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# Calculating EOQ and inventory costs

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The president of the wholesale distributor has recently heard about the EOQ model and is interested in learning whether or not using this model would allow the company to reduce its annual costs by optimizing the number of orders placed each year and the number of toilets purchased in each order. The estimated annual demand for the toilets is 4,475 units. The estimated average demand per day is 15 units. The purchase cost from the toilet manufacturer is \$125.00 per unit. The lead time for a new order is 4 days. The ordering cost is \$110.00 per order. The average holding cost per unit per year is \$1.85. The distributor has traditionally ordered 250 units each time they placed an order.

1. What is the economic order quantity (EOQ) that will minimize inventory costs?
2. What is the average number of units in inventory based upon ordering using the EOQ?
3. What is the average dollar value of inventory based upon ordering using the EOQ?
4. What is the total annual cost (Purchase Cost + Ordering Cost + Holding Cost) based upon using the EOQ?
5. What is the optimal reorder point based upon using the EOQ?
6. How many orders per year will be necessary based upon using the EOQ?

#### Solution Preview

1. What is the economic order quantity (EOQ) that will minimize inventory costs?
D =Total demand= 4475 units per year
S = ordering cost=\$110 per order
H = holding costs=\$1.85 per unit per year
EOQ=(2DS/H)^0.5=(2*4475*110/1.85)^0.5=729.49 or say 729 units

2. What is the average number of units in inventory ...

#### Solution Summary

Solution describes the steps to calculate EOQ, inventory costs and reorder point in the given case.

\$2.19

## Ross White's machine shop

Ross White's machine shop uses 2,500 brackets during the course of a year, and this usage is relatively constant throughout the year. These brackets are purchased from a supplier 100 miles away for \$15 each, and the lead time is 2 days. The holding cost per bracket per year is \$1.50 (or 10% of the unit cost) and the ordering cost per order is \$18.75.

There are 250 working days per year.

(a) What is the EOQ?
(b) Given the EOQ, what is the average inventory? What is the annual inventory holding cost?
(c) In minimizing cost, how many orders would be made each year? What would be the annual ordering cost?
(d) Given the EOQ, what is the total annual inventory cost (including purchase cost)?
(e) What is the time between orders?
(f) What is the ROP?

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