what is the minimum weekly stock he should keep so he can be prepared at a level of 99% of all demands.? (show calculations)

Question

Mr. Ibrahim is responsible for maintaining clean linen for the hospital. The hospital has a contract with a laundry company to clean all dirty linen. He has been informed that the hospital is doing some renovations and he needs to move his clean-linen storage to another smaller storage room until the renovations are finished. As you know, the demand of clean linen is fluctuating from week to week and he used to overstock the storage room to accommodate that demand. Now, he is concerned with the number of clean linen that he should stock in that smaller room with limited space.

Luckily, Mr. Ibrahim has some data about the number of stock/ demand in the past year. When analyzing that data, he found that the average number of linen used per week is 57, with a SD of 9. He wants to be prepared for 99% of all demand levels. So, what is the minimum weekly stock he should keep so he can be prepared at a level of 99% of all demands.? (show calculations)

Answer 1

To determine the minimum weekly stock Mr. Ibrahim should keep to be prepared for 99% of all demands, we need to calculate the stock level corresponding to the 99th percentile of the demand distribution. Here's the step-by-step process:

1. Determine the z-score corresponding to the 99th percentile:
2. The 99th percentile of the standard normal distribution corresponds to a z-score where 99% of the data falls below it. From standard normal distribution tables or using a calculator, the z-score for the 99th percentile is approximately 2.33.
3. Use the z-score formula to calculate the stock level:
4. The formula to find the stock level XXX is:
5. X=μ+z⋅σX = \mu + z \cdot \sigmaX=μ+z⋅σ
6. where:
7. μ\muμ is the mean demand per week (57 linen),
8. zzz is the z-score for the 99th percentile (2.33),
9. σ\sigmaσ is the standard deviation of demand per week (9 linen).
10. Plug in the values:
11. X=57+2.33⋅9X = 57 + 2.33 \cdot 9X=57+2.33⋅9
12. Calculate:
13. X=57+20.97=77.97X = 57 + 20.97 = 77.97X=57+20.97=77.97
14. Round up to the nearest whole number:
15. Since you can't stock a fraction of a linen, round up to the nearest whole number.
16. X≈78X \approx 78X≈78

Therefore, Mr. Ibrahim should stock at least 78 clean linens each week to be prepared for 99% of all demands.