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# Reorder Point/ Optimal Order/ Total Carrying Cost

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The manager of a car wash receives pricing schedule (shown below) from the vendor who supplies soap- and a promise of a 25% shorter lead time for deliveries. Currently, lead time is 4 days. Annual usage of soap is 4500 gallons. The car wash is open 360 days a year. Ordering Costs is \$ 30 per order and annual holding costs are \$ 3 per gallon. Daily usage is normally distributed, the standard deviation of soap 2 gallons.

Quantity Unit Price
1-399 \$2.00
400-799 \$1.70
800+ \$1.62

a. What is the optimal order quantity?
b. What is the reorder point if the acceptable probability of stock-out is 1.5%?
c. What is the total carrying cost at the optimal ordering quantity?

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#### Solution Preview

Please see the attached file.

Quantity Unit price
1-399 \$2
400-799 \$1.70
800 + \$1.62

Annual demand (D) = 4500 Gallons
Ordering cost per order (O) = \$30
Holding cost (C) = \$3

a. What is the optimal order quantity?

Quantity Purchase \$ # of orders Ordering \$ Holding \$ Total \$
1 \$9,000 4500 \$135,000 \$1.50 \$144,001.50
200 \$9,000 23 \$675.00 \$300.00 \$9,975.00
300 \$9,000 15 \$450.00 \$450.00 \$9,900.00
399 \$9,000 12 \$360.00 \$598.50 \$9,958.50
400 \$7,650 12 ...

#### Solution Summary

This solution helps determine optimal order quantity, reorder point and total carrying cost in an Excel spreadsheet.

\$2.49