)

Q = 1,304

Optimal Order Quantity = 1,304 copies