Question

Thompson Paint Company uses 60,000 gallons of pigment per year. The cost of ordering pigment is 200 per order, and the cost of carrying the pigment in inventory is1 per gallon per year. The firm uses pigment at a constant rate every day throughout the year.

a. Calculate the Economic Order Quantity (EOQ).

b. Assuming that it takes 20 days to receive an order once it has been placed, determine the reorder point in terms of gallons of pigment. (Note: Use a 365-day year.)

Answer 1

The Economic Order Quantity (EOQ) for Thompson Paint Company is approximately 4,899 gallons. The reorder point, in terms of gallons of pigment, is approximately 3,288 gallons.

Step-by-step explanation:

a. Calculating the Economic Order Quantity (EOQ):

To calculate the Economic Order Quantity (EOQ), we can use the formula:

EOQ = √((2 * D * S) / H)

Where:

D = Demand (or usage) per year = 60,000 gallons

S = Setup (or ordering) cost per order = $200

H = Holding (or carrying) cost per unit per year = $1

Plugging in the values, we get:

EOQ = √((2 * 60,000 * 200) / 1) = √(24,000,000) = 4,898.98

Therefore, the Economic Order Quantity (EOQ) is approximately 4,899 gallons.

b. Determining the reorder point:

The reorder point can be calculated by multiplying the lead time (the time it takes to receive an order once it has been placed) by the daily usage rate of the pigment.

Lead time = 20 days

Daily usage rate = D / 365 = 60,000 / 365 = 164.38 gallons per day

Reorder point = Lead time * Daily usage rate = 20 * 164.38 = 3,287.6 gallons

Therefore, the reorder point in terms of gallons of pigment is approximately 3,288 gallons.

Answer 2

The Economic Order Quantity (EOQ) for Thompson Paint Company is approximately 4,898 gallons. The reorder point, considering a lead time of 20 days and constant daily usage, is 3,288 gallons.

Step-by-step explanation:

Calculating the Economic Order Quantity (EOQ)

The Economic Order Quantity (EOQ) formula is used to determine the most efficient order quantity for a company. The formula for EOQ is:

EOQ = sqrt((2DS)/H)

Where:

• D = Demand in units (60,000 gallons per year)
• S = Ordering cost per order ($200 per order)
• H = Holding costs per unit per year ($1 per gallon per year)

Plugging in the values, we get:

EOQ = sqrt((2*60,000*200)/1) = sqrt(24,000,000) = 4,898 gallons (approximately)

Determine the Reorder Point

The reorder point is the level of inventory at which a new order should be placed. Thompson Paint Company takes 20 days to receive an order. Since they use pigment at a constant rate throughout the year, the reorder point can be calculated as follows:

Reorder Point = Daily Usage Rate * Lead Time

Daily Usage Rate = Annual Usage / Number of days in a year = 60,000 gallons / 365 days = 164.38 gallons/day

Reorder Point = 164.38 gallons/day * 20 days = 3,288 gallons