Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Chapter 10, Problem 38P
It is surprising (but true) that if 23 people are in the same room, there is about a 50% chance that at least two people will have the same birthday. Suppose you want to estimate the probability that if 30 people are in the same room, at least two of them will have the same birthday. You can proceed as follows.
- a. Generate random birthdays for 30 different people. Ignoring the possibility of a leap year, each person has a 1/365 chance of having a given birthday (label the days of the year 1 to 365). You can use the RANDBETWEEN function to generate birthdays.
- b. Once you have generated 30 people’s birthdays, how can you tell whether at least two people have the same birthday? One way is to use Excel’s RANK function. (You can learn how to use this function in Excel’s online help.) This function returns the rank of a number relative to a given group of numbers. In the case of a tie, two numbers are given the same rank. For example, if the set of numbers is 4, 3, 2, 5, the RANK function returns 2, 3, 4, 1. (By default, RANK gives 1 to the largest number.) If the set of numbers is 4, 3, 2, 4, the RANK function returns 1, 3, 4, 1.
- c. After using the RANK function, you should be able to determine whether at least two of the 30 people have the same birthday. What is the (estimated) probability that this occurs?
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Scenario
You have been given a task to create a demand forecast for the second year of sales of a premium outdoor grill.
Accurate forecasts are important for many reasons, including for the company to ensure they have the materials
they need to create the products required in a certain period of time. Your objective is to minimize the forecast
error, which will be measured using the Mean Absolute Percentage Error (MAPE) with a goal of being below 25%.
You have historical monthly sales data for the past year and access to software that provides forecasts based on
five different forecasting techniques (Naïve, 3-Month Moving Average, Exponential Smoothing for .2, Exponential
Smooth for .5, and Seasonal) to help determine the best forecast for that particular month. Based on the given
data, you will identify trends and patterns to create a more accurate forecast.
Approach
Consider the previous month's forecast to identify which technique is most effective. Use that to forecast the next…
Approach
Consider the previous month's forecast to identify which technique is most effective. Use that to forecast the next
month.
Remember to select the forecasting technique that produces the forecast error nearest to zero. For example:
a. Naïve Forecast is 230 and the Forecast Error is -15.
b. 3-Month Moving Forecast is 290 and the Forecast Error is -75.
c. Exponential Smoothing Forecast for .2 is 308 and the Forecast Error is -93.
d. Exponential Smoothing Forecast for .5 is 279 and the Forecast Error is -64.
e. Seasonal Forecast is 297 and the Forecast Error is -82.
The forecast for the next month would be 230 as the Naïve Forecast had the Forecast Error closest to zero with a
-15. This forecasting technique was the best performing technique for that month. You do not need to do any
external analysis-the forecast error for each strategy is already calculated for you in the tables below.
Naïve
Month Period
Actual
Demand
Naïve Forecast
Error
3-
Month
Moving
Forecast
3-
Month
Moving…
Chapter 10 Solutions
Practical Management Science
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