Question

Rocky Mountain Tire Center sells 13,000 go­cart 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 $25 per tire if fewer than 200 tires are ordered, $18 per tire if 200 or more, but fewer than 5,000, tires are ordered, and $14 per tire if 5,000 or more tires are ordered.

a) How many tires should Rocky Mountain order each time it places an order? Rocky Mountain's optimal order quantity is ______ units (enter your response as a whole number).

b) What is the total cost of this policy? Total annual cost of ordering optimal order size = $ ___________ (round your response to the nearest whole number).

Answer 1

(a)

Annual Demand = D = 13000/year

Ordering Cost = C_o = $35

Let us assume that EOQ is less than 200

Hence, Holding Cost = C_c = 0.5*25 = $12.5/year

Economic Order Quantity Q* = √(2DC_o/C_c) = √(2*13000*35/12.5) = 269.81

Hence, this assumption is not correct.

Let us assume that EOQ is between 200 and 5000

Hence, Holding Cost = C_c = 0.5*18 = $9/year

Economic Order Quantity Q* = √(2DC_o/C_c) = √(2*13000*35/9) = 317.97

Hence, the Economic order quantity is 318

(b)

Annual Inventory Holding cost = average inventory * unit carrying cost = (Q*/2)*C_c = (318/2)*9 = $1431

Annual Order cost = Number of orders * cost/order = (D/Q*) C_o = (13000/318)*35 = $1431

Total Cost = Annual Inventory Holding Cost + Annual Order Cost = 1431 + 1431 = $2862