Forecasting Chapter 9. Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall9 - 2...

Forecasting

Chapter 9

Chapter ObjectivesBe able to:Discuss the importance of forecasting and identify the most appropriate type of forecasting approach, given different forecasting situations. Apply a variety of time series forecasting models, including moving average, exponential smoothing, and linear regression models. Develop causal forecasting models using linear regression and multiple regression. Calculate measures of forecasting accuracy and interpret the results.

Forecasting

Forecast – An estimate of the future level of some variable.

Why Forecast? Assess long-term capacity needs Develop budgets, hiring plans, etc. Plan production or order materials

Types of Forecasts Demand

Firm-level Market-level

Supply Number of current producers and suppliers Projected aggregate supply levels Technological and political trends

Price Cost of supplies and services Market price for firm’s product or service

Laws of Forecasting

Forecasts are almost always wrong by some amount (but they are still useful).

Forecasts for the near term tend to be more accurate.

Forecasts for groups of products or services tend to be more accurate.

Forecasts are no substitute for calculated values.

Forecasting Methods

Qualitative forecasting techniques – Forecasting techniques based on intuition or informed opinion. Used when data are scarce, not available, or

irrelevant.

Quantitative forecasting models – Forecasting models that use measurable, historical data to generate forecasts. Time series and causal models

Selecting a Forecasting Method

Figure 9.2

Qualitative Forecasting Methods

Market surveys

Build-up forecasts

Life-cycle analogy method

Panel consensus forecasting

Delphi method

Quantitative Forecasting Methods

Time series forecasting models – Models that use a series of observations in chronological order to develop forecasts.

Causal forecasting models – Models in which forecasts are modeled as a function of something other than time.

Demand movement

Randomness – Unpredictable movement from one time period to the next.

Trend – Long-term movement up or down in a time series.

Seasonality – A repeated pattern of spikes or drops in a time series associated with certain times of the year.

Time series with randomness

Figure 9.3

Time series with Trend and Seasonality

Figure 9.4

Last Period Model

Last Period Model - The simplest time series model that uses demand for the current period as a forecast for the next period.

Ft+1 = Dt

where Ft+1= forecast for the next period, t+1

and Dt = demand for the current period, t

Last Period Model

Table 9.3 Figure 9.5

Moving Average Model

Moving Average Model – A time series forecasting model that derives a forecast by taking an average of recent demand value.

Moving Average Model

3-period moving averageforecast for Period 8:

= (14 + 8 + 10) / 3= 10.67

Period Demand1 122 153 114 95 106 87 148 12

Weighted Moving Average Model

Weighted Moving Average Model – A form of the moving average model that allows the actual weights applied to past observations to differ.

Weighted Moving Average Model

3-period weighted moving average forecast for Period 8=[(0.5 14) + (0.3 8) + (0.2 10)] / 1 =

Period Demand1 122 153 114 95 106 87 148 12

Exponential Smoothing Model

Exponential Smoothing Model – A form of the moving average model in which the forecast for the next period is calculated as the weighted average of the current period’s actual value and forecast.

Exponential Smoothing Model = .3

Period Demand Forecast1 50 40 2 46 .3 * 50 + (1-.3) * 40 = 43 3 52 .3 * 46 + (1-.3) * 43 = 43.9 4 48 .3 * 52 + (1-.3) * 43.9 = 46.33 5 47 .3 * 48 + (1-.3) * 46.33 = 46.83 6 .3 * 47 + (1-.3) * 46.83 = 46.88

Adjusted Exponential Smoothing

Adjusted Exponential Smoothing Model – An expanded version of the exponential smoothing model that includes a trend adjustment factor.

AFt+1 = Ft+1 +Tt+1

where AFt+1 = adjusted forecast for the next period

Ft+1 = unadjusted forecast for the next period = Dt + (1 – ) Ft

Tt+1 = trend factor for the next period = (Ft+1 – Ft) + (1 – )Tt

Tt = trend factor for the current period

smoothing constant for the trend adjustment factor

Linear Regression

How to calculate the a and b

Linear Regression – Example 9.3

The graph shows an upward trend of 7.33 sales per month.

Figure 9.12

Seasonal Adjustments

Seasonality – Repeated patterns or drops in a time series associated with certain times of the year.

Table 9.8

Seasonal Adjustments

Four-step procedure: For each of the demand values in the time series, calculate the

corresponding forecast using the unadjusted forecast model. For each demand value, calculate (Demand/Forecast). If the ratio is

less than 1, then the forecast model overforecasted; if it is greater than 1, then the model underforecasted.

If the time series covers multiple years, take the average (Demand/Forecast) for corresponding months or quarters to derive the seasonal index. Otherwise use (Demand/Forecast) calculated in Step 2 as the seasonal index.

Multiply the unadjusted forecast by the seasonal index to get the seasonally adjusted forecast value.

Seasonality – Example 9.4

Note that the regression forecast does not reflect the seasonality.

Figure 9.15

Calculate the (Demand/Forecast) for each of the time periods:

January 2012: (Demand/Forecast) = 51/106.9 = .477

January 2013: (Demand/Forecast) = 112/205.6 = .545

Calculate the monthly seasonal indices:Monthly seasonal index, January = (.477 + .545)/2 = .511

Calculate the seasonally adjusted forecasts Seasonally adjusted forecast = unadjusted forecast x seasonal index

January 2012: 106.9 x .511 = 54.63January 2013: 205.6 x .511 = 105.06

Note that the regression forecast now does reflect the seasonality.

Figure 9.16

Causal Forecasting Models

Linear Regression Multiple Regression Examples:

Multiple Regression Multiple Regression – A generalized form of linear regression

that allows for more than one independent variable.

Forecast Accuracy

How do we know: If a forecast model is “best”? If a forecast model is still working? What types of errors a particular forecasting model

is prone to make?

Need measures of forecast accuracy

Measures of Forecast Accuracy

Forecast error for period (i) =

Mean forecast error (MFE) =

Mean absolute deviation (MAD) =

Measures of Forecast Accuracy

Mean absolute percentage error (MAPE) =

Tracking Signal =

Forecast Accuracy – Example 9.7

Table 9.11

Calculate the forecast error for each week, the absolute deviation of the forecast error, and absolute percent errors.

Model 2 has the lowest MFE so it is the least biased.

Model 2 also has the lowest MAD and MAPE values so it appears to be superior.

Calculate the tracking signal for the first 10 weeks.

The tracking signal for Model 2 gets very low in week 5, however the model recovers.

You need to continue to update the tracking signal in the future.

Collaborative Planning, Forecasting, and Replenishment (CPFR)

CPFR – A set of business processes, backed up by information technology, in which members agree to mutual business objectives and measures, develop joint sales and operational plans, and collaborate electronically to generate and update sales forecasts and replenishment plans.

Forecasting Case Study

Top-Slice Drivers

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