Question

At Tires R Us, a retailer of tires, demand for the AAA tire is constant at 32,000 tires per year. The cost of placing an order to replenish stock is $50, and the annual cost of holding is $8 per tire. Each tire costs Tires R US $55 and they retail them for $95. Stock is received 5 working days after an order has been placed. No backorders are allowed. Assume 300 working days per year.

1. What is Tires R Us’ optimal ordering quantity?
2. What is the optimal number of orders per year?
3. What is the optimal interval (in working days) between orders?
4. What is the reorder point?
5. If the AAA tire supplier offers a discount of $1 per tire for orders of 1,000 tires at a time. Is this deal worthwhile?

Answer 1

Solution:

Let,

D = Annual Demand = 32000 tires,

O = Ordering cost per order = 50 $

H = Holding cost per tire per annum = 8 $

P = Purchasing cost per tire = 55 $

L = Lead Time = 5 Days

Answer a) We will find Economic Order Quantity EOQ using the following formula:

EOQ = SQRT [ ( 2 X D X O) / H ]

= SQRT [ ( 2 X 32000 X 50) / 8 ]

= SQRT ( 400000 )

∴ EOQ = 632.45 tires (Rounded to 2 decimal places)

Answer b) We will find Optimal No. of Orders Per Year using the following formula:

Optimal No. of Orders Per Year = Annual Demand / EOQ = 32000 / 632.45 = 50.60 Orders (Rounded to 2 decimal places)

Answer c) We will find Optimum Interval (No. of Days) In Between any Two Orders using the following formula:

Optimum No. of Days In Between any Two Orders = No. of Working Days in a Year / Optimal No. of Orders Per Year

= 300 / 50.60 = 5.93 Days (Rounded to 2 decimal places)

Answer d)

Reorder Point = Avg. Daily Demand X Lead Time

Where Avg Daily Demand = Annual Demand / Working Days Per Year = 32000 / 300 = 106.67 Units Per Day, and Lead Time = 5 Days

Hence, Reorder Point = 106.67 X 5 = 533.35 tires (Rounded to 2 decimal places)