Principles Of Operations Management
Principles Of Operations Management
11th Edition
ISBN: 9780135173930
Author: RENDER, Barry, HEIZER, Jay, Munson, Chuck
Publisher: Pearson,
bartleby

Videos

Textbook Question
Book Icon
Chapter 4, Problem 59P

Sales of tablet computers at Ted Glickman’s electronics store in Washington, D.C., over the past 10 weeks are shown in the table below:

Chapter 4, Problem 59P, Sales of tablet computers at Ted Glickmans electronics store in Washington, D.C., over the past 10

a) Forecast demand for each week, including week 10, using exponential smoothing with α = .5 (initial forecast = 20).

b) Compute the MAD.

c) Compute the tracking signal.

a)

Expert Solution
Check Mark
Summary Introduction

To determine: To forecast the demand for 10 weeks using exponential smoothing.

Introduction: A sequence of data points in successive order is known as time series. Time series forecasting is the prediction based on past events, which are at a uniform time interval. Exponential smoothing is one of the time series methods which use a smoothing constant to emphasis past data.

Answer to Problem 59P

Using exponential smoothing, the forecast for week 10 is done.

Explanation of Solution

Given information:

Week Demand
1 20
2 21
3 28
4 37
5 25
6 29
7 36
8 22
9 25
10 28

Smoothingconstantα=0.5Initialforecast=20

Formula to calculate the forecasted demand:

Ft=Ft-1+α(At-1Ft-1)

Where,

Ft=newforecastFt-1=Previousperiod'sforecastα=smoothingconstantAt-1=PreviousperiodactualDemand

Calculation to forecast demand using exponential smoothing:

Week Demand Ft
1 20 20
2 21 20
3 28 20.50
4 37 24.25
5 25 30.63
6 29 27.81
7 36 28.41
8 22 32.20
9 25 27.10
10 28 26.05

Excel worksheet:

Principles Of Operations Management, Chapter 4, Problem 59P , additional homework tip  1

Calculation of the forecast for week 2:

F2=F1+α(A1F1)=20+0.5(2020)=20

To calculate the forecast for week 2, substitute the value of forecast of week 1, smoothing constant and difference between actual and forecasted demand in the above formula. The result of forecast for week 2 is 20.

Calculation of the forecast for week 3:

F3=F2+α(A2F2)=20+0.5(2120)=20.50

To calculate the forecast for week 3, substitute the value of forecast of week 1, smoothing constant and difference between actual and forecasted demand in the above formula. The result of forecast for week 3 is 20.50.

Calculation of the forecast for week 4:

F4=F3+α(A3F3)=20.50+0.5(2820.50)=24.25

To calculate the forecast for week 4, substitute the value of forecast of week 3, smoothing constant and difference between actual and forecasted demand in the above formula. The result of forecast for week 4 is 24.25.

Calculation of the forecast for week 5:

F5=F4+α(A4F4)=24.25+0.5(2724.25)=30.63

To calculate the forecast for week 5, substitute the value of forecast of week 4, smoothing constant and difference between actual and forecasted demand in the above formula. The result of forecast for week 5 is 30.63.

Calculation of the forecast for week 6:

F6=F5+α(A5F5)=30.63+0.5(2530.63)=27.81

To calculate the forecast for week 6, substitute the value of forecast of week 5, smoothing constant and difference between actual and forecasted demand in the above formula. The result of forecast for week 6 is 27.81.

Calculation of the forecast for week 7:

F7=F6+α(A6F6)=27.81+0.5(2927.81)=28.41

To calculate the forecast for week 7, substitute the value of forecast of week 6, smoothing constant and difference between actual and forecasted demand in the above formula. The result of forecast for week 7 is 28.41.

Calculation of the forecast for week 8:

F8=F7+α(A7F7)=28.41+0.5(3628.41)=32.20

To calculate the forecast for week 8, substitute the value of forecast of week 7, smoothing constant and difference between actual and forecasted demand in the above formula. The result of forecast for week 8 is 32.20.

Calculation of the forecast for week 9:

F9=F8+α(A8F8)=32.20+0.5(2232.20)=27.10

To calculate the forecast for week 9, substitute the value of forecast of year 8, smoothing constant and difference between actual and forecasted demand in the above formula. The result of forecast for week 9 is 27.10.

Calculation of the forecast for week 10:

F10=F9+α(A9F9)=27.10+0.5(2527.10)=26.05

To calculate the forecast for week 10, substitute the value of forecast of year 9, smoothing constant and difference between actual and forecasted demand in the above formula. The result of forecast for week 10 is 26.05.

Thus, using exponential smoothing, the forecast for week 10 is done.

b)

Expert Solution
Check Mark
Summary Introduction

To determine: To compute MAD.

Answer to Problem 59P

MAD is 4.99.

Explanation of Solution

Given information:

Week Demand
1 20
2 21
3 28
4 37
5 25
6 29
7 36
8 22
9 25
10 28

Smoothingconstantα=0.5Initialforecast=20

Formula to calculate MAD:

MAD=|ActualForecast|n

Calculation of MAD:

Week Demand Ft Absolute error
1 20 20 0
2 21 20 1
3 28 20.50 7.50
4 37 24.25 12.75
5 25 30.63 5.63
6 29 27.81 1.19
7 36 28.41 7.59
8 22 32.20 10.20
9 25 27.10 2.10
10 28 26.05 1.95
Total 49.91
MAD 4.99

Table 1

Excel worksheet:

Principles Of Operations Management, Chapter 4, Problem 59P , additional homework tip  2

Calculation of the absolute error for week 2:

Absoluteerror=|ActualForecast|=|2120|=|1|=1

The absolute error for week 1 is the modulus of the difference between 21 and 20, which corresponds to 1. Therefore, the absolute error for week 2 is 1.

Calculation of the absolute error for week 3:

Absoluteerror=|ActualForecast|=|2820.50|=|7.50|=7.50

The absolute error for week 3 is the modulus of the difference between 28 and 20.50, which corresponds to 7.50. Therefore, the absolute error for week 3 is 7.50.

Calculation of the absolute error for week 4:

Absoluteerror=|ActualForecast|=|3724.25|=|12.75|=12.75

The absolute error for week 4 is the modulus of the difference between 37 and 24.25, which corresponds to 12.75. Therefore, the absolute error for week 4 is 12.75.

Calculation of the absolute error for week 5:

Absoluteerror=|ActualForecast|=|2530.63|=|5.63|=5.63

The absolute error for week 5 is the modulus of the difference between 25 and 30.63, which corresponds to 5.63. Therefore, the absolute error for week 5 is 5.63.

Calculation of the absolute error for week 6:

Absoluteerror=|ActualForecast|=|2927.81|=|1.19|=1.19

The absolute error for week 6 is the modulus of the difference between 29 and 27.81, which corresponds to 1.19. Therefore, the absolute error for week 6 is 1.19.

Calculation of the absolute error for week 7:

Absoluteerror=|ActualForecast|=|3628.41|=|7.59|=7.59

The absolute error for week 7 is the modulus of the difference between 36 and 28.41, which corresponds to 7.59. Therefore, the absolute error for week 7 is 7.59.

Calculation of the absolute error for week 8:

Absoluteerror=|ActualForecast|=|2232.20|=|10.20|=10.20

The absolute error for week 8 is the modulus of the difference between 22 and 32.20, which corresponds to 10.20. Therefore, the absolute error for week 8 is 10.20.

Calculation of the absolute error for week 9:

Absoluteerror=|Actual-Forecast|=|2527.10|=|2.10|=2.10

The absolute error for week 9 is the modulus of the difference between 25 and 27.10, which corresponds to 2.10. Therefore, the absolute error for week 9 is 2.10.

Calculation of the absolute error for week 10:

Absoluteerror=|ActualForecast|=|2826.05|=|2.10|=2.10

The absolute error for week 10 is the modulus of the difference between 28 and 26.05, which corresponds to 2.10. Therefore, the absolute error for week 10 is 2.10.

Calculation of the Mean Absolute Deviation:

MAD=|ActualForecast|n=0+1+7.50+12.75+5.63+1.19+7.59+10.20+2.10+1.9510=49.9110=4.99

The substitution of the summation value of absolute error for 10 weeks, divided by the number of weeks, which is 10 yields a MAD of 4.99.

The computed MAD is 4.99.

c)

Expert Solution
Check Mark
Summary Introduction

To determine: To compute the tracking signal.

Answer to Problem 59P

The tracking signal is 2.82.

Explanation of Solution

Given information:

Week Demand
1 20
2 21
3 28
4 37
5 25
6 29
7 36
8 22
9 25
10 28

Smoothingconstantα=0.5Initialforecast=20

Formula to calculate tracking signal:

TrackingSignal=CumulativeerrorMAD=(ActualdemandinperiodiForecasteddemandinperiodi)MADMAD=|ActualForecast|n

Calculation of tracking signal:

Table 1 shows the calculation of MAD

Week Demand Ft Absolute error Error Cumulative error
1 20 20 0 0 0
2 21 20 1 1 1
3 28 20.50 7.50 7.5 8.50
4 37 24.25 12.75 12.75 21.25
5 25 30.63 5.63 -5.63 15.63
6 29 27.81 1.19 1.19 16.81
7 36 28.41 7.59 7.59 24.41
8 22 32.20 10.20 -10.20 14.20
9 25 27.10 2.10 -2.10 12.10
10 28 26.05 1.95 1.95 14.05
Total 49.91
MAD 4.99 Tracking signal 2.82

Excel worksheet:

Principles Of Operations Management, Chapter 4, Problem 59P , additional homework tip  3

Calculation of tracking signal:

TrackingSignal=CumulativeerrorMAD=14.054.99=2.82

The ratio of cumulative error and MAD is known as the tracking signal. The tracking signal of 2.82 is obtained by dividing 14.05 by 4.99.

Hence, the computed tracking signal is 2.82.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Sales of hair dryers at the Walgreens stores in Youngstown, Ohio, over the past 4 months have been 100, 110, 120, and 130 units (with 130 being the most recent sales). Develop a moving-average forecast for next month, using these three techniques:a) 3-month moving average.b) 4-month moving average.c) Weighted 4-month moving average with the most recent month weighted 4, the preceding month 3, then 2, and the oldest month weighted 1.d) If next month’s sales turn out to be 140 units, forecast the following month’s sales (months) using a 4-month moving average.
4. A local moving company has collected data on the number of moves they have been asked to perform over the past two years. Moving is highly seasonal, so the owner/operator, who is both burly and highly educated, decides to apply the multiplicative seasonal method to forecast the number of customers for the coming year. The equation for the trend line of yearly sales is F1 = 100 + 60t. Please forecast demand for each quarter in Year 3. (Round the forecasts to whole numbers and show all calculations t Complete the table below and forecast the sales of Year 3 by quarter. Copy the table below, paste to the answer box and fill in your answers. You need to take a picture of your work and upload the picture in next question. Year 1 Year 2 Year 3 Quarter Demand Quarter Demand Quarter Demand 1 28 1 45 1 43 60 2 120 140 4 49 55 4 Total 240 Total 300 Total Average Average Average For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).
The sales of Bluetooth Headphones at the Dubai Electronics Enterprises in Jebel Ali, UAE, over the past 4 months have been 100, 110, 120, and 130 units (with 130 being the most recent sales). Develop a moving-average forecast for next month, using the following techniques: 5B. If next month's sales turn out to be 140 units, forecast the following month's sales (months) using a 4-month moving average.

Chapter 4 Solutions

Principles Of Operations Management

Ch. 4 - What is the primary difference between a...Ch. 4 - Define time series.Ch. 4 - What effect does the value of the smoothing...Ch. 4 - Explain the value of seasonal indices in...Ch. 4 - Prob. 14DQCh. 4 - In your own words, explain adaptive forecasting.Ch. 4 - Prob. 16DQCh. 4 - Explain, in your own words, the meaning of the...Ch. 4 - Prob. 18DQCh. 4 - Give examples of industries that are affected by...Ch. 4 - Prob. 20DQCh. 4 - Prob. 21DQCh. 4 - CEO John Goodale, at Southern Illinois Power and...Ch. 4 - The following gives the number of pints of type B...Ch. 4 - a) Plot the above data on a graph. Do you observe...Ch. 4 - Refer to Problem 4.2. Develop a forecast for years...Ch. 4 - A check-processing center uses exponential...Ch. 4 - The Carbondale Hospital is considering the...Ch. 4 - The monthly sales for Yazici Batteries, Inc., were...Ch. 4 - Prob. 7PCh. 4 - Daily high temperatures in St. Louis for the last...Ch. 4 - Lenovo uses the ZX-81 chip in some of its laptop...Ch. 4 - Data collected on the yearly registrations for a...Ch. 4 - Use exponential smoothing with a smoothing...Ch. 4 - Prob. 12PCh. 4 - At you can see in the following table, demand for...Ch. 4 - Prob. 14PCh. 4 - Refer to Solved Problem 4.1 on page 144. a) Use a...Ch. 4 - Prob. 16PCh. 4 - Prob. 17PCh. 4 - Prob. 18PCh. 4 - Income at the architectural firm Spraggins and...Ch. 4 - Resolve Problem 4.19 with = .1 and =.8. Using...Ch. 4 - Prob. 21PCh. 4 - Refer to Problem 4.21. Complete the trend-adjusted...Ch. 4 - Prob. 23PCh. 4 - The following gives the number of accidents that...Ch. 4 - In the past, Peter Kelles tire dealership in Baton...Ch. 4 - George Kyparisis owns a company that manufactures...Ch. 4 - Attendance at Orlandos newest Disneylike...Ch. 4 - Prob. 28PCh. 4 - The number of disk drives (in millions) made at a...Ch. 4 - Prob. 30PCh. 4 - Emergency calls to the 911 system of Durham, North...Ch. 4 - Using the 911 call data in Problem 4.31, forecast...Ch. 4 - Storrs Cycles has just started selling the new...Ch. 4 - Prob. 35PCh. 4 - Prob. 36PCh. 4 - Prob. 37PCh. 4 - Prob. 38PCh. 4 - Prob. 39PCh. 4 - Prob. 40PCh. 4 - Prob. 41PCh. 4 - Prob. 42PCh. 4 - Mark Gershon, owner of a musical instrument...Ch. 4 - Prob. 44PCh. 4 - Cafe Michigans manager, Gary Stark, suspects that...Ch. 4 - Prob. 46PCh. 4 - The number of auto accidents in Athens, Ohio, is...Ch. 4 - Rhonda Clark, a Slippery Rock, Pennsylvania, real...Ch. 4 - Accountants at the Tucson firm, Larry Youdelman,...Ch. 4 - Prob. 50PCh. 4 - Using the data in Problem 4.30, apply linear...Ch. 4 - Bus and subway ridership for the summer months in...Ch. 4 - Prob. 53PCh. 4 - Dave Fletcher, the general manager of North...Ch. 4 - Prob. 55PCh. 4 - Prob. 56PCh. 4 - Prob. 57PCh. 4 - Sales of tablet computers at Ted Glickmans...Ch. 4 - The following are monthly actual and forecast...Ch. 4 - Prob. 1CSCh. 4 - Prob. 2CSCh. 4 - Prob. 3CSCh. 4 - Prob. 1.1VCCh. 4 - Prob. 1.2VCCh. 4 - Using Perezs multiple-regression model, what would...Ch. 4 - Prob. 1.4VCCh. 4 - Prob. 2.1VCCh. 4 - Prob. 2.2VCCh. 4 - Prob. 2.3VCCh. 4 - Prob. 2.4VCCh. 4 - Prob. 2.5VC
Knowledge Booster
Background pattern image
Operations Management
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
  • Text book image
    Practical Management Science
    Operations Management
    ISBN:9781337406659
    Author:WINSTON, Wayne L.
    Publisher:Cengage,
    Text book image
    Contemporary Marketing
    Marketing
    ISBN:9780357033777
    Author:Louis E. Boone, David L. Kurtz
    Publisher:Cengage Learning
    Text book image
    Marketing
    Marketing
    ISBN:9780357033791
    Author:Pride, William M
    Publisher:South Western Educational Publishing
  • Text book image
    Purchasing and Supply Chain Management
    Operations Management
    ISBN:9781285869681
    Author:Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
    Publisher:Cengage Learning
Text book image
Practical Management Science
Operations Management
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:Cengage,
Text book image
Contemporary Marketing
Marketing
ISBN:9780357033777
Author:Louis E. Boone, David L. Kurtz
Publisher:Cengage Learning
Text book image
Marketing
Marketing
ISBN:9780357033791
Author:Pride, William M
Publisher:South Western Educational Publishing
Text book image
Purchasing and Supply Chain Management
Operations Management
ISBN:9781285869681
Author:Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
Publisher:Cengage Learning
Forecasting 2: Forecasting Types & Qualitative methods; Author: Adapala Academy & IES GS for Exams;https://www.youtube.com/watch?v=npWni9K6Z_g;License: Standard YouTube License, CC-BY
Introduction to Forecasting - with Examples; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=98K7AG32qv8;License: Standard Youtube License