Forecasting Chapter 9

Chapter Objectives Be 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 Supply Price Firm-level Market-level 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 Ft+1 = Dt 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 Period Demand 1 12 2 15 3 11 4 9 5 10 6 8 7 14 3-period moving average forecast for Period 8: = (14 + 8 + 10) / 3 = 10.67

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 Period Demand 1 12 2 15 3 11 4 9 5 10 6 8 7 14 3-period weighted moving average forecast for Period 8= [(0.5  14) + (0.3  8) + (0.2  10)] / 1 = 11.4

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 a = .3 Period Demand Forecast 1 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  

Linear Regression How to calculate the a and b

Linear Regression – Example 9.3

Linear Regression – Example 9.3

Linear Regression – Example 9.3 Figure 9.12 The graph shows an upward trend of 7.33 sales per month.

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

Seasonality – Example 9.4

Seasonality – Example 9.4 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 = 54.63 January 2013: 205.6 x .511 = 105.06

Seasonality – Example 9.4 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.

Need measures of 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

Forecast Accuracy – Example 9.7 Calculate the forecast error for each week, the absolute deviation of the forecast error, and absolute percent errors.

Forecast Accuracy – Example 9.7

Forecast Accuracy – Example 9.7 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.

Forecast Accuracy – Example 9.7

Forecast Accuracy – Example 9.7 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

Printed in the United States of America. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.