Question

The weekly requirement of a part is 950 units. The order cost is $85 per order, the holding cost is $5 per unit per year, and the part cost is $250 per unit. The firm operates fifty-two weeks per year. (A) Compute the EOQ. (B) What is the average inventory level of a part? (C) What is the lowest total annual inventory cost.

Answer 1

Calculating the EOQ for a part with given weekly requirements, order cost, and holding cost results in an EOQ of approximately 1294.45 units, an average inventory level of approximately 647.23 units, and the lowest total annual inventory cost of approximately $6,467.78.

Step-by-step explanation:

Calculating the Economic Order Quantity (EOQ)

The question involves the calculation of the Economic Order Quantity (EOQ), the average inventory level, and the lowest total annual inventory cost for a part that a firm requires weekly. To answer this question, we will use the classic EOQ formula:

EOQ = √((2DS)/H), where:

• D = demand in units (for the firm's operating period, typically one year)
• S = order cost (per order)
• H = holding cost (per unit per year)

In this case:

• D = 950 units/week * 52 weeks/year = 49,400 units/year
• S = $85/order
• H = $5/unit/year

Plugging these values into the EOQ formula:

EOQ = √((2 * 49,400 * 85)/5) = √(8378000/5) = √1675600 ≈ 1294.45 units

The average inventory level is half of the EOQ, so it would be 1294.45 units / 2 ≈ 647.23 units.

The lowest total annual inventory cost can be calculated by adding the annual holding cost and the annual ordering cost, which are derived from the EOQ:

• Annual holding cost = (EOQ/2) * H
• Annual ordering cost = (D/EOQ) * S

This will give us:

Annual holding cost = (1294.45/2) * 5 ≈ $3,236.13

Annual ordering cost = (49,400/1294.45) * 85 ≈ $3,231.65

The lowest total annual inventory cost is the sum of the annual holding cost and the annual ordering cost, which is approximately $6,467.78.

Answer 2

(A) EOQ = 387 units

(B) Average inventory level = 193.5 units

(C) Lowest total annual inventory cost = $36,363.75

Step-by-step explanation:

A. Economic Order Quantity (EOQ):

Use the EOQ formula:

EOQ = sqrt[(2 * Annual Demand * Ordering Cost) / Holding Cost per Unit]

Annual Demand = Weekly Demand * Weeks per Year = 950 units/week * 52 weeks/year = 49,400 units

Ordering Cost = $85 per order

Holding Cost per Unit = $5 per unit per year

EOQ = sqrt[(2 * 49,400 units * $85) / $5/unit] ≈ 387 units

B. Average Inventory Level:

Use the formula for average inventory in an EOQ model:

Average Inventory = EOQ / 2

Average Inventory = 387 units / 2 ≈ 193.5 units

C. Lowest Total Annual Inventory Cost:

The total annual inventory cost consists of ordering cost and holding cost:

Total Annual Inventory Cost = Ordering Cost per Order * Number of Orders per Year + Holding Cost per Unit * Average Inventory

Number of Orders per Year = Annual Demand / EOQ = 49,400 units / 387 units ≈ 127.6 orders

Holding Cost per Year = Holding Cost per Unit * Average Inventory = $5/unit * 193.5 units ≈ $967.5

Total Annual Inventory Cost = $85/order * 127.6 orders + $967.5 ≈ $36,363.75

Therefore, the EOQ is 387 units, the average inventory level is 193.5 units, and the lowest total annual inventory cost is $36,363.75.