1. Forecasting
Chapter 9

2. 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.

3. 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

4. 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

5. 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.

6. 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

7. Selecting a Forecasting Method
Figure 9.2

8. Qualitative Forecasting Methods
Market surveys
Build-up forecasts
Life-cycle analogy method
Panel consensus forecasting
Delphi method

9. 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.

10. 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.

11. Time series with randomness
Figure 9.3

12. Time series with Trend and Seasonality
Figure 9.4

13. 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

14. Last Period Model
Table 9.3
Figure 9.5

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

16. 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:
= ( ) / 3
= 10.67

17. 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.

18. 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

19. 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.

20. 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) * = 46.83 6
.3 * 47 + (1-.3) * = 46.88

21. 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

22. Linear Regression

23. Linear Regression
How to calculate the a and b

24. Linear Regression – Example 9.3

25. Linear Regression – Example 9.3

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

27. Seasonal Adjustments
Seasonality – Repeated patterns or drops in a time series associated with certain times of the year.
Table 9.8

28. 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.

29. Seasonality – Example 9.4
Note that the regression forecast does not reflect the seasonality.
Figure 9.15

30. Seasonality – Example 9.4

31. 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 = ( )/2 = .511
Calculate the seasonally adjusted forecasts
Seasonally adjusted forecast = unadjusted forecast x seasonal index
January 2012: x .511 = 54.63
January 2013: x .511 =

32. Seasonality – Example 9.4
Note that the regression forecast now does reflect the seasonality.
Figure 9.16

33. Causal Forecasting Models
Linear Regression
Multiple Regression
Examples:

34. Multiple Regression
Multiple Regression – A generalized form of linear regression that allows for more than one independent variable.

35. 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

36. Measures of Forecast Accuracy
Forecast error for period (i) =
Mean forecast error (MFE) =
Mean absolute deviation (MAD) =

37. Measures of Forecast Accuracy
Mean absolute percentage error (MAPE) =
Tracking Signal =

38. Forecast Accuracy – Example 9.7
Table 9.11

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

40. Forecast Accuracy – Example 9.7

41. 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.

42. Forecast Accuracy – Example 9.7

43. 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.

44. 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.

45. Forecasting Case Study
Top-Slice Drivers

46. 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.