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Calculate a forecast using a simple three month moving average

04/01/2021 Client: saad24vbs Deadline: 2 Day

Problem 18-4


Here are the data for the past 21 months for actual sales of a particular product:




LAST YEAR


THIS YEAR


  January


365


300


  February


455


375


  March


400


375


  April


430


455


  May


432


440


  June


505


380


  July


400


385


  August


320


305


  September


395


365


  October


500




  November


590




  December


490




Develop a forecast for the fourth quarter using a three-quarter, weighted moving average. Weight the most recent quarter 0.50, the second most recent 0.25, and the third 0.25. Do the problem using quarters, as opposed to forecasting separate months. (Round your answer to 2 decimal places.)


  Forecast for the fourth quarter






Explanation:


Third most recent quarter 300 + 375 + 375 = 1,050


Second most recent quarter 455 + 440 + 380 = 1,275


Most recent quarter 385 + 305 + 365 = 1,055




WMA = (0.25 × 1,050) + (0.25 × 1,275) + (0.50 × 1,055) = 1,108.75


References


WorksheetDifficulty: Challenge


Problem 18-4Learning Objective: 18-02 Evaluate demand using quantitative forecasting models.


Problem 18-7


The following table contains the demand from the last 10 months:


MONTH


ACTUAL DEMAND


1


32


2


35


3


36


4


38


5


41


6


39


7


39


8


41


9


44


10


40


a.


Calculate the single exponential smoothing forecast for these data using an α of 0.30 and an initial forecast (F1) of 32. (Round your answers to 2 decimal places.)


Month


        Exponential Smoothing


1




2




3




4




5




6




7




8




9




10




b.


Calculate the exponential smoothing with trend forecast for these data using an α of 0.30, a δ of 0.20, an initial trend forecast (T1) of 1.00, and an initial exponentially smoothed forecast (F1) of 31. (Round your answers to 2 decimal places.)


Month


          FITt


1




2




3




4




5




6




7




8




9




10




c-1.


Calculate the mean absolute deviation (MAD) for the last nine months of forecasts. (Round your answers to 2 decimal places.)




MAD


  Single exponential smoothing forecast




  Exponential smoothing with trend forecast




c-2.


Which is best?








Exponential smoothing with trend forecast


Single exponential smoothing forecast


Explanation:


a. to c.


Month


Demand


Exponential Smoothing


Absolute Deviation


Tt


Ft


FITt


Absolute Deviation


1


32


32.00




1.00


31.00


32.00




2


35


32.00


3.00


1.00


32.00


33.00


2.00


3


36


32.90


3.10


1.12


33.60


34.72


1.28


4


38


33.83


4.17


1.20


35.10


36.30


1.70


5


41


35.08


5.92


1.30


36.81


38.11


2.89


6


39


36.86


2.14


1.47


38.98


40.45


1.45


7


39


37.50


1.50


1.38


40.02


41.40


2.40


8


41


37.95


3.05


1.24


40.68


41.92


0.92


9


44


38.87


5.13


1.18


41.64


42.82


1.18


10


40


40.41


0.41


1.25


43.17


44.42


4.42














  MAD






3.16








2.03














Based upon the MAD of each forecast, the exponential smoothing with trend is the better forecasting model.


References


WorksheetDifficulty: Challenge


Problem 18-7Learning Objective: 18-02 Evaluate demand using quantitative forecasting models.


Problem 18-10


The number of cases of merlot wine sold by the Connor Owen winery in an eight-year period is as follows:


YEAR


CASES OF MERLOT WINE


2005


291


2006


377


2007


419


2008


477


2009


379


2010


521


2011


431


2012


397


Using an exponential smoothing model with an alpha value of 0.40, estimate the smoothed value calculated as of the end of 2012. Use the average demand for 2005 through 2007 as your initial forecast for 2008, and then smooth the forecast forward to 2012. (Round your intermediate calculations and final answer to the nearest whole number.)


  Forecast for 2012






Explanation:


Year


Demand


F(t)


2005


291




2006


377




2007


419




2008


477


362


2009


379


408


2010


521


396


2011


431


446


2012


397


440


References


WorksheetDifficulty: Challenge


Problem 18-10Learning Objective: 18-02 Evaluate demand using quantitative forecasting models.


Problem 18-15


Historical demand for a product is




DEMAND


  January


16


  February


14


  March


18


  April


16


  May


19


  June


18


a.


Using a weighted moving average with weights of 0.50 (June), 0.20 (May), and 0.30 (April), find the July forecast. (Round your answer to 1 decimal place.)


  July forecast




b.


Using a simple three-month moving average, find the July forecast. (Round your answer to 1 decimal place.)


  July forecast




c.


Using single exponential smoothing with α = 0.20 and a June forecast = 12, find the July forecast. (Round your answer to 1 decimal place.)


  July forecast




d.


Using simple linear regression analysis, calculate the regression equation for the preceding demand data. (Do not round intermediate calculations. Round your intercept value to 1 decimal place and slope value to 2 decimal places.)


  Y = + t


e.


Using the regression equation in d, calculate the forecast for July. (Do not round intermediate calculations. Round your answer to 1 decimal place.)


  July forecast






Explanation:


a.


FJuly = 0.50(18) + 0.20(19) + 0.30(16) = 17.6


b.


FJuly = (18 + 19 + 16)/3 = 17.7


c.


FJuly = FJune + α(AJune – FJune) = 12 + 0.20(18 − 12) = 13.2


d.




   t


   y


   ty


    t2


  January


1


16


16


1


  February


2


14


28


4


  March


3


18


54


9


  April


4


16


64


16


  May


5


19


95


25


  June


6


18


108


36




  Total


21


101


365


91




Average


3.5


16.8






 = 3.5


 = 16.833


Y = a + bt = 14.5 + 0.66t


e.


FJuly, where July is the 7th month.


Y = a + bt = 14.5 + 0.66(7) = 19.1


References


WorksheetDifficulty: Challenge


Problem 18-15Learning Objective: 18-02 Evaluate demand using quantitative forecasting models.


Problem 18-22


Your manager is trying to determine what forecasting method to use. Based upon the following historical data, calculate the following forecast and specify what procedure you would utilize.


MONTH


ACTUAL DEMAND


1


61


2


64


3


67


4


66


5


71


6


70


7


73


8


74


9


74


10


83


11


84


12


86


a.


Calculate the simple three-month moving average forecast for periods 4–12. (Round your answers to 3 decimal places.)


 Month


Three-Month Moving Average


4




5




6




7




8




9




10




11




12




b.


Calculate the weighted three-month moving average for periods 4–12 using weights of 0.40 (for the period t−1); 0.40 (for the period t−2), and 0.20 (for the period t−3). (Do not round intermediate calculations. Round your answers to 1 decimal place.)


 Month


Three-Month Weighted Moving Average


4




5




6




7




8




9




10




11




12




c.


Calculate the single exponential smoothing forecast for periods 2–12 using an initial forecast (F1) of 66 and an α of 0.30. (Do not round intermediate calculations. Round your answers to 3 decimal places.)


 Month


Single Exponential Smoothing Forecast


2




3




4




5




6




7




8




9




10




11




12




d.


Calculate the exponential smoothing with trend component forecast for periods 2–12 using an initial trend forecast (T1) of 1.70, an initial exponential smoothing forecast (F1) of 65, an α of 0.30, and a δ of 0.20. (Do not round intermediate calculations. Round your answers to 3 decimal places.)


 Month


Exponential Smoothing with Trend


2




3




4




5




6




7




8




9




10




11




12




e-1.


Calculate the mean absolute deviation (MAD) for the forecasts made by each technique in periods 4–12. (Do not round intermediate calculations. Round your answers to 3 decimal places.)




       Mean Absolute Deviation


  Three-month moving average




  Three-month weighted moving average




  Single exponential smoothing forecast




  Exponential smoothing with trend




e-2.


Which forecasting method do you prefer?








Three-month moving average


Three-month weighted moving average


Single exponential smoothing forecast


Exponential smoothing with trend forecast




*******Explanation: see second page for chart


a. to e.












Single Exponential Smoothing


Exponential Smoothing with Trend




 Month (t)


Demand


Three-Month Moving Average


Absolute Deviation


  Three-Month Weighted Moving Average


  Absolute Deviation


Ft


  Absolute Deviation


Ft


  Tt


   FITt


Absolute Deviation


1


61










66.000




65.000


1.700


66.700




2


64










64.500




64.990


1.358


66.348




3


67










64.350




65.644


1.217


66.861




4


66


64.000


2.000


64.6


1.400


65.145


0.855


66.903


1.225


68.128


2.128


5


71


65.667


5.333


66.0


5.000


65.402


5.598


67.490


1.098


68.587


2.413


6


70


68.000


2.000


68.2


1.800


67.081


2.919


69.311


1.243


70.554


0.554


7


73


69.000


4.000


69.6


3.400


67.957


5.043


70.388


1.209


71.597


1.403


8


74


71.333


2.667


71.4


2.600


69.470


4.530


72.018


1.294


73.311


0.689


9


74


72.333


1.667


72.8


1.200


70.829


3.171


73.518


1.335


74.853


0.853


10


83


73.667


9.333


73.8


9.200


71.780


11.220


74.597


1.284


75.881


7.119


11


84


77.000


7.000


77.6


6.400


75.146


8.854


78.016


1.711


79.727


4.273


12


86


80.333


5.667


81.6


4.400


77.802


8.198


 81.009


1.967


 82.976


3.024


















      MAD






4.407




3.933




5.599








2.495


















Based upon MAD, the exponential smoothing with trend forecast component appears to be the best method.


References


WorksheetDifficulty: Challenge


Problem 18-22Learning Objective: 18-02 Evaluate demand using quantitative forecasting models.

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