Tsg Hobby Shop Case Study

Sample Inventory Problems
The TSG Hobby Shop carries a line of radio-controlled model racing cars. Demand for the cars is assumed to be constant at a rate of 40 cars per month. The cars cost $60 each, and ordering costs are approximately $15 per order, regardless of the order size. The annual holding cost rate is 20%.

1. What is the Economic Order Quantity and the total annual cost under the assumption that no backorders are permitted?

A monthly demand of 40 cars translates to an annual demand, D, of 480 cars. Given a purchase cost, c, of $60 per car, an ordering cost, co, of $15 per order, and an annual unit holding cost rate, h, of 20%, we can compute the Economic Order Quantity, Q :
*

⎡ 2c D ⎤ Q = ⎢ o ⎥ ⎣ hc ⎦
*

12
≈ 35 cars

This allows us, then, to compute for the Annual Ordering Cost, OC(Q ):

*

⎡ D ⎤ ⎡ 480 ⎤ OC Q = co ⎢ * ⎥ = (15 )⎢ ⎣ 34.64... ⎥ ⎦ ⎣ Q ⎦

( )
*

12

≈ $207.85

and the Annual Holding Cost, HC(Q ):

*

⎡ Q * ⎤ ⎡ 34.64... ⎤ HC Q * = ch ⎢ ⎥ = (0.20 )(60 )⎢ ≈ $207.85 ⎣ 2 ⎥ ⎦ ⎣ 2 ⎦

( )

Consequently, we can compute for the Annual Total Cost at the Economic Order Quantity, TC(Q ):

*

TC Q * = OC Q * + HC Q * = $207.85 + $207.85 ≈ $415.69

( )

( )

( )

Sample Inventory Problems
2. What will happen to the Economic Order Quantity if the ordering cost increases to $20 per order?

If the ordering cost increases from $15 per order to $20 per order, the Economic Order Quantity increases from 35 cars to 40 cars, which is computed as follows:

⎡ 2c D ⎤ Q = ⎢ o ⎥ ⎣ hc ⎦