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1 4 Forecasting Demand PowerPoint presentation to accompany
Heizer and Render Operations Management, 10e, Global Edition Principles of Operations Management, 8e, Global Edition PowerPoint slides by Jeff Heyl © 2011 Pearson Education

2 Chapter Outline What Is Forecasting? Forecasting definition
The differences between forecasting & prediction Forecasting Time Horizons The Influence of Product Life Cycle Types Of Forecasts The Strategic Importance of Forecasting Seven Steps in the Forecasting System Forecasting Approaches Qualitative approach Quantitative approach © 2011 Pearson Education

3 Outline – Continued Time-Series Forecasting
Decomposition of a Time Series Naive Approach Moving Averages Exponential Smoothing Exponential Smoothing with Trend Adjustment Trend Projections Seasonal Variations in Data Cyclical Variations in Data © 2011 Pearson Education

4 Associative Forecasting Methods: Regression and Correlation Analysis
Monitoring and Controlling Forecasts Adaptive Smoothing Focus Forecasting Forecasting in the Service Sector © 2011 Pearson Education

5 ?? What is Forecasting? Process of predicting a future event
Underlying basis of all business decisions Production Inventory Personnel Facilities ?? © 2011 Pearson Education

6 Forecasting definition
Forecasting is defined as a planning tool that helps management in its attempts to cope with the uncertainty of the future, relying mainly on data from the past and present and analysis of trends There is a dereferences between forecasting and prediction © 2011 Pearson Education

7 The Differences Between Forecasting & Prediction
Prediction involves judgment in management after taking all available information into account. Forecasting involves the projection of the past into the future Prediction involves the anticipated change into the future. It may include even new factors that may affect future demand Forecast involves estimating the level of demand of a product on the basis of factors that generated the demand in the past Prediction is more intuitive Forecasting is more scientific © 2011 Pearson Education

8 It is more governed by personal bias and preferences.
It is relatively free from personal bias. It is more subjective It is more objective Prediction does not contain error analysis Error analysis is possible © 2011 Pearson Education

9 Forecasting Time Horizons
Short-range forecast Up to 1 year, generally less than 3 months Purchasing, job scheduling, workforce levels, job assignments, production levels Medium-range forecast 1 year to 3 years Sales and production planning, budgeting Long-range forecast 3+ years New product planning, facility location, research and development © 2011 Pearson Education

10 Influence of Product Life Cycle
Introduction – Growth – Maturity – Decline Introduction and growth require longer forecasts than maturity and decline As product passes through life cycle, forecasts are useful in projecting Staffing levels Inventory levels Factory capacity © 2011 Pearson Education

11 Product Life Cycle Introduction Growth Maturity Decline
Forecasting Time Horizon Long run forecasting + 3 years Medium forecasting 1 year – 3 years Short run forecasting Up to 1 year Internet search engines Sales Drive-through restaurants CD-ROMs Analog TVs iPods Boeing 787 LCD & plasma TVs Twitter Avatars Xbox 360 Figure 2.5 © 2011 Pearson Education

12 Types of Forecasts Economic forecasts Technological forecasts
Address business cycle – inflation rate, money supply, dollar price, etc. Technological forecasts Predict rate of technological progress Impacts development of new products Demand forecasts Predict sales of existing products and services © 2011 Pearson Education

13 Strategic Importance of Forecasting
Human Resources – Hiring, training, laying off workers Capacity – Capacity shortages can result in undependable delivery, loss of customers, loss of market share Supply Chain Management – Good supplier relations and price advantages © 2011 Pearson Education

14 Seven Steps in Forecasting
Determine the use of the forecast Select the items to be forecasted Determine the time horizon of the forecast Select the forecasting model(s) Gather the data Make the forecast Validate and implement results © 2011 Pearson Education

15 The Realities! Forecasts are seldom perfect
Most techniques assume an underlying stability in the system The aggregated forecasts are more accurate than individual forecasts © 2011 Pearson Education

16 Forecasting Approaches
Qualitative Methods Used when situation is vague and little data exist New products New technology Involves intuition, experience e.g., forecasting sales on Internet © 2011 Pearson Education

17 Forecasting Approaches
Quantitative Methods Used when situation is ‘stable’ and historical data exist Existing products Current technology Involves mathematical techniques e.g., forecasting sales of color televisions © 2011 Pearson Education

18 Overview of Qualitative Methods
Sales force composite Delphi method Consumer Market Survey © 2011 Pearson Education

19 Sales Force Composite Each salesperson projects his or her sales
Combined at district and national levels Salesperson know customers’ wants Tends to be overly optimistic © 2011 Pearson Education

20 Delphi Method Iterative group process, continues until agreement is reached 3 types of participants Decision makers Staff Respondents Decision Makers (Evaluate responses and make decisions) Staff (Administering survey) Respondents (People who can make valuable judgments) © 2011 Pearson Education

21 Consumer Market Survey
Ask customers about purchasing plans What consumers say, and what they actually do are often different Sometimes difficult to answer © 2011 Pearson Education

22 Overview of Quantitative Approaches
Naive approach Simple average Moving averages Exponential smoothing Trend projection Linear regression time-series models associative model © 2011 Pearson Education

23 Time Series Forecasting
Forecast based only on past values, no other variables important Assumes that factors influencing past and present will continue influence in future © 2011 Pearson Education

24 Time Series Components
Trend Cyclical Seasonal Random © 2011 Pearson Education

25 COMPONENTS OF TIME SERIES DEMAND
.1 average: the mean of the observations over time 2. trend: a gradual increase or decrease in the average over time 3. seasonal influence: predictable short-term cycling behavior due to time of day, week, month, season, year, etc. 4. cyclical movement: unpredictable long-term cycling behavior due to business cycle or product/service life cycle 5. random error: remaining variation that cannot be explained by the other four components © 2011 Pearson Education

26 Average demand over 4 years
Components of Demand Trend component Demand for product or service | | | | Time (years) Seasonal peaks Actual demand line Average demand over 4 years Random variation Figure 4.1 © 2011 Pearson Education

27 Trend Component Persistent, overall upward or downward pattern
Changes due to population, technology, age, culture, etc. Typically several years duration © 2011 Pearson Education

28 Seasonal Component Regular pattern of up and down fluctuations
Due to weather, customs, etc. Occurs within a single year Number of Period Length Seasons Week Day 7 Month Week 4-4.5 Month Day 28-31 Year Quarter 4 Year Month 12 Year Week 52 © 2011 Pearson Education

29 Cyclical Component Repeating up and down movements
Affected by business cycle, political, and economic factors Multiple years duration Often causal or associative relationships © 2011 Pearson Education

30 Random Component Erratic, unsystematic, ‘residual’ fluctuations
Due to random variation or unforeseen events Short duration and non- repeating M T W T F © 2011 Pearson Education

31 Naive Approach It is assume that demand in next period is the same as demand in most recent period e.g., If January sales were 68 units , then February sales will be 68 This simple way is the most cost- effective and efficient forecasting model It can be a good starting point © 2011 Pearson Education

32 Naive approach Suppose the demand for York factory last year was 1000 cars According to the naive approach the demand of the next year is 1000 car © 2011 Pearson Education

33 Simple Average Method It is assume that demand in the next period is the mean of the actual demand in last periods © 2011 Pearson Education

34 Simple average example
A XYZ television supplier found a demand of 200 sets in July, 225 sets in August & 245 sets in September. Find the demand forecast for the month of October using simple average method. F = D1+D2+D3/3= /3=223.3 224 units © 2011 Pearson Education

35 Moving Average Method MA
MA is a series of arithmetic means Used if little or no trend Used often for smoothing Provides overall impression of data over time Moving average = ∑ demand in previous n periods n © 2011 Pearson Education

36 Moving Average Method example
Donna’s garden supply wants a 3 – month moving average forecast including a forecast for next January, for shed sales © 2011 Pearson Education

37 Moving Average Example
January 10 February 12 March 13 April 16 May 19 June 23 July 26 Actual 3-Month Month Shed Sales Moving Average 10 12 13 ( )/3 = 11 2/3 ( )/3 = 13 2/3 ( )/3 = 16 ( )/3 = 19 1/3 © 2011 Pearson Education

38 Graph of Moving Average
Moving Average Forecast | | | | | | | | | | | | J F M A M J J A S O N D Shed Sales 30 – 28 – 26 – 24 – 22 – 20 – 18 – 16 – 14 – 12 – 10 – Actual Sales © 2011 Pearson Education

39 Weighted Moving Average
Used when some trend might be present Older data usually less important Weights based on experience and intuition Weighted moving average = ∑ (weight for period n) x (demand in period n) ∑ weights © 2011 Pearson Education

40 Weighted Moving Average example
Donna’s garden supply wants to forecast shed sales by weighted the past 3 months ,with more weight given to recent data to make them more significant © 2011 Pearson Education

41 Weighted Moving Average
Weights Applied Period 3 Last month 2 Two months ago 1 Three months ago 6 Sum of weights Weighted Moving Average January 10 February 12 March 13 April 16 May 19 June 23 July 26 Actual 3-Month Weighted Month Shed Sales Moving Average 10 12 13 [(3 x 13) + (2 x 12) + (10)]/6 = 121/6 [(3 x 16) + (2 x 13) + (12)]/6 = 141/3 [(3 x 19) + (2 x 16) + (13)]/6 = 17 [(3 x 23) + (2 x 19) + (16)]/6 = 201/2 © 2011 Pearson Education

42 Moving Average And Weighted Moving Average
30 – 25 – 20 – 15 – 10 – 5 – Sales demand | | | | | | | | | | | | J F M A M J J A S O N D Actual sales Moving average Figure 4.2 © 2011 Pearson Education

43 Potential Problems With Moving Average
Increasing n smooths the forecast but makes it less sensitive to changes Do not forecast trends well Require extensive historical data © 2011 Pearson Education

44 Exponential Smoothing
Form of weighted moving average Weights decline exponentially Most recent data weighted most Requires smoothing constant () Ranges from 0 to 1 Subjectively chosen Involves little record keeping of past data © 2011 Pearson Education

45 Exponential Smoothing
New forecast = Last period’s forecast + a (Last period’s actual demand – Last period’s forecast) Ft = Ft – 1 + a(At – 1 - Ft – 1) where Ft = new forecast Ft – 1 = previous forecast a = smoothing (or weighting) constant (0 ≤ a ≤ 1) © 2011 Pearson Education

46 Exponential Smoothing Example
In January , a car dealer predicted February demand for 142 ford mustangs , Actual Febrruary demand = 153 autos, using a Smoothing constant a = .20 , the dealer wants to forecast march demand using the exponential smoothing model © 2011 Pearson Education

47 Exponential Smoothing Example
Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20 New forecast = (153 – 142) © 2011 Pearson Education

48 Exponential Smoothing Example
Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20 New forecast = (153 – 142) = = ≈ 144 cars © 2011 Pearson Education

49 Effect of Smoothing Constants
Weight Assigned to Most 2nd Most 3rd Most 4th Most 5th Most Recent Recent Recent Recent Recent Smoothing Period Period Period Period Period Constant (a) a(1 - a) a(1 - a)2 a(1 - a)3 a(1 - a)4 a = a = © 2011 Pearson Education

50 Impact of Different  Actual demand a = .5 a = .1 225 – 200 – 175 –
225 – 200 – 175 – 150 – | | | | | | | | | Quarter Demand Actual demand a = .5 a = .1 © 2011 Pearson Education

51 Impact of Different  225 – 200 – 175 – 150 – | | | | | | | | | Quarter Demand Chose high values of  when underlying average is likely to change Choose low values of  when underlying average is stable Actual demand a = .5 a = .1 © 2011 Pearson Education

52 Choosing  The objective is to obtain the most accurate forecast no matter the technique We generally do this by selecting the model that gives us the lowest forecast error Forecast error = Actual demand - Forecast value = At - Ft © 2011 Pearson Education

53 Common Measures of Error
Mean Absolute Deviation (MAD) MAD = ∑ |Actual - Forecast| n Mean Squared Error (MSE) MSE = ∑ (Forecast Errors)2 n © 2011 Pearson Education

54 Comparison of Forecast Error
Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded a = .10 a = .10 a = .50 a = .50 © 2011 Pearson Education

55 Comparison of Forecast Error
MAD = ∑ |deviations| n Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded a = .10 a = .10 a = .50 a = .50 = 82.45/8 = 10.31 For a = .10 = 98.62/8 = 12.33 For a = .50 © 2011 Pearson Education

56 Comparison of Forecast Error
MSE = ∑ (forecast errors)2 n Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded a = .10 a = .10 a = .50 a = .50 = 1,526.54/8 = For a = .10 MAD = 1,561.91/8 = For a = .50 © 2011 Pearson Education

57 Comparison of Forecast Error
Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded a = .10 a = .10 a = .50 a = .50 MAD MSE © 2011 Pearson Education

58 Exponential Smoothing with Trend Adjustment
When a trend is present, exponential smoothing must be modified Forecast including (FITt) = trend Exponentially Exponentially smoothed (Ft) + smoothed (Tt) forecast trend © 2011 Pearson Education

59 Exponential Smoothing with Trend Adjustment
Ft = a(At - 1) + (1 - a)(Ft Tt - 1) Tt = b(Ft - Ft - 1) + (1 - b)Tt - 1 Step 1: Compute Ft Step 2: Compute Tt Step 3: Calculate the forecast FITt = Ft + Tt © 2011 Pearson Education

60 Exponential Smoothing with Trend Adjustment Example
Forecast Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 2 17 3 20 4 19 5 24 6 21 7 31 8 28 9 36 10 Table 4.1 © 2011 Pearson Education

61 Exponential Smoothing with Trend Adjustment Example
Forecast Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 2 17 3 20 4 19 5 24 6 21 7 31 8 28 9 36 10 Step 1: Forecast for Month 2 F2 = aA1 + (1 - a)(F1 + T1) F2 = (.2)(12) + (1 - .2)(11 + 2) = = 12.8 units Table 4.1 © 2011 Pearson Education

62 Exponential Smoothing with Trend Adjustment Example
Forecast Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 3 20 4 19 5 24 6 21 7 31 8 28 9 36 10 Step 2: Trend for Month 2 T2 = b(F2 - F1) + (1 - b)T1 T2 = (.4)( ) + (1 - .4)(2) = = 1.92 units Table 4.1 © 2011 Pearson Education

63 Exponential Smoothing with Trend Adjustment Example
Forecast Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 3 20 4 19 5 24 6 21 7 31 8 28 9 36 10 Step 3: Calculate FIT for Month 2 FIT2 = F2 + T2 FIT2 = = units Table 4.1 © 2011 Pearson Education

64 Exponential Smoothing with Trend Adjustment Example
Forecast Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 3 20 4 19 5 24 6 21 7 31 8 28 9 36 10 Table 4.1 © 2011 Pearson Education

65 Exponential Smoothing with Trend Adjustment Example
| | | | | | | | | Time (month) Product demand 35 – 30 – 25 – 20 – 15 – 10 – 5 – 0 – Actual demand (At) Forecast including trend (FITt) with  = .2 and  = .4 Figure 4.3 © 2011 Pearson Education

66 Trend Projections Fitting a trend line to historical data points to project into the medium to long-range Linear trends can be found using the least squares technique y = a + bx ^ where y = computed value of the variable to be predicted (dependent variable) a = y-axis intercept b = slope of the regression line x = the independent variable ^ © 2011 Pearson Education

67 Least Squares Method Equations to calculate the regression variables
y = a + bx ^ b = Sxy - nxy Sx2 - nx2 a = y - bx © 2011 Pearson Education

68 Least Squares Example Time Electrical Power
Year Period (x) Demand (y) x2 xy ∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063 x = 4 y = 98.86 b = = = 10.54 ∑xy - nxy ∑x2 - nx2 3,063 - (7)(4)(98.86) 140 - (7)(42) a = y - bx = (4) = 56.70 © 2011 Pearson Education

69 Least Squares Example The trend line is y = 56.70 + 10.54x ^
Time Electrical Power Year Period (x) Demand x2 xy ∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063 x = 4 y = 98.86 The trend line is y = x ^ b = = = 10.54 ∑xy - nxy ∑x2 - nx2 3,063 - (7)(4)(98.86) 140 - (7)(42) a = y - bx = (4) = 56.70 © 2011 Pearson Education

70 Least Squares Requirements
We always plot the data to insure a linear relationship We do not predict time periods far beyond the database Deviations around the least squares line are assumed to be random © 2011 Pearson Education

71 Seasonal Variations In Data
The multiplicative seasonal model can adjust trend data for seasonal variations in demand © 2011 Pearson Education

72 Seasonal Variations In Data
Steps in the process: Find average historical demand for each season Compute the average demand over all seasons Compute a seasonal index for each season Estimate next year’s total demand Divide this estimate of total demand by the number of seasons, then multiply it by the seasonal index for that season © 2011 Pearson Education

73 Seasonal Index Example
Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec Demand Average Average Seasonal Month Monthly Index © 2011 Pearson Education

74 Seasonal Index Example
Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec Demand Average Average Seasonal Month Monthly Index 0.957 Seasonal index = Average monthly demand Average monthly demand = 90/94 = .957 © 2011 Pearson Education

75 Seasonal Index Example
Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec Demand Average Average Seasonal Month Monthly Index © 2011 Pearson Education

76 Seasonal Index Example
Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec Demand Average Average Seasonal Month Monthly Index Forecast for 2010 Expected annual demand = 1,200 Jan x .957 = 96 1,200 12 Feb x .851 = 85 1,200 12 © 2011 Pearson Education

77 Seasonal Index Example
2010 Forecast 2009 Demand 2008 Demand 2007 Demand 140 – 130 – 120 – 110 – 100 – 90 – 80 – 70 – | | | | | | | | | | | | J F M A M J J A S O N D Time Demand © 2011 Pearson Education

78 Associative Forecasting
Used when changes in one or more independent variables can be used to predict the changes in the dependent variable Most common technique is linear regression analysis We apply this technique just as we did in the time series example © 2011 Pearson Education

79 Associative Forecasting
Forecasting an outcome based on predictor variables using the least squares technique y = a + bx ^ where y = computed value of the variable to be predicted (dependent variable) a = y-axis intercept b = slope of the regression line x = the independent variable though to predict the value of the dependent variable ^ © 2011 Pearson Education

80 Correlation How strong is the linear relationship between the variables? Correlation does not necessarily imply causality! Coefficient of correlation, r, measures degree of association Values range from -1 to +1 © 2011 Pearson Education

81 Correlation Coefficient
nSxy - SxSy [nSx2 - (Sx)2][nSy2 - (Sy)2] © 2011 Pearson Education

82 Correlation Coefficient
y x (a) Perfect positive correlation: r = +1 y x (b) Positive correlation: 0 < r < 1 Correlation Coefficient r = nSxy - SxSy [nSx2 - (Sx)2][nSy2 - (Sy)2] y x (c) No correlation: r = 0 y x (d) Perfect negative correlation: r = -1 © 2011 Pearson Education

83 Correlation Coefficient of Determination, r2, measures the percent of change in y predicted by the change in x Values range from 0 to 1 Easy to interpret For example if: r = .901 r2 = .81 © 2011 Pearson Education

84 (positive +)or( negative (-)
R to what extent there is a correlation relationship between two variables (-1 to 1) (positive +)or( negative (-) (strong more than .5) or( weak less than .5 ) R to what extent the change in one variable can be explained by the other variables % © 2011 Pearson Education

85 Multiple Regression Analysis
If more than one independent variable is to be used in the model, linear regression can be extended to multiple regression to accommodate several independent variables y = a + b1x1 + b2x2 … ^ Computationally, this is quite complex and generally done on the computer © 2011 Pearson Education

86 Multiple Regression Analysis
In the Nodel example, including interest rates in the model gives the new equation: y = x x2 ^ An improved correlation coefficient of r = .96 means this model does a better job of predicting the change in construction sales Sales = (6) - 5.0(.12) = 3.00 Sales = $3,000,000 © 2011 Pearson Education

87 Monitoring and Controlling Forecasts
Tracking Signal Measures how well the forecast is predicting actual values Ratio of cumulative forecast errors to mean absolute deviation (MAD) Good tracking signal has low values If forecasts are continually high or low, the forecast has a bias error © 2011 Pearson Education

88 Monitoring and Controlling Forecasts
Tracking signal Cumulative error MAD = Tracking signal = ∑(Actual demand in period i - Forecast demand in period i) (∑|Actual - Forecast|/n) © 2011 Pearson Education

89 Tracking Signal Signal exceeding limit Tracking signal +
0 MADs Upper control limit Lower control limit Time Acceptable range © 2011 Pearson Education

90 Tracking Signal Example
Cumulative Absolute Absolute Actual Forecast Cumm Forecast Forecast Qtr Demand Demand Error Error Error Error MAD © 2011 Pearson Education

91 Tracking Signal Example
Cumulative Absolute Absolute Actual Forecast Cumm Forecast Forecast Qtr Demand Demand Error Error Error Error MAD Tracking Signal (Cumm Error/MAD) -10/10 = -1 -15/7.5 = -2 0/10 = 0 +5/11 = +0.5 +35/14.2 = +2.5 The variation of the tracking signal between -2.0 and +2.5 is within acceptable limits © 2011 Pearson Education

92 Adaptive Forecasting It’s possible to use the computer to continually monitor forecast error and adjust the values of the a and b coefficients used in exponential smoothing to continually minimize forecast error This technique is called adaptive smoothing © 2011 Pearson Education

93 Forecasting in the Service Sector
Presents unusual challenges Special need for short term records Needs differ greatly as function of industry and product Holidays and other calendar events Unusual events © 2011 Pearson Education

94 Fast Food Restaurant Forecast
20% – 15% – 10% – 5% – (Lunchtime) (Dinnertime) Hour of day Percentage of sales Figure 4.12 © 2011 Pearson Education

95 FedEx Call Center Forecast
12% – 10% – 8% – 6% – 4% – 2% – 0% – Hour of day A.M. P.M. 2 4 6 8 10 12 Figure 4.12 © 2011 Pearson Education


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