FORCASTING AND DEMAND PLANNING CHAPTER 11 DAVID A. COLLIER AND JAMES R. EVANS

11-1 Describe the importance of forecasting to the value chain. 11-2 Explain basic concepts of forecasting and time series. 11-3 Explain how to apply single moving average and exponential smoothing models. 11-4 Describe how to apply regression as a forecasting approach. 11-5 Explain the role of judgment in forecasting. 11-6 Describe how statistical and judgmental forecasting techniques are applied in practice.

Forecasting and Demand Planning Forecasting is the process of projecting the values of one or more variables into the future. Types of forecasts: Long-range forecasts in total sales dollars (top management level) Aggregate forecasts of sales volume (middle management level) Forecasts of individual units (operational level)

Exhibit 11.1 The Need for Forecasts in a Value Chain

Basic Concepts in Forecasting The planning horizon is the length of time on which a forecast is based. This spans from short-range forecasts with a planning horizon of under 3 months to long-range forecasts of 1 to 10 years. The time bucket is the unit of measure for the time period used in a forecast.

Basic Concepts in Forecasting A time series is a set of observations measured at successive points in time or over successive periods of time. A time series pattern may have one or more of the following five characteristics: Trend Seasonal patterns Cyclical patterns Random variation (or noise) Irregular (one time) variation

Basic Concepts in Forecasting A trend is the underlying pattern of growth or decline in a time series. Seasonal patterns are characterized by repeatable periods of ups and downs over short periods of time. Cyclical patterns are regular patterns in a data series that take place over longer periods of time. Random variation (sometimes called noise) is the unexplained deviation of a time series from a predictable pattern, such as a trend, seasonal, or cyclical pattern. Irregular variation is a one-time variation that is explainable.

Exhibit 11.3 Seasonal Pattern of Home Natural Gas Usage

Exhibit Extra Trend and Business Cycle Characteristics (each data point is 1 year apart)

Exhibit 11.4 Call Center Volume Example of a time series with trend and seasonal components:

Exhibit 11.5 Chart of Call Volume

Basic Concepts in Forecasting Forecast error is the difference between the observed value of the time series and the forecast, or At – Ft . Mean Square Error (MSE) Mean Absolute Deviation Error (MAD) Mean Absolute Percentage Error (MAPE) Σ(At – Ft )2 MSE = [11.1] T ׀At – Ft ׀ MAD = [11.2] T Σ׀(At – Ft )/At ׀ X 100 MAPE = [11.3] T

Basic Concepts in Forecasting MSE is influenced much more by large forecasts errors than by small errors (because the errors are squared). The measurement scale factor in MAPE is eliminated by dividing the absolute error by the time-series data value, making it easier to interpret. The selection of the best measure of forecast accuracy is not a simple matter; indeed, forecasting experts often disagree on which measure should be used.

Statistical Forecasting Models Statistical forecasting is based on the assumption that the future will be an extrapolation of the past. Judgmental forecasting relies upon opinions and expertise of people in developing forecasts.

Single Moving Average A moving average (MA) forecast is an average of the most recent “k” observations in a time series. Ft+1 = ∑(most recent “k” observations)/k = (At + At–1 + At–2 + ... + At–k+1)/k [11.4] MA methods work best for short planning horizons when there is no major trend, seasonal, or business cycle pattern. As the value of “k” increases, the forecast reacts slowly to recent changes in the time series data.

Solved Problem Period Demand 1 86 7 91 2 93 8 3 88 9 96 4 89 10 97 5 Develop three-period and four-period moving-average forecasts and single exponential smoothing forecasts with a = 0.5. Compute the MAD, MAPE, and MSE for each. Which method provides a better forecast? Period Demand 1 86 7 91 2 93 8 3 88 9 96 4 89 10 97 5 92 11 6 94 12 95

Solved Problem Based on these error metrics (MAD, MSE, MAPE), the 3-month moving average is the best method among the three.

Exhibit 11.7 Summary of Three-Month Moving-Average Forecasts

Exhibit 11.8 Milk-Sales Forecast Error Analysis

Single Exponential Smoothing Single Exponential Smoothing (SES) is a forecasting technique that uses a weighted average of past time-series values to forecast the value of the time series in the next period. Ft+1 = At + (1 – )Ft = Ft +  (At – Ft) [11.5]

Exhibit 11.9 Summary of Single Exponential Smoothing Milk-Sales Forecasts with α = 0.2

Exhibit 11.10 Excel Moving Average Forecasting Template

Regression as a Forecasting Approach Regression analysis is a method for building a statistical model that defines a relationship between a single dependent variable and one or more independent variables, all of which are numerical. Yt = a + bt (11.7) Simple linear regression finds the best values of a and b using the method of least squares. Excel provides a very simple tool to find the best-fitting regression model for a time series by selecting the Add Trendline option from the Chart menu.

Exhibit 11.11 Factory Energy Costs

Exhibit 11.12 Format Trendline Dialog Box

Exhibit 11.13 Least-Squares Regression Model for Energy Cost Forecasting

Causal Forecasting with Multiple Regression A linear regression model with more than one independent variable is called a multiple linear regression model. Multiple regression models can include other independent variables such as economic indexes or demographic factors that may influence the time series.

Exhibit 11.14 Gasoline Sales Data

Exhibit 11.15 Chart of Sales versus Time

Exhibit 11.16 Multiple Regression Results

Judgmental Forecasting Judgmental forecasting relies upon opinions and expertise of people in developing forecasts. Grass Roots forecasting is simply asking those who are close to the end consumer, such as salespeople, about the customers’ purchasing plans. The Delphi method consists of forecasting by expert opinion by gathering judgments and opinions of key personnel based on their experience and knowledge of the situation.

Forecasting in Practice Managers use a variety of judgmental and quantitative forecasting techniques. Statistical methods alone cannot account for such factors as sales promotions, competitive strategies, unusual economic disturbances, new products, large one-time orders, labor complications, etc. Statistical forecasts are often adjusted to account for qualitative factors.

Forecasting in Practice A tracking signal provides a method for monitoring a forecast by quantifying bias—the tendency of forecasts to consistently be larger or smaller than the actual values of the time series. Tracking signal = Σ(At – Ft) [11.8] MAD Tracking signals between plus and minus 4 indicate an adequate forecasting model.