Demand Forecasting : Time Series Models Professor Stephen R. Lawrence College of Business and Administration University

1. Demand Forecasting:Time Series ModelsProfessor Stephen R. LawrenceCollege of Business and AdministrationUniversity of ColoradoBoulder, CO 80309-0419

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

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?

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.

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.

6. Simple Moving Average • Forecast Ft is average of n previous observations or actuals Dt: • 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.

7. Simple Moving Average • Include n most recent observations • Weight equally • Ignore older observations weight 1/n ... n 2 1 3 today

8. Moving Average n = 3

9. Example:Moving Average Forecasting

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

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

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

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

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

15. Exponential Smoothing: Math

16. Exponential Smoothing: Math

17. Exponential Smoothing: Math • Thus, new forecast is weighted sum of old forecast and actual demand • Notes: • Only 2 values (Dt and Ft-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:

18. Exponential Smoothing a = 0.2

19. Example:Exponential Smoothing

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

21. A trendy clothing boutique has had the following sales over the past 6 months: 1 2 3 4 5 6 510 512 528 530 542 552 Holt’s Method:Double Exponential Smoothing • What happens when there is a definite trend? Actual Demand Forecast Month

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 baseforecast Bt • Smooth the trendforecast Tt • Forecast kperiods into future Ft+kwith base and trend

23. ES with Trend a = 0.2, b = 0.4

24. Example:Exponential Smoothing with Trend

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 trendand seasonalityeffects • Smooth base in usual manner using  • Smooth trend forecasts in usual manner using  • Smooth seasonality forecasts using g • Assume mseasons in a cycle • 12 months in a year • 4 quarters in a month • 3 months in a quarter • et cetera

26. Winter’s Method: Exponential Smoothing w/ Trend and Seasonality • Smooth the base forecast Bt • Smooth the trend forecast Tt • Smooth the seasonality forecast St

27. Winter’s Method: Exponential Smoothing w/ Trend and Seasonality • Forecast Ft with trend and seasonality • Smooth the trend forecast Tt • Smooth the seasonality forecast St

28. ES with Trend and Seasonality a = 0.2, b = 0.4, g = 0.6

29. Example:Exponential Smoothing withTrend and Seasonality

30. Forecasting Performance How good is the forecast? • 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

31. Forecasting Performance Measures

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

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

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

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

36. Fortunately, there is software...