Quantitative Analysis for Management Forecasting To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-1

Exponential Smoothing Forecasting Techniques Forecasting Models Moving Average Exponential Smoothing Trend Projections Time Series Methods Forecasting Techniques Delphi Methods Jury of Executive Opinion Sales Force Composite Consumer Market Survey Qualitative Models Causal Methods Regression Analysis Multiple Regression To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-2

Scatter Diagram for Sales Radios Televisions Compact Discs To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-3

Decomposition of Time Series Time series can be decomposed into: Trend (T): gradual up or down movement over time Seasonality (S): pattern of fluctuations above or below trend line that occurs every year Cycles(C): patterns in data that occur every several years Random variations (R): “blips”in the data caused by chance and unusual situations To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-4

Product Demand Showing Components Actual Data Trend Cyclic Random To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-5

Moving Averages Moving average : å (demand in period n ) n 5-6 To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-6

Calculation of Three-Month Moving Average Actual Shed Sales Three-Month Moving Average January 10 February 12 March 13 April 16 3 2 11 13)/3 (10 = + May 19 16)/3 (12 June 23 19)/3 (13 July 26 1 23)/3 (16 To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-7

Weighted Moving Averages weights ) period in )(demand for (weight average moving Weighted å = n To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-8

Calculating Weighted Moving Averages Weights Applied Period 3 Last month 2 Two months ago 1 Three months ago 3 *Sales last month + 2 *Sales two months ago + 1 *Sales three months ago 6 Sum of weights To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-9

Calculation of Three-Month Moving Average Actual Shed Sales Three-Month Moving Average January 10 February 12 March 13 April 16 6 1 10)]/6 * (1 12) (2 13) [(3 = + May 19 3 14 12)]/6 16) June 23 17 13)]/6 19) July 26 2 20 16)]/6 23) To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-10

Exponential Smoothing New forecast = previous forecast + (previous actual - previous) or: where ( ) 1 a - + = t F A actual period previous constant between 0~1 smoothing forecast new t- To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-11

Table 5.5 To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-12

Actual Tonnage Unloaded Table 5.5 Continued  =0.50 Qtr Actual Tonnage Unloaded Forecast using  =0.50 1 180 175 2 168 177.50 =175.00+0.50(180-175) 3 159 172.75 =177.50+0.50(168-177.50) 4 165.38 =172.25+0.50(159-172.25) 5 190 170.19 =165.38+0.50(175-165.38) 6 205 179.09 =170.19+0.50(190-170.19) 7 179.54 =179.09+0.50(180-179.09) 8 182 182.00 =179.54+0.50(182-179.54) 9 ? To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-13

Trend Projection General regression equation: + = 2 X n Y XY b a where bX - å intercept axis variable) (dependent predicted be to variable the of value computed To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-14

Table5.7 To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-15

Solved Formula To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-16

Midwestern Manufacturing’s Demand Trend Line Forecast points Actual demand line To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-17

Computing Seasonality Indices Using Answering Machine Sales To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-18

Trend Analysis with Seasonal Indices Y = 1150 + 20x Where x=1,2,…12 for Jan, Feb,….Dec So; Jan =[1150+20(1)]*.957 = 1119.69 Feb =[1150+50(2)]*.851 = 1012.69 Mar =[1150+20(3)]*.904 = 1093.84 . Dec = [1150*20(12)]*.851 = 1182.89 To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-19

Trend Analysis Example with Seasonality: Trend analysis was used to forecast the number of new hotel registrants (in ooo’s). The following data was used. yr1 yr2 1 Jan 17 17 2 Feb 16 15 3 Mar 16 17 4 Apr 25 24 5 May 24 23 6 June 25 25 7 July 23 24 8 Aug 20 19 9 Sep 20 20 10 Oct 16 15 11 Nov 16 15 12 Dec 17 17 To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-20

Trend Analysis Example : The trend analysis, using year1 data was Y= 20.5 + 0.1455X Compute the seasonal index Forecast July of year3, October of year3 What is the forecast for December if the average yearly demand for year is thought to increase by 10% higher than year1? To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-21

Using Regression Analysis to Forecast(Causal) Triple A' Sales ($100,000's) X Local Payroll ($100,000,000) 2.0 1 3.0 3 2.5 4 2 3.5 7 To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-22

Using Regression Analysis to Forecast - continued Sales, Y Payroll, X X 2 XY 2.0 1 3.0 3 9 9.0 2.5 4 16 10.0 4.0 3.5 7 49 24.5 S Y = 15.0 X = 18 = 80 XY = 51.5 To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-23

Using Regression Analysis to Forecast - continued Calculating the required parameters: ( ) X . Y ˆ b a n XY 25 75 1 3 5 2 6 80 51 15 18 + = - å To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-24

Regression Equation Y = 1.75 + 0.25x 5-25 To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-25

Methods to evaluate the Casual Regression Equation Standard Error of the Estimate (the standard deviation) Correlation Coefficient -1 < r <1 Coefficient of Determination 0 < r <1 the percent of variation in Y ( the dependent variable ) that is described by the X’s (independent variables ) 2 To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-26

Standard Error of the Estimate - continued ( ) points data of number equation regression the from computed variable dependent value point each = - å n Y where S c X , 2 For Payroll example, S = 0.306 Y,X This is the standard deviation of the regression To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-27

Correlation Coefficient = ( ) [ ] å - 2 Y n X XY r For Payroll example, r = 0.91 To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-28

Coefficient - Four Values Fig. 5.7 To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-29

Multiple Regression to Forecast #5-32 To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-30

Multiple Regression to Forecast #5-32 To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-31

Regression SAS printout Problem Attendance Wins 40,000 6 60,000 11 60,000 9 50,000 9 45,000 8 55,000 8 50,000 10 a) What is the dependent variable? b) Plot the data is it correlated? To accompany Quantitative Analysis for Management, 7e by Render/ Stair 5-32