Question

Suppose the inventory manager at the ABC company is concerned about combined variability in sales and lead time for one of its line of products and has provided you with the following sales data:

Mean Sales (S)= 20 unit, with a standard deviation of 3.0
Mean Leadtime (R) = 10 days, with a standard deviation of 2.0
The manager plans to order on the basis of EOQ. Assume EOQ= 300 units
What is the one standard deviation of safety stock for ABC’s line of product. (Note: you may us the convoluted formula for this question)
a. approximately 1690 units
b. approximately 60 units
c. approximately 40 units
d. 110 units

Answer 1

To find the one standard deviation of safety stock for ABC's line of products, we combined the standard deviation of sales and lead time yielding approximately 722 units. However, this answer does not match any of the proposed options.

Step-by-step explanation:

To calculate the one standard deviation of safety stock for ABC's line of product, we need to consider the combined variability in sales (demand) and lead time. The formula to determine the safety stock with one standard deviation (σ0) incorporates the mean sales, the sales standard deviation, the mean leadtime, and the lead time standard deviation.

Firstly, we calculate the combined standard deviation (σ0) using the square root of the sum of the squared standard deviations:

• Sales standard deviation: 3.0 units² = 9 units²
• Lead time standard deviation: 2.0 days² = 4 days²
• Combined standard deviation: √(9 + 4) = √13 ≈ 3.61 units

Next, because one standard deviation corresponds to the calculated combined standard deviation, the one standard deviation of safety stock is:

Safety Stock = Mean Sales (×) Mean Leadtime (×) Combined Standard Deviation ≈ 20 units/day (×) 10 days (×) 3.61 units ≈ 722 units

However, since none of the provided answer options are close to 722 units, there might be an error in the question or a misunderstanding of the provided data or EOQ relevance. Therefore, my answer, as calculated, is not reflected in the options a, b, c or d.

Answer 2

The one standard deviation of safety stock for ABC's line of product is approximately 49.5 units.Option c is correct answer.

Step-by-step explanation:

The formula for calculating safety stock is:

Safety Stock = Z * √(S^2 * L^2 + S^2 * L^2)

Where:

Z = the number of standard deviations needed for a desired service level (e.g. 1.65 for a 95% service level)

S = the standard deviation of demand

L = the lead time in days

For this question, since the manager plans to order on the basis of EOQ (Economic Order Quantity), we can assume a service level of 95%, which corresponds to a Z value of 1.65.

Plugging in the values from the question:

Z = 1.65

S = 3.0 units

L = 10 days

Using the formula, we can calculate the safety stock:

Safety Stock = 1.65 * √[(3.0^2 * 10^2) + (3.0^2 * 10^2)]

Safety Stock = 1.65 * √(900 + 900)

Safety Stock = 1.65 * 30

Safety Stock ≈ 49.5 units

Therefore, the one standard deviation of safety stock for ABC's line of product is approximately 49.5 units.