Question

1. An eyeglass retailer buys lenses from a supplier at $100 each. The retailer orders 250 lens pairs every year and the ordering cost is $36 for each pair. Carrying costs per year (based on average inventory) are estimated to be 20 percent for each pair. The supplier offers a 10 percent on order quantities of 50 or more lens pairs. Determine the best order quantity and total cost.
2. An electronic store sells 3,000 HD TV sets every quarter of the year. Each TV set costs the store $ 270.00. The carrying cost is set at 2% of the purchase price per unit per year. Each time an order is placed it costs the store $ 120.00 The supplier charges $10 for delivery of each order. Calculate:

a. Optimal order quantity

                                b. Number of orders per year

c. The supplier is willing to give a discount of 3% on the price of each set if the manager of the store orders 3,000 sets at a time. Should the manager accept the offer?

Answer 1

Please find below answer to first question :

Following are the relevant details :

Annual demand = D = 250 lens pairs every year

Ordering cost = C = $36

Unit inventory carrying cost = I = 20% of $100= $20

Therefore, optimum order quantity which minimizes sum of annual ordering cost and inventory holding cost (EOQ)

= Square root ( 2 x 250 X 36/20)

= 30 PAIRS

Annual ordering cost = C x D/EOQ = $36 x 250/30 = $300

Annual inventory holding cost = I x EOQ / 2 = $20 X 30/2 = $300

Annual cost of lens pairs = $100 x 250 = $25,000

Total cost = $300 + $300 + $25000 = $25600

Different scenario : Order quantity 50lens pairs

Revised cost of lens pairs after 10% discount = 90% of $100 = $90

Annual unit inventory cost = I = 20% of $90 = $18

Annual ordering cost = C X D/ORDER QTY = $36 x 250/50 = $180

Annual inventory holding cost = I x Order qty/ 2 = $18 x 50/2 = $450

Annual cost of lens pairs = $90 x 250 = $22500

Total cost = $180 + $450 +$22500 = $23130

Therefore, lesser total cost is incurred when order quantity is 50 or more.

Best order quantity will be 50or more with total annual cost = $23130