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Demand Forecasting: Time Series Models Professor Stephen R. Lawrence College of Business and Administration University of Colorado Boulder, CO 80309-0419.

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Presentation on theme: "Demand Forecasting: Time Series Models Professor Stephen R. Lawrence College of Business and Administration University of Colorado Boulder, CO 80309-0419."— Presentation transcript:

1 Demand Forecasting: Time Series Models Professor Stephen R. Lawrence College of Business and Administration University of Colorado Boulder, CO 80309-0419 www.ePowerPoint.com

2 Forecasting Horizons Long Term 5+ years into the future R&D, plant location, product planning Principally judgement-based Medium Term 1 season to 2 years Aggregate planning, capacity planning, sales forecasts Mixture of quantitative methods and judgement Short Term 1 day to 1 year, less than 1 season Demand forecasting, staffing levels, purchasing, inventory levels Quantitative methods www.ePowerPoint.com

3 Short Term Forecasting: Needs and Uses Scheduling existing resources How many employees do we need and when? How much product should we make in anticipation of demand? Acquiring additional resources When are we going to run out of capacity? How many more people will we need? How large will our back-orders be? Determining what resources are needed What kind of machines will we require? Which services are growing in demand? declining? What kind of people should we be hiring? www.ePowerPoint.com

4 Types of Forecasting Models Types of Forecasts Qualitative --- based on experience, judgement, knowledge; Quantitative --- based on data, statistics; Methods of Forecasting Naive Methods --- eye-balling the numbers; Formal Methods --- systematically reduce forecasting errors; time series models (e.g. exponential smoothing); causal models (e.g. regression). Focus here on Time Series Models Assumptions of Time Series Models There is information about the past; This information can be quantified in the form of data; The pattern of the past will continue into the future. www.ePowerPoint.com

5 Forecasting Examples Examples from student projects: Demand for tellers in a bank; Traffic on major communication switch; Demand for liquor in bar; Demand for frozen foods in local grocery warehouse. Example from Industry: American Hospital Supply Corp. 70,000 items; 25 stocking locations; Store 3 years of data (63 million data points); Update forecasts monthly; 21 million forecast updates per year. www.ePowerPoint.com

6 Simple Moving Average Forecast F t is average of n previous observations or actuals D t : Note that the n past observations are equally weighted. Issues with moving average forecasts: All n past observations treated equally; Observations older than n are not included at all; Requires that n past observations be retained; Problem when 1000's of items are being forecast. www.ePowerPoint.com

7 Simple Moving Average Include n most recent observations Weight equally Ignore older observations weight today 12 3... n 1/n www.ePowerPoint.com

8 Moving Average n = 3 www.ePowerPoint.com

9 Example: Moving Average Forecasting www.ePowerPoint.com

10 Exponential Smoothing I Include all past observations Weight recent observations much more heavily than very old observations: weight today Decreasing weight given to older observations www.ePowerPoint.com

11 Exponential Smoothing I Include all past observations Weight recent observations much more heavily than very old observations: weight today Decreasing weight given to older observations www.ePowerPoint.com

12 Exponential Smoothing I Include all past observations Weight recent observations much more heavily than very old observations: weight today Decreasing weight given to older observations www.ePowerPoint.com

13 Exponential Smoothing I Include all past observations Weight recent observations much more heavily than very old observations: weight today Decreasing weight given to older observations www.ePowerPoint.com

14 Exponential Smoothing: Concept Include all past observations Weight recent observations much more heavily than very old observations: weight today Decreasing weight given to older observations www.ePowerPoint.com

15 Exponential Smoothing: Math www.ePowerPoint.com

16 Exponential Smoothing: Math www.ePowerPoint.com

17 Exponential Smoothing: Math Thus, new forecast is weighted sum of old forecast and actual demand Notes: Only 2 values (D t and F t-1 ) are required, compared with n for moving average Parameter a determined empirically (whatever works best) Rule of thumb:  < 0.5 Typically,  = 0.2 or  = 0.3 work well Forecast for k periods into future is: www.ePowerPoint.com

18 Exponential Smoothing  = 0.2 www.ePowerPoint.com

19 Example: Exponential Smoothing www.ePowerPoint.com

20 Complicating Factors Simple Exponential Smoothing works well with data that is “moving sideways” (stationary) Must be adapted for data series which exhibit a definite trend Must be further adapted for data series which exhibit seasonal patterns www.ePowerPoint.com

21 Holt’s Method: Double Exponential Smoothing What happens when there is a definite trend? A trendy clothing boutique has had the following sales over the past 6 months: 1 2 3 4 5 6 510512528530542552 Month Demand Actual Forecast www.ePowerPoint.com

22 Holt’s Method: Double Exponential Smoothing Ideas behind smoothing with trend: ``De-trend'' time-series by separating base from trend effects Smooth base in usual manner using  Smooth trend forecasts in usual manner using  Smooth the base forecast B t Smooth the trend forecast T t Forecast k periods into future F t+k with base and trend www.ePowerPoint.com

23 ES with Trend  = 0.2,  = 0.4 www.ePowerPoint.com

24 Example: Exponential Smoothing with Trend www.ePowerPoint.com

25 Winter’s Method: Exponential Smoothing w/ Trend and Seasonality Ideas behind smoothing with trend and seasonality: “De-trend’: and “de-seasonalize”time-series by separating base from trend and seasonality effects Smooth base in usual manner using  Smooth trend forecasts in usual manner using  Smooth seasonality forecasts using  Assume m seasons in a cycle 12 months in a year 4 quarters in a month 3 months in a quarter et cetera www.ePowerPoint.com

26 Winter’s Method: Exponential Smoothing w/ Trend and Seasonality Smooth the base forecast B t Smooth the trend forecast T t Smooth the seasonality forecast S t www.ePowerPoint.com

27 Winter’s Method: Exponential Smoothing w/ Trend and Seasonality Forecast F t with trend and seasonality Smooth the trend forecast T t Smooth the seasonality forecast S t www.ePowerPoint.com

28 ES with Trend and Seasonality  = 0.2,  = 0.4,  = 0.6 www.ePowerPoint.com

29 Example: Exponential Smoothing with Trend and Seasonality www.ePowerPoint.com

30 Forecasting Performance Mean Forecast Error (MFE or Bias): Measures average deviation of forecast from actuals. Mean Absolute Deviation (MAD): Measures average absolute deviation of forecast from actuals. Mean Absolute Percentage Error (MAPE): Measures absolute error as a percentage of the forecast. Standard Squared Error (MSE): Measures variance of forecast error How good is the forecast? www.ePowerPoint.com

31 Forecasting Performance Measures www.ePowerPoint.com

32 Mean Forecast Error (MFE or Bias) Want MFE to be as close to zero as possible -- minimum bias A large positive (negative) MFE means that the forecast is undershooting (overshooting) the actual observations Note that zero MFE does not imply that forecasts are perfect (no error) -- only that mean is “on target” Also called forecast BIAS www.ePowerPoint.com

33 Mean Absolute Deviation (MAD) Measures absolute error Positive and negative errors thus do not cancel out (as with MFE) Want MAD to be as small as possible No way to know if MAD error is large or small in relation to the actual data www.ePowerPoint.com

34 Mean Absolute Percentage Error (MAPE) Same as MAD, except... Measures deviation as a percentage of actual data www.ePowerPoint.com

35 Mean Squared Error (MSE) Measures squared forecast error -- error variance Recognizes that large errors are disproportionately more “expensive” than small errors But is not as easily interpreted as MAD, MAPE -- not as intuitive www.ePowerPoint.com

36 Fortunately, there is software... www.ePowerPoint.com

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