ASSIGNMENT2_INDU320

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Concordia University *

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320

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Industrial Engineering

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Oct 30, 2023

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Concordia University INDU 320 Course Assignment #2 Name: Karim Al-Sharara ID: 40190684 Date: October 17, 2023

The data plotted vs Time starting Jan 2020 till Sept 2022 is shown below : 0 5 01 51 02 52 03 53 04 54 05 0 002 004 006 008 01 21 41 61 81 02 ataD dnameD The data seems to exhibit seasonal fluctuations and an upward trend. Seasonal cycles reaches peaks every five months, while troughs typically occur in the subsequent five month. Demand tends to be higher during the summer months (June to Aug) and decreases afterwards. Hence a possible model could be Holt-Winters Exponential Smoothing; Holt-Winters’s method is appropriate for forecasting time series data that exhibit trends and seasonality. It uses triple exponential smoothing to capture the level, trend, and seasonal components of the data. In addition to Holt-Winter’s method, we can use a linear regression line to find an equation to forecast future data, to obtain more accurate forecast, the data will be combined into four seasons, which will then obtain a deseasonalized regression line in which each point represents a season ( 3 months ), since deviations in data occur every season and no significant change within the same season each year, however each season is trending upward, making this model reasonable . Regression Line model :

The above data structure groups months into four quarters a year, adding up to fifteen periods, each period is a season with an average and sum, the actual columns shows the sum, average of same quarter shows the average of all quarter in different years. Using this model, we can obtain an equation, Y=89.48x +2322 that can forecast the next four quarters . These are the obtained results from this model :

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MAE 571.554 7 MSE 610.377 9 0 2 4 6 8 01 21 41 61 .2- 2- .1- 1- .0- 0 5.0 1 5.1 2 gS gnikcarT For the Holt-Winter Method :

1 3 5 7 9 11 31 51 71 91 12 32 52 72 92 13 33 53 73 93 14 34 54 0 002 004 006 008 01 21 41 61 81 02 sretniW tloH dnameD tsaceroF For Alpha: 0.75, Beta: 0.05, Gamma: 0.00001 using trial and error to obtain the optimal choice of these three parameters . MSE : 280 ME : 17.8211 P{ -4  ET/ MAD  4}= 0.955 0 2 4 6 8 01 21 0 2 4 6 8 1 1 langiS gnikcarT In control forecasting process, no tracking signal exceeds 4 . The second model (Holt-Winter) is most appropriate in this context, it integrates seasonality and trend while producing in control errors. Hence forecasting the next 12 months using this method as below

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