# Reorder Point/ Optimal Order/ Total Carrying Cost

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?

https://brainmass.com/statistics/probability/reorder-point-optimal-order-total-carrying-cost-188977

#### 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.