Forecasting

1
Forecasting

• Y.-H. Chen, Ph.D.
• Production / Operations Management
• International College
• Ming-Chuan University

2
Forecasting Outline

• Introduction
• Forecasting Process
• Forecasting Methods
• Forecast Accuracy and Control
• Forecast Method Selection and Usage

3
Introduction

• A forecast
• is a statement of future,
• is a basis for planning,
• is not for forecasting demand only,
• requires a skillful blending of art and science,
• assumes that the underlying system will continue
  to exist in the future, and
• is rarely perfect.

4
Forecasting Process
5
Elements of A Good Forecast

• The forecast horizon must cover the time
  necessary to implement possible changes.
• The degree of accuracy should be stated.
• The forecast should be reliable it should work
  consistently.
• The forecast should be expressed in meaningful
  units.
• The forecast should be in writing.
• The forecast should be simply to understand and
  use, or consistent with historical data
  intuitively.

6
Additional Properties

• Forecasts for groups of items tend to be more
  accurate than forecasts for individual items,
  because forecasting errors among items in a group
  usually have a canceling effect.
• Forecast accuracy decreases as the time period
  covered by the forecast increases.

7
Forecasting Methods

• Basic Methods
• Judgmental Forecast
• Statistical (Time Series) Forecast
• Trend
• Seasonality
• Cycle
• Association

8
Basic Forecasting Methods

• Judgmental Forecast
• Statistical (Time Series) Forecast
• Averaging
• Weighted Moving Average
• Exponential Smoothing

9
Judgmental Forecast
Executive opinions.
Mostly for long-range planning and introduction
of new products. The view of one person may
prevail.
Direct customer contact composites.

• Unable to distinguish between what customers
  would like to do and what they will actually do.
• Could overly influenced by recent sales
  experiences. Low sales could lead to low
  estimates.
• Conflict of interest. Low sales estimates lead to
  better sales performance.

Consumer survey or point-of-sales (POS) data.

• Expensive and time-consuming.
• Possible existence of irrational patterns.
• Low response rates.

Opinions of managers and staff.
Delphi method (Rand Corp., 1948) Managers and
staff complete a series of questionnaires, each
developed from the previous one, to achieve a
consensus forecast. Technological forecasting.
Long-term single-time forecasting. Data are
costly to obtain.
10
Statistical (Time Series) Forecast

• It is extremely important to plot data and
  examine them before doing any analysis or
  forecast. A demand forecast should be based on a
  time series of past demand rather than sales or
  shipment.
• Data patterns

Trend
A long term upward or downward movement in data.
Seasonality
Short-term regular variations related to weather,
holiday, or other factors.
Cycle
Wavelike variation lasting more than one year.
Irregular Variation
Caused by unusual circumstances, not reflective
of typical behavior.
Random variation
Residual variation after all other behaviors are
accounted for.
11
Data Patterns
Irregularvariation
Trend
Cycles
90
89
88
Seasonal variations
12
Simple Naive Forecast

• No cost.
• Quick and easy to prepare.
• Easy to understand.
• Can be applied to data with seasonality and trend

13
General Naive Forecast
14
Weighted Moving Average
15
Moving Average Example

• Compute a 3-period moving average forecast given
  demand for shopping carts for the last five
  periods.

• If the actual demand in period 6 turns out to be
  39, what would be the moving average forecast for
  period 7?

41.33
40.00
16
Weighted Moving Average Example

• Compute a weighted average forecast using a
  weight of .40 for the most recent period, .30 for
  the next most recent, .20 for the next, and .10
  for the next.

• If the actual demand in period 6 turns out to be
  39, what would be the weighted moving average
  forecast for period 7?

41.0
40.2
17
Properties of Weighted Moving Average

• Easy to compute and understand.
• Moving average forecast lags and smoothens the
  actual forecast.
• The number of data points in the average
  determines its sensitivity to each new data
  point the fewer the data points in an average,
  the more responsive the average tends to be.
• Weights can be added to values in the average to
  make the resulting average more responsive to
  some recent data points. However, weights involve
  the use of trial-and-error to find suitable
  weights.

18
Exponential Smoothing

• Exponential smoothing is a weighted averaging
  method based on previous forecast plus a
  percentage of its forecast error.

19
Properties of Exponential Smoothing

• Commonly used values of alpha range from 0.05 to
  0.50. Low values are used when the underlying
  average tends to be stable higher values are
  used when the underlying average is susceptible
  to change.
• Moving average or naive forecast can be used to
  generate starting forecast for exponential
  smoothing.

20
Picking A Smooth Constant
21
Exponential Smoothing Example

• Use exponential smoothing to develop a series of
  forecasts for the data, and compute
  (actual-forecast)error for each period.
• Use a smoothing factor of .10.
• Use a smoothing factor of .40.
• Plot the actual data and both sets of forecasts
  on a single graph.

22
Exponential Smoothing Example
23
Forecasting Method Extension

• Trend
• Linear Trend
• Trend-Adjusted Exponential Smoothing
• Seasonality
• Cycle
• Association

24
Linear Trend
25
Linear Trend Coefficients
26
Linear Trend Example

• Calculate sales for a California-based firm over
  the last 10 weeks are shown in the table. Plot
  the data and visually check to see if a linear
  trend line would be appropriate. Then, determine
  the equation of the trend line, and predict sales
  for weeks 11 and 12.

27
Linear Trend Example Solution
a. A plot suggests that a linear trend line would
be appropriate.
b. For n10, we have
Thus, the trend line is yt699.407.51t, where
t0 for period 0.
c. By letting t11 and t12, we have
28
Seasonality
29
Cycle

• Cycles are similar to seasonal variations but of
  longer duration, e.g., two to six years between
  peaks.
• It is difficult to project cycles from past data,
  because turning points are difficult to identify.
• A short moving average or a naive approach may be
  of some value.

30
Associative Forecasts

• High correlation of a forecast with leading
  variables can be useful in computing the
  forecast.
• The simple linear regression is the simplest and
  most widely used method.

31
Simple Linear Regression Coefficients
32
Simple Linear Regression Example

• Healthy Hamburgers has a chain of 12 stores in
  northern Illinois. Sales figures and profits for
  the stores are given in the following table.
  Obtain a regression line for the data and predict
  profit for a store assuming sales of 10 million.

33
Simple Linear Regression Example Data Plot
34
Simple Linear Regression Example Solution
35
An Important Measure of Simple Linear Regression

• Correlation measures the strength and direction
  of the relationship between two variables.
• 1, positive correlation.
• -1, negative correlation.
• 0, zero correlation.
• The square of the correlation coefficient
  provides a measure of how well a regression line
  fits the data. The values ranges from 0 to
  1.00.
• 0.80,1.00, good fit.
• 0.25,0.80), moderate fit.
• 0.00,0.25), poor fit.

36
Simple Linear Regression and Correlation Example

• Sales of 19-inch color television sets and
  3-month lagged unemployment are shown in the
  table below. Determine if unemployment levels can
  be used to predict demand for 19-inch color TVs
  and, if so, derive a predictive equation.

37
Simple Linear Regression and Correlation Example
Data Plot
38
Simple Linear Regression and Correlation Example
Solution
39
Linear Regression Assumptions

• No patterns such as cycles or trends should be
  apparent.
• Deviations around the line should be normally
  distributed.
• Predictions are best being made within the range
  of observed values.

40
Linear Regression Usage Guidelines

• Always plot the data to verify that a linear
  relationship is appropriate.
• The data may be time-dependent. If patterns
  appear, use analysis of time series or use time
  as an independent variable as part of a multiple
  regression analysis.
• A small correlation may imply that other
  variables are important.

41
Linear Regression Summary

• Simple linear regression applies only to linear
  relationship with one independent variable.
• One needs a considerable amount of data to
  establish the relationship --- in practice, 20 or
  more observations.
• All observations are weighted equally.

42
Forecast Accuracy

• Error - difference between actual value and
  predicted value
• Mean absolute deviation (MAD)
• Average absolute error
• Mean squared error (MSE)
• Average of squared error

43
Forecast AccuracyMAD MSE
Example 10 (page 97).
44
Forecast Control

• It is necessary to monitor forecast errors to
  ensure that the forecast is performing adequately
  over time. This is generally accomplished by
  comparing forecast errors to predefined values,
  or action limits.

45
Why Do We Need Forecast Control?

• The omission of an important variable.
• Appearance of a new variable.
• A sudden or unexpected change in the variable
  (causing by severe weather or other nature
  phenomena, temporary shortage or breakdown,
  catastrophe, or similar events).
• Being used incorrectly.
• Data being misinterpreted.
• Random variation.

46
Forecasting Control Methods

• Tracking Signal
• Control Chart

47
Forecast Control Tracking Signal
48
Forecast Control Control Chart

• The control chart sets the limits as multiples of
  the squared root of MSE.

49
Forecast Control Control Chart

• For a normal distribution, 95 of the errors fall
  within /-2s, and approximately 99.7 of the
  errors fall within /-3s. Errors fall outside
  these limits should be regarded as evidence that
  corrective action is needed.

Example 11 (Page 93).
50
Forecast Method Selection

• Most important
• Cost
• Accuracy

• Need to consider
• Historical performance
• Ability to respond to change