Question

Rocky Mountain Tire Center sells 14,000 go-cart tires per year. The ordering cost for each order is $40, and the holding cost is 40% of the purchase price of the tires per year. The purchase price is $25 per tire if fewer than 200 tires are ordered, $16 per tire if 200 or more, but fewer than 5000, - tires are ordered, and $14 per tire if 5000 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?

Answer 1

Annual demand D = 14000

Ordering cost S = 40

Holding cost H = 40% of P

Purchase price P = 25, 16, or 14

a.

Let’s assume that the price is 25. Then H = 10 and economic order quantity Q = sqrt(2DS/H) = sqrt(2*14000*40/10) = 334.6

Let’s assume that the price is 16. Then H = 6.4 and Q = sqrt(2*14000*40/6.4) = 418.3

Let’s assume that price is 14. Then H = 5.6 and Q = sqrt(2*14000*40/5.6) = 447.2

We can see that in all possibility the optimum order quantity falls in the second slot (between 200 and 4999). This means that we should consider the extreme points of other ranges that is closest to the second slot. We have to check the total cost at Q = 199, 418 and 5000.

Formula for total cost = HQ/2 + DS/Q + PD

For Q = 199, total cost = 10*199/2 + 14000*40/199 + 25*14000 = 353809.07

For Q = 418, total cost = 6.4*418/2 + 14000*40/418 + 16*14000 = 226677.31

For Q = 5000, total cost = 5.6*5000/2 + 14000*40/5000 + 14*14000 = 210112

The lowest total cost is at Q = 5000

Rocky Mountains should order 5000 tires each time it places order.

b.

The total cost of this policy is 210112