深圳大学管理学院：《运筹学》课程教学资源（PPT课件讲稿）预测 运筹学3类 FORECASTING

CHAPTER13 FORECASTING

CHAPTER13: FORECASTING

13.1|NTR○ DUCTION Typical business forecasting situations A company wishes to forecast the sales of its products Forecast the returns resulting to the company from the purchase of new equipment A local authority forecasts the number of children for the next ten years The Treasury has a large economic model that allows the investigation of the likely effects on the economy if the Chancellor changes the income tax rate, or alters the interest rate

13.1 INTRODUCTION • Typical business forecasting situations – A company wishes to forecast the sales of its products – Forecast the returns resulting to the company from the purchase of new equipment. – A local authority forecasts the number of children for the next ten years – The Treasury has a large economic model that allows the investigation of the likely effects on the economy if the Chancellor changes the income tax rate, or alters the interest rate

13.1.1 Approaches to Forecasting If the company has available the month sales figures for its products for the previous twelve months then this information can be used to make a forecast of sales for the next month

13.1.1 Approaches to Forecasting • If the company has available the monthly sales figures for its products for the previous twelve months then this information can be used to make a forecast of sales for the next month

750 600 550 45 To forecast the sales for the next three time points: projecting the sales trend line

To forecast the sales for the next three time points: projecting the sales trend line

projecting the sales trend line is not so simple Intuitively any forecast made from this data would be less reliable

• projecting the sales trend line is not so simple • Intuitively any forecast made from this data would be less reliable

Time-series method Use historical data collected over time and use this data to project forward to make a forecast Other methods of forecasting For local authority example, to predict the number of couples within age bands, the birth rate for each age band hence the forecast number of children as required The Treasury has a large econometric model that allows the investigation of the ikely effects on the economy if the Chancellor changes the income tax rate, or alters the interest rate

• Time-series method – Use historical data collected over time and use this data to project forward to make a forecast • Other methods of forecasting – For local authority example, to predict the number of couples within age bands, the birth rate for each age band hence the forecast number of children as required. – The Treasury has a large econometric model that allows the investigation of the likely effects on the economy if the Chancellor changes the income tax rate, or alters the interest rate

13.1.2 Time-Series A time-series may be formally defined as A set of observations made on a particular variable at equidistant time intervals Some examples of time-series The sales data used in the two examples above The number of people recorded as unemployed at the end of each month The daily closing price for a company shares quoted by London Stock Exchange The temperature of a hospital patient recorded on an hourly basis Measure of the accuracy of the forecast

13.1.2 Time-Series • A time-series may be formally defined as: – A set of observations made on a particular variable at equidistant time intervals. • Some examples of time-series: – The sales data used in the two examples above. – The number of people recorded as unemployed at the end of each month. – The daily closing price for a company shares quoted by London Stock Exchange – The temperature of a hospital patient recorded on an hourly basis. • Measure of the accuracy of the forecast

13.1.3 Time-Series Graphs Time-series plot A visual inspection: useful information about the nature of the time-series Well-defined trend seasonal structure EXAMPLE 1 well-defined trend having little variability about the trend give relatively precise forecasts forecasts for time points 13, 14&15 measure of the forecast accuracy for different forecasting methods

13.1.3 Time-Series Graphs • Time-series plot: – A visual inspection : useful information about the nature of the time-series. – well-defined trend – seasonal structure. • EXAMPLE 1: – well-defined trend having little variability about the trend. – give relatively precise forecasts. – forecasts for time points 13, 14 & 15 – measure of the forecast accuracy for different forecasting methods

EXAMPLE 2 more problematical forecasts produced from time-series data less reliable forecasts for time points 13, 14&15 The measure of forecast accuracy in this situation would suggest the forecasts were not very reliable Forecasting method calculating the forecast for each required time point calculating measure of forecast accuracy

• EXAMPLE 2 – more problematical – forecasts produced from time-series data: less reliable. – forecasts for time points 13, 14 & 15 – The measure of forecast accuracy in this situation would suggest the forecasts were not very reliable. • Forecasting method: – calculating the forecast for each required time point – calculating measure of forecast accuracy

13.1.4 Exponential Smoothing Methods Methodology for exponential smoothing is based on intuitive ideas a set of 'custom and practice methods rather than having a well defined underlying theoretical structure Exponential smoothing model simple exponential smoothing model model to deal with time-series that contain a trend Model to deal with time-series that contain both trend and seasonality

13.1.4 Exponential Smoothing Methods: • Methodology for exponential smoothing is based on intuitive ideas, – a set of 'custom and practice methods' rather than having a well defined underlying theoretical structure. • Exponential smoothing model – simple exponential smoothing model – model to deal with time-series that contain a trend – Model to deal with time-series that contain both trend and seasonality