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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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    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.

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