Rocky Mountain Tire Center sells 11,000 go-cart tires per year. The ordering cos

ID: 365381 • Letter: R

Question

Rocky Mountain Tire Center sells 11,000 go-cart tires per year. The ordering cost for each order is $35, and the holding cost is 50% of the purchase price of the tires per year. The purchase price is $21 per tire if fewer than 200200 tires are ordered, $17 per tire if 200 or more, but fewer than 5,000, tires are ordered, and $13 per tire if 5,000 or more tires are ordered.

a. How many tires should Rocky Mountains tire order each time it time it places an order?

b. What is the total cost of this policy?

Explanation / Answer

Annual demand of tires = D = 11000

Ordering cost = Co = $35/ order

Annual unit inventory holding cost = Ch = 50% of purchase price of tire

However since purchase price varies along with order quantity , Inventory holding cost Ch will also vary along with order quantity

The Optimal order quantity which minimizes total inventory related cost i..e Annual ordering cost + Annual inventory holding cost will be defined as Economic Order Quantity ( EOQ)

Thus , EOQ = Square root ( 2 x Co x D/Ch)

Since Ch will vary depending on quantity slab, so will be EOQ. Following table highlights values of Ch and EOQ for different quantity slabs accordingly :

Quantity Slab

Purchase price ($/tire)

Ch ( 50% of purchase price), $

EOQ ( rounded to nearest whole number)

< 200

10.5

271

200 – 4999

8.5

301

5000 and more

6.5

344

Except for 2nd row, derived values of EOQ do not match with the corresponding quantity slabs for other 2 and hence they are rejected.

Thus EOQ = 301

Total annual ordering cost for EOQ = 301 will be

= Ordering cost x Annual Demand / EOQ ( i.e. number of orders )

= 35 x 11000/301

= $1279.07

Total annual holding cost for EOQ = 301 will be

= Annual unit inventory holding cost x EOQ/2 ( i.e. average inventory )

= 8.5 x 301/2

= $1279.25

Corresponding annual cost of material

= Annual demand x Unit price = 11000 x 17 = $187000

Therefore , Total cost

= Total annual ordering cost + Total annual inventory Holding cost + Total annual cost of material

= $1279.07 + $1279.25 + $187000

= $189558.32

Above total cost however to be compared against total cost relevant to other quantity slabs i.e. for order quantity = 199 and order quantity = 500

Calculation for Order Quantity = 199:

Annual ordering cost

= 35 x 11000/199

= $1934.67

Total annual holding cost

= Annual inventory holding cost x Order Quantity /2

= 10.5 x 199/2

= $1044.75

Annual cost of material

= Annual demand x Purchase price/ unit

= 11000 x 21

= $231000

Therefore Total annual cost

= $1934.67 + $1044.75 + $231000

= $233979.42

Calculation for Order quantity = 5000:

Annual ordering cost

= $35 x 11000/ 5000

= $77

Total annual holding cost

= $6.5 x 5000/2

= $16250

Annual cost of material

= Annual demand x Purchase price / unit

= 11000 x 13

= 143000

Therefore ,

Total annual cost

= $77 + $16250 + $143000

= $159327

To Summarize , following table highlights total cost for various order quantity options :

ORDER QUANTITY

TOTAL COST ( $)

199

233979.42

301

189558.32

5000

159327

Thus Rocky mountain should order 500 tires each time

ROCKY MOUNTAIN SHOULD ORDER 500O TIRES EACH TIME IT PLACES AN ORDER

TOTAL COST OF THIS POLICY = $159327