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**4 Forecasting PowerPoint presentation to accompany Heizer and Render**

Operations Management, 10e Principles of Operations Management, 8e PowerPoint slides by Jeff Heyl © 2011 Pearson Education, Inc. publishing as Prentice Hall

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**?? What is Forecasting? Process of predicting a future event**

Underlying basis of all business decisions Production Inventory Personnel Facilities ?? © 2011 Pearson Education, Inc. publishing as Prentice Hall

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**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 3 months to 3 years Sales and production planning, budgeting Long-range forecast 3+ years New product planning, facility location, research and development © 2011 Pearson Education, Inc. publishing as Prentice Hall

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**Types of Forecasts Economic forecasts Technological forecasts**

Address business cycle – inflation rate, money supply, housing starts, 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, Inc. publishing as Prentice Hall

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**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, Inc. publishing as Prentice Hall

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**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, Inc. publishing as Prentice Hall

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**Overview of Quantitative Approaches**

Naive approach Moving averages Exponential smoothing Trend projection Linear regression time-series models associative model © 2011 Pearson Education, Inc. publishing as Prentice Hall

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**Time Series Forecasting**

Set of evenly spaced numerical data Obtained by observing response variable at regular time periods 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, Inc. publishing as Prentice Hall

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**Time Series Components**

Trend Cyclical Seasonal Random © 2011 Pearson Education, Inc. publishing as Prentice Hall

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**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, Inc. publishing as Prentice Hall

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**Trend Component Persistent, overall upward or downward pattern**

Changes due to population, technology, age, culture, etc. Typically several years duration © 2011 Pearson Education, Inc. publishing as Prentice Hall

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**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, Inc. publishing as Prentice Hall

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**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, Inc. publishing as Prentice Hall

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**Random Component Erratic, unsystematic, ‘residual’ fluctuations**

Due to random variation or unforeseen events Short duration and nonrepeating M T W T F © 2011 Pearson Education, Inc. publishing as Prentice Hall

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**∑ demand in previous n periods**

Moving Average Method 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, Inc. publishing as Prentice Hall

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**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, Inc. publishing as Prentice Hall

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**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, Inc. publishing as Prentice Hall

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**Common Measures of Error**

Mean Absolute Deviation (MAD) MAD = ∑ |Actual - Forecast| n Mean Squared Error (MSE) MSE = ∑ (Forecast Errors)2 n © 2011 Pearson Education, Inc. publishing as Prentice Hall

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**Common Measures of Error**

Mean Absolute Percent Error (MAPE) MAPE = ∑100|Actuali - Forecasti|/Actuali n i = 1 © 2011 Pearson Education, Inc. publishing as Prentice Hall

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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, Inc. publishing as Prentice Hall

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**Seasonal Variations In Data**

The multiplicative seasonal model can adjust trend data for seasonal variations in demand © 2011 Pearson Education, Inc. publishing as Prentice Hall

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**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, Inc. publishing as Prentice Hall

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**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, Inc. publishing as Prentice Hall

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**Associative Forecasting Example**

Sales Area Payroll ($ millions), y ($ billions), x 2.0 1 3.0 3 2.5 4 2.0 2 3.5 7 4.0 – 3.0 – 2.0 – 1.0 – | | | | | | | Sales Area payroll © 2011 Pearson Education, Inc. publishing as Prentice Hall

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**Associative Forecasting Example**

Sales, y Payroll, x x2 xy ∑y = 15.0 ∑x = 18 ∑x2 = 80 ∑xy = 51.5 b = = = .25 ∑xy - nxy ∑x2 - nx2 (6)(3)(2.5) 80 - (6)(32) x = ∑x/6 = 18/6 = 3 y = ∑y/6 = 15/6 = 2.5 a = y - bx = (.25)(3) = 1.75 © 2011 Pearson Education, Inc. publishing as Prentice Hall

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**Associative Forecasting Example**

y = x ^ Sales = (payroll) If payroll next year is estimated to be $6 billion, then: 4.0 – 3.0 – 2.0 – 1.0 – | | | | | | | Nodel’s sales Area payroll 3.25 Sales = (6) Sales = $3,250,000 © 2011 Pearson Education, Inc. publishing as Prentice Hall

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**Standard Error of the Estimate**

A forecast is just a point estimate of a future value This point is actually the mean of a probability distribution 4.0 – 3.0 – 2.0 – 1.0 – | | | | | | | Nodel’s sales Area payroll 3.25 Figure 4.9 © 2011 Pearson Education, Inc. publishing as Prentice Hall

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**Standard Error of the Estimate**

Sy,x = ∑(y - yc)2 n - 2 where y = y-value of each data point yc = computed value of the dependent variable, from the regression equation n = number of data points © 2011 Pearson Education, Inc. publishing as Prentice Hall

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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, Inc. publishing as Prentice Hall

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**Correlation Coefficient**

nSxy - SxSy [nSx2 - (Sx)2][nSy2 - (Sy)2] © 2011 Pearson Education, Inc. publishing as Prentice Hall

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**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, Inc. publishing as Prentice Hall

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**For the Nodel Construction example:**

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 the Nodel Construction example: r = .901 r2 = .81 © 2011 Pearson Education, Inc. publishing as Prentice Hall

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**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, Inc. publishing as Prentice Hall

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**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, Inc. publishing as Prentice Hall

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