Thomas’ Bike Shop stocks a high volume item that has a normally distributed demandduring the reorder period. The average daily demand is 70 units, the lead time is 4 days,and the standard deviation of demand during the reorder period is 15.a. How much safety stock provides a 95% service level to Thomas?b. What should the reorder point be **Inventory Management at Thomas' Bike Shop**Thomas' Bike Shop stocks a high-volume item with a demand that follows a normal distribution during the reorder period. Key details are as follows:- **Average Daily Demand**: 70 units- **Lead Time**: 4 days- **Standard Deviation of Demand During Reorder Period**: 15**Questions:**a. How much safety stock is needed to provide a 95% service level?b. What should the reorder point be?To solve these questions, consider the following:1. **Safety Stock Calculation**: - To achieve a 95% service level, find the Z-score for 95% from the standard normal distribution table (approximately 1.65). - Calculate safety stock using the formula: \[ \text{Safety Stock} = Z \times (\text{Standard Deviation of Demand} \times \sqrt{\text{Lead Time}}) \]2. **Reorder Point Calculation**: - Calculate the expected demand during lead time: \[ \text{Expected Demand during Lead Time} = \text{Average Daily Demand} \times \text{Lead Time} \] - Add safety stock to determine the reorder point: \[ \text{Reorder Point} = \text{Expected Demand during Lead Time} + \text{Safety Stock} \]These calculations will ensure that Thomas' Bike Shop meets customer demands efficiently during the reorder period.

Given information: Average daily demand = 70 units Lead time…

Answered: Thomas’ Bike Shop stocks a high volume…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Related questions

Question

Thomas’ Bike Shop stocks a high volume item that has a normally distributed demand

during the reorder period. The average daily demand is 70 units, the lead time is 4 days,

and the standard deviation of demand during the reorder period is 15.

a. How much safety stock provides a 95% service level to Thomas?

b. What should the reorder point be

**Inventory Management at Thomas' Bike Shop**

Thomas' Bike Shop stocks a high-volume item with a demand that follows a normal distribution during the reorder period. Key details are as follows:

- **Average Daily Demand**: 70 units
- **Lead Time**: 4 days
- **Standard Deviation of Demand During Reorder Period**: 15

**Questions:**

a. How much safety stock is needed to provide a 95% service level?

b. What should the reorder point be?

To solve these questions, consider the following:

1. **Safety Stock Calculation**:
- To achieve a 95% service level, find the Z-score for 95% from the standard normal distribution table (approximately 1.65).
- Calculate safety stock using the formula:
\[
\text{Safety Stock} = Z \times (\text{Standard Deviation of Demand} \times \sqrt{\text{Lead Time}})
\]

2. **Reorder Point Calculation**:
- Calculate the expected demand during lead time:
\[
\text{Expected Demand during Lead Time} = \text{Average Daily Demand} \times \text{Lead Time}
\]
- Add safety stock to determine the reorder point:
\[
\text{Reorder Point} = \text{Expected Demand during Lead Time} + \text{Safety Stock}
\]

These calculations will ensure that Thomas' Bike Shop meets customer demands efficiently during the reorder period.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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