Question

A component arrives gradually and at the rate of 20 units per week and is used at the rate of 5 units per week. The item costs 2,000 per unit. The cost per order is10,000 and the annual holding cost is 0.25

a. Which inventory model should be used: EOQ (Economic Order Quantity) model or POQ (Production Order Quantity) model? Why?
b. What is the optimal order quantity?
c. What is the optimal annual ordering cost?
d. What is the optimal annual holding cost?

Answer 1

The POQ (Production Order Quantity) model should be used in this case. The optimal order quantity is approximately 46 units. The optimal annual ordering cost is approximately $22,609 and the optimal annual holding cost is approximately $5.75.

Step-by-step explanation:

To determine which inventory model should be used, we need to compare the EOQ (Economic Order Quantity) model and the POQ (Production Order Quantity) model. The EOQ model is used when the ordering cost is significant, while the POQ model is used when the holding cost is significant. In this case, the annual holding cost is 0.25a, which suggests that the holding cost is significant compared to the ordering cost. Therefore, the POQ model should be used.

The optimal order quantity can be calculated using the formula:

Qopt = sqrt((2DS)/H)

Where D is the annual demand, S is the ordering cost, and H is the holding cost per unit. Plugging in the values, we get:

Qopt = sqrt((2*20*52) / 0.25) = sqrt(2080) ≈ 45.61

Therefore, the optimal order quantity is approximately 46 units.

The optimal annual ordering cost can be calculated using the formula:

ACopt = (D/Qopt) * S

Plugging in the values, we get:

ACopt = (20*52 / 46) * 10,000 ≈ 22,609

Therefore, the optimal annual ordering cost is approximately $22,609.

The optimal annual holding cost can be calculated using the formula:

HCopt = (Qopt/2) * H

Plugging in the values, we get:

HCopt = (46/2) * 0.25 ≈ 5.75

Therefore, the optimal annual holding cost is approximately $5.75.