Final Report Project 2

8/11/2019 Final Report Project 2

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Forecasting Sales for Pizza Hut Restaurant ina volatile market

Team Members:Kimberly Lynch

Kelsey DawsonQuang MaiBrijal Patel

Background and Introduction

This project provides forecasts using the nave! moving average! simplee"ponential smoothing! regression! and classical decomposition methods#The purpose of this research is to understand the changes in Pi$$a %ut salesduring the year &''(# By analy$ing their data! we are able to help Pi$$a %utprepare for the future# )ccurately forecasting sales and building a sales plan

can help a business manage their production! sta*! and +nancing needsmore e*ectively and avoid unforeseen problems# Being armed with thisinformation can allow one to rapidly identify problems and opportunities anddo something about them# ,ur group was motivated to conduct a study onPi$$a %ut sales for one year to learn more about an actual company# )sstudents! we often do not get to see real sales +gures! therefore our groupfelt compelled to see what sales are li-e for a restaurant we often eat at# Thistype of information would be valuable to Pi$$a %ut! their competitors! andany pi$$a.restaurant entrepreneur#

Raw ata

,ur data was collected from a Pi$$a %ut in )tlanta! /)# This raw dataaccurately presents sales for 0& wee-s for the year of &''(# The chart belowshows that our data is stationary because there is no trend or seasonalitypresent# Because of this! the best way to predict sales for the ne"t periodwould be to use heuristic and 1uantitative forecasting techni1ues! such asnave! moving average! and simple e"ponential methods# )s one can see! allsales are scattered between the 2&&!'''#''32&4!'''#'' range with twovisible outliers located between 254!'''#''32&5!'''#''# The variable6sales!7 was collected by ta-ing the amount the seller received from everybuyer each day from a seven day period to get the net sales for one wee-#


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Forecasting

MagnitudeMeasures

#eek$%

Forecast

BI"S M" M"P& MS& RMS&'Standard

&rror(

)a*ve 18,858.55

(131.26)

1,790.92 7.47%

4,997,538.90

2,235.52

Two+PeriodM"

21,309.09

(158.42)

1,534.20 6.43%

3,711,472.07

1,926.52

T,ree+Period M"

22,253.15

(168.23)

1,422.25 5.99%

3,344,869.90

1,828.90

&-.onential

Smoot,ing

23,144.90

(277.74)

1,253.05 5.31%

2,890,364.91

1,700.11

Regression 24,011.28

0.00

1,219.60 5.13%

2,654,637.68

1,629.31

/lassicalecom.osition

22,495.30

(11.06)

1,183.79 4.82%

2,507,136.96

1,583.39

&valuation

)fter we collected the data! our group developed a scatter plot to see if therewere any trends in the data that might dictate what method would be more

appropriate and accurate to forecast# 8ome of the techni1ues that weconsidered were the 9ave! Three3 Period Moving )verage! 8imple:"ponential 8moothing! ;egression and to be 0122$23$$# ?e assumed that the price from the previouswee- is the forecasted price for the very ne"t month# )ccording to the tableabove! the predicted sales for the 0>rd wee- using nave was the lowest interms of bias# %owever! it has the highest M)D! M)P:! M8: and 8:! thereforeit is not signi+cant#

%+Period Moving "verage:@sing a >3period moving average! the predicted gas sales for wee- 0>

is 0444$%31$# ?hen compared with a &3period moving average! the >3period has a lower 8tandard :rror but has a higher Bias# The sales arecalculated by ta-ing the average of the sales during the previous n numberof periods# ?e used the actual sales from the last two and three wee-s# Both


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models are also not signi+cant because its 8: is still higher than the othermethods#

Sim.le &-.onential Smoot,ing:By using e"ponential smoothing with the constant )lpha of 5316! we

were able to predict sales for the 0>rd

wee-! which came out to be 023,144.90#An the model! forecasts were made by adjusting last periods forecast withfactor based on last periods error# ?e also changed the )lpha around as to+nd the one giving us the lowest 8: C8tandard :rror as possible# ?ith )lphaof '#5(! the 8tandard :rror was 5(''#55! but it still is not the lowest in the+ve methods#

Regression:?ith a 8imple Linear ;egression model! we were able to predict sales

for the 0>rdwee-! which is 024011.28# 8ales! dependent variable! is forecastedbased on a linear relationship with wee-s! independent variable# 8uch a

relationship is e"pressed asE FG &0>44#H53&0#I4(>" and ;&

G '#'0J5I(#Therefore! the predicted sales was obtained by plugging the period 0> intothe e1uationE &J'55#&4G &0>44#H53&0#I4(>C0># Based on the summaryoutput! sales are e"pected to decrease on average by 2&0#I4 as 5 wee-past# The model has a 8tandard :rror of 5H&I#>5! yet it is only the secondlowest#

/lassical ecom.osition:?ith decomposition we were able to predict sales for the 0> rdwee- to

be 04478$3%3 ?e started by dividing the 0& wee-s in the year into four

1uarters to +nd the 8easonal Ande" C8A for de3seasonali$ing the sales#;egression was used on the de3seasonali$ed values to +nd the predictedsales CFd hat# The Fd hat sales is then re3seasonali$ed to provide thepredicted sales CF hat# The model has a 8tandard :rror of 504>#>I and is thelowest of the models#


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/onclusion

An conclusion! we determined the most signi+cant forecast was themethod that produced the lowest 8:# Thus we concluded that the bestforecasting method would be classical decomposition# )s shown in ourresults! classical decomposition has the lowest 8: C;M8: of 504>#>I#Therefore classical decomposition was determined to be the most accuratemethod to forecast the wee-ly sales for Pi$$a %uts during &''4 Cperiod 0>!which comes out to be 2&&JI0#>'# :ven though classical decomposition hasthe lowest 8:! there are no trends or seasonality in the actual sales so thisforecast holds very little signi+cance# Therefore! using one of the heuristicmethods! since the data are stationary is most appropriate! and simple

e"ponential smoothing method was our best result# @sing e"ponentialsmoothing! we predicted that sales for the 0>rdwee- would be 023,144.90. ?ithforecasting! businesses li-e Pi$$a %ut can loo- into the future with someideas as to how much to e"pect from sales#

Documents

Final Report Project 2