# Management at Ardmore Farm and Seed has never analyzed the cost associated with their inventory...

## Question:

Management? at Ardmore Farm and Seed has never analyzed the cost associated with their inventory policy, and they currently have a large stock of insecticide in the warehouse. They estimate it costs $25 to place an order, and it costs$0.25 per gallon to hold the spray. The firm requires 80,000 gallons for the year (assume 365 days).

a. Calculate the EOQ

b. Calculate the total cost of inventory implied by the EOQ from a.

c. Calculate the total cost of inventory at the EOQ +/- 1,000 gallons.

d. If it takes 7 days to receive an order from suppliers, determine the appropriate reorder point.

## Economic Order Quantity:

EOQ is a central element of inventory management. It reflects the optimal order quantity, i.e., an order quantity that leads to the lowest possible total inventory costs.

Let {eq}D = 80,000 {/eq}, {eq}S = 25 {/eq}, and {eq}H = 0.25 {/eq}.

a. Calculating the EOQ

We find the economic order quantity (EOQ) as {eq}EOQ= \displaystyle \sqrt{\frac{2SD}{H}} = \displaystyle\sqrt{\frac{2\cdot 25 \cdot 80,000}{0.25}} = 4,000 {/eq} gallons.

b. Calculating the total cost of inventory implied by the EOQ from a.

The total cost (TC) of inventory can be found as {eq}TC(Q)=\frac{Q}{2}H+\frac{D}{Q}S {/eq}.

For our case, {eq}TC (4,000) = \displaystyle \frac{4,000}{2}0.25+\frac{80,000}{4,000}25 = 500+500=\$1,000 {/eq}. c. Calculating the total cost of inventory at the EOQ +/- 1,000 gallons. Now, we will calculate the cost for +/- 1,000 gallons, i.e., for 3,000 and 5,000 gallons: • {eq}TC (3,000) = \displaystyle\frac{3,000}{2}0.25+\frac{80,000}{3,000}25 = 667+375 = \$1,042 {/eq}
• {eq}TC (5,000) = \displaystyle\frac{5,000}{2}0.25+\frac{80,000}{5,000}25 = 400+625 = \\$1.025 {/eq}

d. Determine the appropriate reorder point:

Finally, to find the reorder point, we need to find the demand during lead time, which is {eq}\displaystyle\frac{80,000 \cdot 7}{365}\approx 1,534 {/eq} gallons. In the absence of variability, the reorder point should be 1,534 gallons (or 1,535 gallons if rounding up is required). 