Operations Management
Operations Management
13th Edition
ISBN: 9781259667473
Author: William J Stevenson
Publisher: McGraw-Hill Education
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Chapter 3, Problem 22P

Two independent methods of forecasting based on judgment and expenence have been prepared each month for the past 10 months. The forecasts and actual sales are as follows:

Chapter 3, Problem 22P, Two independent methods of forecasting based on judgment and expenence have been prepared each month

a. Compute the MSE and MAD for each forecast. Does either forecast seem superior? Explain.

b. Compute MAPE for each forecast.

c. Prepare a naive forecast for periods 2 through 11 using the given sales data Compute each of the following: (1) MSE, (2) MAD, (3) tracking signal at month 10, and (4) 2s control limits How do the naive results compare with the other two forecasts?

a)

Expert Solution
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Summary Introduction

To compare: The MAD and MSE for two forecasts given below, including actual sales for 10 months.

Introduction: Mean Absolute Deviation (MAD) is the average distance between the data values and the mean. Mean Squared Error (MSE) is the average of the squares of the deviation and error.

Explanation of Solution

Given information:

Operations Management, Chapter 3, Problem 22P , additional homework tip  1

Compute the MAD and MSE as shown below in the table:

Operations Management, Chapter 3, Problem 22P , additional homework tip  2

Compute the Mean absolute deviation (MAD) for the forecasting method F1 as shown below

MAD=|error|n

Substitute the value of |error|=28 and the value of n=10 to obtain the Mean absolute deviation (MAD)

MAD=2810=2.8_

Compute the Mean squared error (MSE) for the forecasting method F1 as shown below

MSE=|error2|n1

Substitute the value of |error2|=94 and the value of n=10 to obtain the Mean squared error (MSE)

MSE=94101=10.44_

Compute the Mean absolute deviation (MAD) for the forecasting method F2 as shown below

MAD=|error|n

Substitute the value of |error|=36 and the value of n=10 to obtain the Mean absolute deviation (MAD)

MAD=3610=3.6_

Compute the Mean squared error (MSE) for the forecasting method F2 as shown below

MSE=|error2|n1

Substitute the value of |error2|=382 and the value of n=10 to obtain the Mean squared error (MSE)

MSE=382101=42.44_

The first forecasting method F1 gives both a low value of MAD as well as MSE compared to the second forecasting method F2

b)

Expert Solution
Check Mark
Summary Introduction

To compute: Mean Absolute Percentage Error for both the forecasts F1 and F2 as shown below.

Introduction: Forecasting is the planning process that helps to predict the future demand using present or past data. It uses certain assumptions based the knowledge and experience of the management.

Explanation of Solution

Determine MAPE for both the forecasts:

Operations Management, Chapter 3, Problem 22P , additional homework tip  3

The Mean absolute percentage error is lower at 0.36% for the first forecasting method F1 compared to MAPE of 0.46% for the second forecasting method F2

c)

Expert Solution
Check Mark
Summary Introduction

To prepare: A naïve forecast.

Introduction: Forecasting is the planning process that helps to predict the future demand using present or past data. It uses certain assumptions based the knowledge and experience of the management.

Explanation of Solution

Determine MAD and MSE using a naïve forecast:

Use the naïve method for forecasting as shown below.

Operations Management, Chapter 3, Problem 22P , additional homework tip  4

(i)

Compute the Mean absolute deviation (MAD) for the naïve forecasting method as shown below

MAD=|error|n

Substitute the value of |error|=96 and the value of n=9 to obtain the Mean absolute deviation (MAD)

MAD=969=10.67_

(ii)

Compute the Mean squared error (MSE) for the naïve forecasting method as shown below

MSE=|error2|n1

Substitute the value of |error2|=1,248 and the value of n=9 to obtain the Mean squared error (MSE)

MSE=1,24891=156_

(iii)

Compute the tracking signal on the 10th month as shown below.

First compute the cumulative forecast error (CFE) as shown below

12.49=

CFE=19+51412+412+15+11+4=20

Compute the tracking signal (TS) by dividing the cumulative forecast error by MAD as shown below.

TS=2010.67=1.87_

(iv)

Given the Mean Squared Error is 156, the standard deviation σ is 12.49

The two sigma control limits are +2×12.49=24.98 and -2×12.49=–24.98

Since the tracking signal 1.87 falls between +24.98 and –24.98, the forecasting process is in control

The comparison of the naïve method with the other two forecasting methods is shown below.

Operations Management, Chapter 3, Problem 22P , additional homework tip  5

Obviously the naïve method compares very poorly with the other two methods F1 and F2, since both the Mean Absolute Deviation (MAD) and Mean Squared Error (MSE) are worse than the other two methods.

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Students have asked these similar questions
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Here are the actual tabulated demands for an item for a nine-month period (January through September). Your supervisor wants to test two forecasting methods to see which method was better over this period.   MONTH ACTUAL January 120 February 145 March 146 April 171 May 154 June 182 July 138 August 135 September 146     a. Forecast April through September using a three-month moving average. b. Use simple exponential smoothing with an alpha of  0.20 to estimate April through September, using the average of January through March as the initial forecast for April.  c-1. Calculate MAD for Three-month moving average and Exponential smoothing. c-2. Use MAD to decide which method produced the better forecast over the six-month period.
Two independent methods of forecasting based on judgment and experience have been prepared each month for the past 10 months. The forecasts and actual sales are as follows:

Chapter 3 Solutions

Operations Management

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