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Using Computer applications for Forecasting (التنبؤ)

Using Computer applications for Forecasting (التنبؤ). Introduction. يسعى ال مديرو ن دائما للحد من عدم اليقين وجعل أفضل تقديرات إلى ما سيحدث في المستقبل وهذا هو الغرض الرئيسي من التنبؤ بعض الشركات ت ستخدم أساليب نوعية مثل الحدس والخبرة

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Using Computer applications for Forecasting (التنبؤ)

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  1. Using Computer applications for Forecasting (التنبؤ) Dr. Abdullah Abuhamad

  2. Introduction يسعى المديرون دائما للحد من عدم اليقين وجعل أفضل تقديرات إلى ما سيحدث في المستقبل وهذا هو الغرض الرئيسي من التنبؤ بعض الشركات تستخدم أساليب نوعيةمثل الحدس والخبرة هناك أيضا العديد من التقنيات الكمية مثل المتوسطات المتحركة ،التسريح أو التمهيد الأسي ، التنبؤ بالاتجاه ، طريقة المربعات الصغرى و تحليل الانحدار Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 2

  3. خطوات عملية التنبؤ تحديد استخدام التنبؤ و تحديد الهدف الذينحاول الحصول عليه تحديد الأفق الزمني للتنبؤ اختيار نموذج أو نماذج التنبؤ جمع البيانات اللازمة لعملية التنبؤ التأكد من صحة نموذج التنبؤ تنفيذ النتائج Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 3

  4. Forecasting Models Forecasting Techniques Qualitative Models Time-Series Methods Causal Methods Delphi Methods Moving Average Regression Analysis Jury of Executive Opinion Exponential Smoothing Multiple Regression Sales Force Composite Trend Projections Decomposition Consumer Market Survey Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 4

  5. Scatter Diagrams مخططات الانتشار والسلاسل الزمنية • Petra Distributors wants to forecast sales for three different products Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 5

  6. Scatter Diagrams (a) 330 – 250 – 200 – 150 – 100 – 50 –           Annual Sales of Televisions | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 Time (Years) • Sales appear to be constant over time Sales = 250 • A good estimate of sales in year 11 is 250 televisions Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 6

  7. Scatter Diagrams (b) 420 – 400 – 380 – 360 – 340 – 320 – 300 – 280 –         Annual Sales of Radios   | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 Time (Years) • Sales appear to be increasing at a constant rate of 10 radios per year Sales = 290 + 10(Year) • A reasonable estimate of sales in year 11 is 400 televisions Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 7

  8. Scatter Diagrams (c) 200 – 180 – 160 – 140 – 120 – 100 –        Annual Sales of CD Players    | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 Time (Years) • This trend line may not be perfectly accurate because of variation from year to year • Sales appear to be increasing • A forecast would probably be a larger figure each year Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 8

  9. Time-Series Models (نماذج السلاسل الزمنية) Time-series models attempt to predict the future based on the past Common time-series models are Moving averageالمتوسط المتحرك Exponential smoothing Trend projections Decompositionاسلوب التحليل Regression analysis is used in trend projections and one type of decomposition model Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 9

  10. Moving Averages • Moving averages can be used when demand is relatively steady over time • The next forecast is the average of the most recent n data values from the time series • This methods tends to smooth out short-term irregularities in the data series Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 10

  11. Moving Averages where = forecast for time period t + 1 = actual value in time period t n = number of periods to average • Mathematically Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 11

  12. Weighted Moving Averages • Mathematically where wi = weight for the ith observation • Weighted moving averages use weights to put more emphasis on recent periods • Often used when a trend or other pattern is emerging Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 12

  13. Exponential Smoothing Exponential smoothing is easy to use and requires little record keeping of data It is a type of moving average New forecast = Last period’s forecast + (Last period’s actual demand – Last period’s forecast) Where  is a weight (or smoothing constant) with a value between 0 and 1 inclusive Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 13

  14. Exponential Smoothing Mathematically where Ft+1 = new forecast (for time period t + 1) Ft = pervious forecast (for time period t)  = smoothing constant (0 ≤  ≤ 1) Yt = pervious period’s actual demand • The idea is simple – the new estimate is the old estimate plus some fraction of the error in the last period Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 14

  15. Exponential Smoothing Example In January, February’s demand for a certain car model was predicted to be 142 Actual February demand was 153 autos Using a smoothing constant of  = 0.20, what is the forecast for March? New forecast (for March demand) = 142 + 0.2(153 – 142) = 144.2 or 144 autos • If actual demand in March was 136 autos, the April forecast would be New forecast (for April demand) = 144.2 + 0.2(136 – 144.2) = 142.6 or 143 autos Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 15

  16. Selecting the Smoothing Constant • Selecting the appropriate value for  is key to obtaining a good forecast • The objective is always to generate an accurate forecast • The general approach is to develop trial forecasts with different values of  and select the  that results in the lowest MAD Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 16

  17. Selecting the Best Value of  Best choice Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 17

  18. Trend Projection • Trend projection fits a trend line to a series of historical data points • The line is projected into the future for medium- to long-range forecasts • Several trend equations can be developed based on exponential or quadratic models • The simplest is a linear model developed using regression analysis Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 18

  19. ˆ = + Y b b t 0 1 where = predicted value b0 = intercept b1 = slope of the line t = time period (i.e., X = 1, 2, 3, …, n) Trend Projection • The mathematical form is Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 19

  20. * Dist7 * Dist5 Dist6 * * Dist3 Dist4 * * Value of Dependent Variable Dist2 Dist1 * Time Trend Projection Figure 5.4 Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 20

  21. Causal Models (النماذج السببية) Causal models use variables or factors that might influence the quantity being forecasted The objective is to build a model with the best statistical relationship between the variable being forecast and the independent variables Regression analysis is the most common technique used in causal modeling Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 21

  22. Causal Models (النماذج السببية) • تستخدم هذه الطريقة عندما تتوفر معلومات اكثر عن العلاقة بين الطلب و مجموعة من العوامل الداخلية أوالخارجية. • و يطلق على الطلب تسمية ”المتغير التابع“((Dependent variable و يرمز لها y • أما العوامل المؤثرة في الطلب فيطلق عليها تسمية ”المتغيرات المستقلة“ Independent variables و يرمز لها X • و تستخدم المعادلة التالية لوصف العلاقة بين المتغير: • حيث b 1, b 0 ثوابت المعادلة و يحسبان بطريقة المربعات الصغرى. = b + b + e Y X 0 1 Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 22

  23. Causal Models: Simple (Linear) and multiple regression Regression analysis is a very valuable tool for a manager Regression can be used to Understand the relationship between variables Predict the value of one variable based on another variable Simple linear regression models have only two variables Multiple regression models have more than two variables Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 23

  24. Simple (Linear) and multiple regression The variable to be predicted is called the dependent variable Sometimes called the response variable The value of this variable depends on the value of the independent variable Sometimes called the explanatory or predictor variable Independent variable Independent variable Dependent variable = + Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 24

  25. Example: Alarabi Construction Company Alarabi Construction company renovates old homes They have found that the dollar volume of renovation work is dependent on the area payroll Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 25

  26. Alarabi Construction Company 12 – 10 – 8 – 6 – 4 – 2 – 0 – Sales ($100,000) | | | | | | | | 0 1 2 3 4 5 6 7 8 Payroll ($100 million) Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 26

  27. Simple Linear Regression • Regression models are used to test if there is a relationship between variables • There is some random error that cannot be predicted where Y = dependent variable (response) X = independent variable (predictor or explanatory) 0 = intercept (value of Y when X = 0) 1 = slope of the regression line e = random error Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 27

  28. Simple Linear Regression where Y = dependent variable (response) X = independent variable (predictor or explanatory) b0 = intercept (value of Y when X = 0) b1 = slope of the regression line ^ • True values for the slope and intercept are not known so they are estimated using sample data Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 28

  29. Alarabi construction company Alarabi construction company is trying to predict sales based on area payroll Y = Sales X = Area payroll • The line chosen in the previous figure is the one that minimizes the errors Error = (Actual value) – (Predicted value) Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 29

  30. Alarabi Construction company For the simple linear regression model, the values of the intercept and slope can be calculated using the formulas below Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 30

  31. Regression calculations Alarabi construction company Y X (X – X)2 (X – X)(Y – Y) 6 3 (3 – 4)2 = 1 (3 – 4)(6 – 7) = 1 8 4 (4 – 4)2 = 0 (4 – 4)(8 – 7) = 0 9 6 (6 – 4)2 = 4 (6 – 4)(9 – 7) = 4 5 4 (4 – 4)2 = 0 (4 – 4)(5 – 7) = 0 4.5 2 (2 – 4)2 = 4 (2 – 4)(4.5 – 7) = 5 9.5 5 (5 – 4)2 = 1 (5 – 4)(9.5 – 7) = 2.5 ΣY= 42 Y = 42/6 = 7 ΣX= 24 X = 24/6 = 4 Σ(X – X)2= 10 Σ(X – X)(Y – Y) = 12.5 Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 31

  32. Alarabi construction company Regression calculations Therefore Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 32

  33. Alarabi construction company Regression calculations sales = 2 + 1.25(payroll) If the payroll next year is $600 million Therefore Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 33

  34. Measuring the Fit of the Regression Model • Regression models can be developed for any variables X and Y • How do we know the model is actually helpful in predicting Y based on X? • We could just take the average error, but the positive and negative errors would cancel each other out • Three measures of variability are • SST – Total variability about the mean • SSE – Variability about the regression line • SSR – Total variability that is explained by the model Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 34

  35. Measuring the Fit of the Regression Model • Sum of the squares total • Sum of the squared error • Sum of squares due to regression • An important relationship Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 35

  36. Measuring the Fit of the Regression Model ^ ^ ^ ^ ^ Table 4.3 Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 36

  37. Measuring the Fit of the Regression Model • Sum of the squares total For Alarabi construction company SST = 22.5 SSE = 6.875 SSR = 15.625 • Sum of the squared error • Sum of squares due to regression • An important relationship Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 37

  38. Measuring the Fit of the Regression Model 12 – 10 – 8 – 6 – 4 – 2 – 0 – ^ Y = 2 + 1.25X Used in Sum of the squares total Used in Sum of the squared error Sum of squares due to regression (SSR) (SST) (SSE) ^ Y – Y Y Sales ($100,000) Y – Y Y – Y ^ | | | | | | | | 0 1 2 3 4 5 6 7 8 Payroll ($100 million) Figure 4.2 Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 38

  39. Coefficient of Determination The proportion of the variability in Y explained by regression equation is called the coefficient of determination The coefficient of determination is r2 • For Alarabi construction company • About 69% of the variability in Y is explained by the equation based on payroll (X) Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 39

  40. Correlation Coefficient Thecorrelation coefficientis an expression of the strength of the linear relationship It will always be between +1 and –1 The correlation coefficient is r ± • For Alarabi construction company = 2 r r Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 40

  41. Correlation Coefficient Y Y * * * * * * * * * * * * * * * * X X (a) Perfect PositiveCorrelation: r = +1 (b) PositiveCorrelation: 0 < r < 1 Y Y * * * * * * * * * * * * * * * * * * X X (c) No Correlation: r = 0 (d) Perfect Negative Correlation: r = –1 Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 41

  42. Using The Computer to Forecast Spreadsheets can be used by small and medium-sized forecasting problems More advanced programs (SAS, SPSS, Minitab) handle time-series and causal models May automatically select best model parameters Dedicated forecasting packages may be fully automatic May be integrated with inventory planning and control Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 42

  43. Using The Computer to Forecast QM for Windows software Four sub-modules are available with the Forecasting module. Forecasting can be used for the analysis of a series of data over time or you may choose multiple regression. Time Series Analysis. If you choose time series then there are eight general methods which can be chosen. Least squares- Simple (Linear) and multiple regression. Please note that simple regression can be performed using either time series analysis or multiple regression. The third option, regression projector, is used to plug values into a known regression equation. The fourth option is Error Analysis Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 43

  44. Using The Computer to Forecast Sub-module 1: Time series analysis A time series is a sequence of evenly spaced events Time-series forecasts predict the future based solely of the past values of the variable Other variables are ignored When you begin a new problem you will be asked to enter the problem title the number of periods of past data. (Do NOT enter the number of the period for which you are going to do the forecasting.) Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 44

  45. The main data screen contains a method box at the top left. You will select the method/model from: Naive method n-period moving averages weighted n period moving average Exponential smoothing Exponential smoothing with trend Trend analysis (Regression with x set to 1 through n) Least squares/linear regression Decomposition (multiplicative) Decomposition (additive) User input (for error analysis) Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 45

  46. You may return to this method box and change models as often as you like which makes it very easy to run different techniques on the same data set. Additional information about the required information is as follows. Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 46

  47. In this sub- module the independent variable DOES NOT REPRESENT TIME. For regression, it is allowable to go to the column marked 'PERIOD(x)' and to change the values in this column. When you begin a new problem using Multiple Regression sub-module you will be asked to enter: the problem title the number of observations the number of independent variables If the number of independent variables is one then this is simple regression. Otherwise, enter the sets of data as y, x1, x2, etc. The program finds the Beta coefficents that create the line y= beta0 + beta1*x1 beta2*x2 + .... Using The Computer to ForecastSub-module 2: Least squares- Simple (Linear) and multiple regression Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 47

  48. Using The Computer to ForecastSub-module 3: Regression Projector You may make several forecasts by filling in the values for the regression coefficients in the first column and the values for the independent variables in the remaining columns. Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 48

  49. The results of the forecasting depend on the forecasting technique but generally speaking, you will be given the forecast for the next period and an error analysis which includes: bias = mean of (demand - forecast ) MAD = mean of (absolute value of (demand-forecast)) MSE = mean of (square of (demand - forecast)) standard error MAPE = mean average percent error Using The Computer to ForecastSub-module 4: Error Analysis Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 49

  50. Measures of Forecast Accuracy We compare forecasted values with actual values to see how well one model works or to compare models Forecast error = Actual value – Forecast value • One measure of accuracy is the mean absolutedeviation (MAD) Petra University Dr. Abdullah Abuhamad Dr. Abdullah Abuhamad 50

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