Question

A toy store must decide on how many bears to order for the next year. Each bear is sold for $6 and costs $3. After January 1st 2019, any unsold bears are returned to the publisher for a refund of $1 each. If demand is normally distributed with a mean of 3000 and a standard deviation of 500, how many bears should the toy store order?

Answer 1

To be calculated:

Number of bears to order

Given values:

Mean demand, = 3000

Standard deviation, = 500

Purchase price = $3

Selling price = $6

Salvage value = $1

Cost of under-ordering, Cu = $6 - $3 =$3

Cost of over-ordering, Co = $3 - $1 =$2

Solution:

The optimal service level is computed as;

Service level = Cu / (Cu + Co)

Service level = $3 / ($3 + $2)

Service level = $3 / $5

Service level = 0.6

By using NORMSINV function in Excel, we get the value of z;

NORMSINV (0.6), z = 0.2533

Number of bears the toy store should order is calculated as;

Number of bears = Mean + (z-value x Standard deviation)

Number of bears = + (z-value x )

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

Number of bears = 3000 + (0.2533 x 500)

Number of bears = 3126.65 or 3127 (rounding off to the next whole number)

Number of bears to order = 3127 units