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Speedy Wheels is a wholesale distributor of bicycles for the western United States
Speedy Wheels is a wholesale distributor of bicycles for the western United States. Its Inventory Manager, Ricky Sapolo, is currently reviewing the inventory policy for one popular model — a small, one-speed girl's bicycle that is selling at the rate of 250 per month. The administrative cost for placing an order for this model from the manufacturer is $200 and the purchase price is $70 per bicycle. The annual cost of the capital tied up in inventory is 20 percent of the value of these bicycles. The additional cost of storing the bicycles — including leasing warehouse space, insurance, taxes, and so on — is $6 per bicycle per year.
EOQ = 245 units
Total Variable Cost = $4898.98
QUESTIONS:
Speedy Wheel's customers (retail outlets) generally do not object to short delays in having their orders filled. Therefore, management has agreed to a new policy of having small planned shortages occasionally to reduce the variable inventory cost. After consultations with management, Ricky estimates that the unit shortage cost (including lost future business) would be $30.
Use the EOQ model with planned shortages to determine the new optimal inventory policy.
1) What is the quantity that will now be ordered?
2) What is the maximum shortage?
3) Total Variable Cost (TVC)?
Expert Solution
Answer:
Total annual demand, D = 250*12 = 3,000
Ordering cost, K = $200
Unit cost, C = $70
Holding cost per unit, h = 70*20% + 6 = $20
Cost of backorder per unit, b = $30
1)
EOQ = (2.D.K. (h + b) / h.b)1/2 = sqrt(2*3000*200*(20+30) / (20*30)) = 316 units
2)
Maximum shortage during placing an order, S = Q * h / (h + b) = 316*20 / (20+30) = 126 units
3)
TC (excluding the purchase cost) = (D/Q)*K + h.(Q - S)2/ 2Q + b.S2/ 2Q
= (3000/316)*200 + 20*((316 - 126)^2) / (2*316) + 30*(126^2)/(2*316)
= $3,794.7
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