Leyla Tas Has Determined That The Annual Demand For 6 Scre

A Leyla Tas Has Determined That The Annual Demand For 6 Screws Is 1

A Leyla Tas has determined that the annual demand for #6 screws is 100,000 screws. Leyla estimates that it costs 10 MU every time an order is placed. This cost includes wages, the cost of the forms used in placing the order, and other associated expenses. Furthermore, she estimates that the cost of carrying a screw in inventory for a year is one-half of 0.01 MU. Assume that the demand is constant throughout the year.

a. How many #6 screws should Leyla order at a time to minimize total inventory cost?

b. How many orders per year would be placed? What would be the annual ordering cost?

c. What would be the average inventory? What would be the annual holding cost?

Paper For Above instruction

To determine the optimal order quantity and related inventory costs for Leyla Tas's #6 screws, we apply the Economic Order Quantity (EOQ) model, a fundamental principle in inventory management that balances ordering costs with holding costs to minimize total inventory costs.

Step 1: Data Summarization

- Annual demand (D): 100,000 screws

- Ordering cost per order (S): 10 MU

- Holding cost per unit per year (H): 0.5 * 0.01 MU = 0.005 MU

(since she estimates that the carrying cost of a screw per year is half of 0.01 MU)

Step 2: EOQ Calculation

The EOQ formula is given by:

\[ EOQ = \sqrt{\frac{2DS}{H}} \]

Plugging in the values:

\[ EOQ = \sqrt{\frac{2 \times 100,000 \times 10}{0.005}} \]

\[ EOQ = \sqrt{\frac{2,000,000}{0.005}} \]

\[ EOQ = \sqrt{400,000,000} \]

\[ EOQ \approx 20,000 \text{ screws} \]

Therefore, Leyla should order approximately 20,000 screws each time to minimize total inventory costs.

Step 3: Number of Orders Per Year

Number of orders (N):

\[ N = \frac{D}{EOQ} = \frac{100,000}{20,000} = 5 \]

Leyla would place about five orders per year.

Step 4: Total Ordering Cost Annually

Total ordering cost:

\[ \text{Ordering Cost} = N \times S = 5 \times 10 = 50 \text{ MU} \]

Step 5: Average Inventory Level

Average inventory:

\[ \text{Average Inventory} = \frac{EOQ}{2} = \frac{20,000}{2} = 10,000 \text{ screws} \]

Step 6: Annual Holding Cost

Annual holding cost:

\[ \text{Holding Cost} = \text{Average Inventory} \times H = 10,000 \times 0.005 = 50 \text{ MU} \]

Summary:

- Leyla should order approximately 20,000 screws each time.

- She will place 5 orders annually.

- The total annual ordering cost will be approximately 50 MU.

- The average inventory level will be 10,000 screws.

- The annual holding cost will also be approximately 50 MU.

These calculations demonstrate an optimal balance between ordering and holding costs, offering Leyla an efficient inventory management strategy for her #6 screws.

References

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