Tyler is hoping to get a lot of custom cake and cookie orders in his new bakery for various parties and celebrations. He considers keeping a stock of celebratory helium balloons in his bakery so that he can sell them alongside the cakes and cookies to add more value for his customers. However, he knows that the demand for custom goods as well as the balloons is like to be probabilistic in nature instead of deterministic. He is trying to create a model of how many balloons to order to keep in stock to minimize the costs of inventory in his little bakery. He identifies the following characteristics and needs your help in filling out the table given below the information.Ordering Cost is $14.00 per orderCost of balloons is $4.00 per balloonThe bakery uses the 20% annual holding cost rate for all inventoryThe lead time for a new order of helium balloons is 14 days.Data from other bakeries indicate that the demand during the 14-day lead time follows a normal probability distribution with a weekly mean of 25 balloons and a standard deviation of 7 balloons per week.The number of working days per year is 300Acceptable probability of a stock-out, for Tyler is 10% or 0.10. # Optimal Inventory Policy OverviewThis table outlines the components of an optimal inventory policy. It provides spaces for entering values related to inventory management, expressed in either units (balloons) or currency (dollars), depending on the specific metric.### Components:1. **Economic Order Quantity (Q*):** - Measurement Unit: Balloons - Definition: The optimal quantity to order that minimizes total inventory costs.2. **Annual Inventory Holding Cost (H):** - Measurement Unit: Dollars - Definition: The cost associated with holding inventory over a year.3. **Annual Ordering Cost (O):** - Measurement Unit: Dollars - Definition: The total cost incurred from ordering inventory each year.4. **Total Annual Cost (TC):** - Measurement Unit: Dollars - Definition: The combined total of holding and ordering costs annually.5. **Maximum Inventory Level (Q* + S):** - Measurement Unit: Balloons - Definition: The highest quantity of stock available, considering safety stock (S).6. **Average Inventory Level ((Q*/2) + S):** - Measurement Unit: Balloons - Definition: The average stock level over time, factoring in safety stock.7. **Reorder Point (r):** - Measurement Unit: Balloons - Definition: The inventory level that triggers a new order to replenish stock.8. **Number of Orders per Year (D/Q*):** - Definition: How many times an order is placed annually, determined by demand (D) and EOQ (Q*).9. **Cycle Time (Days) (T):** - Measurement Unit: Days - Definition: The time interval between placing orders.10. **Safety Stock (S):** - Measurement Unit: Balloons - Definition: Extra stock kept to prevent stockouts.11. **Expected Stockouts per Year (SO):** - Definition: The forecasted occurrences of running out of stock annually.This structured approach helps businesses effectively manage inventory, balancing costs, and ensuring product availability.

We are allowed to do first three sub-parts only. The answer is as below:

Answered: onomic Order Quantity Q* balloons anual…

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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Tyler is hoping to get a lot of custom cake and cookie orders in his new bakery for various parties and celebrations. He considers keeping a stock of celebratory helium balloons in his bakery so that he can sell them alongside the cakes and cookies to add more value for his customers. However, he knows that the demand for custom goods as well as the balloons is like to be probabilistic in nature instead of deterministic. He is trying to create a model of how many balloons to order to keep in stock to minimize the costs of inventory in his little bakery. He identifies the following characteristics and needs your help in filling out the table given below the information.

Ordering Cost is $14.00 per order
Cost of balloons is $4.00 per balloon
The bakery uses the 20% annual holding cost rate for all inventory
The lead time for a new order of helium balloons is 14 days.
Data from other bakeries indicate that the demand during the 14-day lead time follows a normal probability distribution with a weekly mean of 25 balloons and a standard deviation of 7 balloons per week.
The number of working days per year is 300
Acceptable probability of a stock-out, for Tyler is 10% or 0.10.

# Optimal Inventory Policy Overview

This table outlines the components of an optimal inventory policy. It provides spaces for entering values related to inventory management, expressed in either units (balloons) or currency (dollars), depending on the specific metric.

### Components:

1. **Economic Order Quantity (Q*):**
- Measurement Unit: Balloons
- Definition: The optimal quantity to order that minimizes total inventory costs.

2. **Annual Inventory Holding Cost (H):**
- Measurement Unit: Dollars
- Definition: The cost associated with holding inventory over a year.

3. **Annual Ordering Cost (O):**
- Measurement Unit: Dollars
- Definition: The total cost incurred from ordering inventory each year.

4. **Total Annual Cost (TC):**
- Measurement Unit: Dollars
- Definition: The combined total of holding and ordering costs annually.

5. **Maximum Inventory Level (Q* + S):**
- Measurement Unit: Balloons
- Definition: The highest quantity of stock available, considering safety stock (S).

6. **Average Inventory Level ((Q*/2) + S):**
- Measurement Unit: Balloons
- Definition: The average stock level over time, factoring in safety stock.

7. **Reorder Point (r):**
- Measurement Unit: Balloons
- Definition: The inventory level that triggers a new order to replenish stock.

8. **Number of Orders per Year (D/Q*):**
- Definition: How many times an order is placed annually, determined by demand (D) and EOQ (Q*).

9. **Cycle Time (Days) (T):**
- Measurement Unit: Days
- Definition: The time interval between placing orders.

10. **Safety Stock (S):**
- Measurement Unit: Balloons
- Definition: Extra stock kept to prevent stockouts.

11. **Expected Stockouts per Year (SO):**
- Definition: The forecasted occurrences of running out of stock annually.

This structured approach helps businesses effectively manage inventory, balancing costs, and ensuring product availability.

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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