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 PolicyEconomic Order Quantity Q*balloonsAnnual Inventory Holding CostHdollarsAnnual Ordering Cost OdollarsTotal Annual Cost TCdollarsMaximum Inventory Level Q*+ SballoonsAverage Inventory Level(Q*/2)+SballoonsReorder Point rballoonsNumber of Orders per Year|(D/Q*)Cycle Time (Days) TdaysSafety Stock SballoonsExpected Stockouts per Year SO

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
Economic Order Quantity Q*
balloons
Annual Inventory Holding Cost
H
dollars
Annual Ordering Cost O
dollars
Total Annual Cost TC
dollars
Maximum Inventory Level Q*+ S
balloons
Average Inventory Level
(Q*/2)+S
balloons
Reorder Point r
balloons
Number of Orders per Year
|(D/Q*)
Cycle Time (Days) T
days
Safety Stock S
balloons
Expected Stockouts per Year SO

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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