Operations management 12th stevenson ch03 forecasting

Two Important Aspects of Forecasts Expected level of demand The level of demand may be a function of some structural variation such as trend or seasonal variation  Accuracy Related

Chapter 3

McGraw-Hill/Irwin

You should be able to:

1. List the elements of a good forecast

2. Outline the steps in the forecasting process

3. Describe at least three qualitative forecasting techniques and the advantages and

disadvantages of each

4. Compare and contrast qualitative and quantitative approaches to forecasting

5. Describe averaging techniques, trend and seasonal techniques, and regression analysis,

and solve typical problems

6. Explain three measures of forecast accuracy

7. Compare two ways of evaluating and controlling forecasts

8. Assess the major factors and trade-offs to consider when choosing a forecasting technique

Chapter 3: Learning Objectives

 Forecast – a statement about the future value of a variable of interest

We make forecasts about such things as weather, demand, and resource

availability

Forecasts are an important element in making informed decisions

Accounting Cost/profit estimates

Human Resources Hiring/recruiting/training

Product/service design New products and services

Forecasts affect decisions and activities throughout an organization

Two Important Aspects of Forecasts

 Expected level of demand

The level of demand may be a function of some structural variation such as trend

or seasonal variation

 Accuracy

Related to the potential size of forecast error

Features Common to All Forecasts

1. Techniques assume some underlying causal system that existed in the past will

persist into the future

2. Forecasts are not perfect

3. Forecasts for groups of items are more accurate than those for individual items

4. Forecast accuracy decreases as the forecasting horizon increases

Elements of a Good Forecast

 technique should be simple to understand and use

 should be cost effective

Steps in the Forecasting Process

1 Determine the purpose of the forecast

2 Establish a time horizon

3 Obtain, clean, and analyze appropriate data

4 Select a forecasting technique

5 Make the forecast

6 Monitor the forecast

 Quantitative techniques involve either the projection of historical data or the development of associative

methods that attempt to use causal variables to make a forecast

 These techniques rely on hard data

Judgmental Forecasts

 Forecasts that use subjective inputs such as opinions from consumer

surveys, sales staff, managers, executives, and experts

Executive opinions

Salesforce opinions

Delphi method

Time-Series Forecasts

 Forecasts that project patterns identified in recent time-series observations

Time-series - a time-ordered sequence of observations taken at regular time

intervals

 Assume that future values of the time-series can be estimated from past values

of the time-series

Trends and Seasonality

 Short-term, fairly regular variations related to the calendar or time of day

 Restaurants, service call centers, and theaters all experience seasonal demand

Cycles and Variations

Cycle

 Wavelike variations lasting more than one year

These are often related to a variety of economic, political, or even agricultural conditions

Time-Series Behaviors

Time-Series Forecasting - Nạve Forecast

 Nạve Forecast

Uses a single previous value of a time series as the basis for a forecast

The forecast for a time period is equal to the previous time period’s value

Can be used with

a stable time series

seasonal variations

trend

Nạve Forecast Example

Week Sales (actual) Sales (forecast) Error

 Simple to use

 Virtually no cost

 Quick and easy to prepare

 Data analysis is nonexistent

 Easily understandable

 Cannot provide high accuracy

 Can be a standard for accuracy

Nạve Forecasts

Uses for Nạve Forecasts

Time-Series Forecasting - Averaging

 These Techniques work best when a series tends to vary about an average

Averaging techniques smooth variations in the data

They can handle step changes or gradual changes in the level of a series

 Technique that averages a number of the most recent actual values in

generating a forecast

Moving Average

average moving

in the periods

of Number

1 period

in value Actual

average moving

period MA

period for time

Forecast

n

t F

n

A F

t n t

n i

i t n

t

Moving Average

 As new data become available, the forecast is updated by adding the newest

value and dropping the oldest and then re-computing the average

 The number of data points included in the average determines the model’s

sensitivity

Fewer data points used more responsive

More data points used less responsive

Week Sales (actual) Sales (forecast) Error

• Why is MA3 longer than MA5?

• Which curve fluctuate the most?

• Which curve is the smoothest?

• Smaller m, responsiveness ↑, stability ↓

• Larger m, responsiveness ↓, stability ↑

• Must maintain stability when fluctuations are high

 The most recent values in a time series are given more weight in computing a

forecast

The choice of weights, w, is somewhat arbitrary and involves some trial and error

Weighted Moving Average

etc , 1 period

for value

actual the

, period for

value actual

the

etc.

, 1 period

for weight ,

period for

weight

where

) (

) (

) (

1 1

1 1

t A

t w

t w

A w

A w

A w

F

t t

t t

n t n t t

t t

t t

Weighted Moving Average Example

Week Sales (actual) Sales (forecast) Error

 A weighted averaging method that is based on the previous forecast plus a

percentage of the forecast error

Exponential Smoothing

period previous

the from

sales

or demand

Actual

constant Smoothing

=

period previous

for the Forecast

period for

Forecast

where

) (

1 1

1 1

t t

t t

A

F

t F

F A

F F

α

α

Exponential Smoothing

 Weighted averaging method based on previous forecast plus a

percentage of the forecast error

 A-F is the error term, α is the % feedback

Example 3 - Exponential Smoothing

Period Actual Alpha = 0.1 Error Alpha = 0.4 Error

Picking a Smoothing Constant

α = .1

α = .4 Actual

35 40 45 50

Other Forecasting Methods - Focus

 Focus Forecasting

Some companies use forecasts based on a “best current performance” basis

Apply several forecasting methods to the last several periods of historical data

The method with the highest accuracy is used to make the forecast for the following

period

This process is repeated each month

Other Forecasting Methods - Diffusion

 Diffusion Models

Historical data on which to base a forecast are not available for new products

Predictions are based on rates of product adoption and usage spread from other

Techniques for Trend

 Linear trend equation

 Non-linear trends

Linear Trend

 A simple data plot can reveal the existence and nature of a trend

 Linear trend equation

b = Slope of the line

t = Specified number of time periods from t = 0

Linear Trend Equation

 Ft = Forecast for period t

 t = Specified number of time periods

0 20 40 60 80 100 120 140 160 180

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Actual Trend

Linear Trend Equation

 Easy to use: a built-in function in

spreadsheet software

 Based on Least Squares method used in

linear regression, which

Minimizes the sum of the squares of the

deviations

Uses equal weight for all time periods

 Both a and b must be recalculated on

regular basis to include new data.

DeviationYt

At

0 20 40 60 80 100 120 140 160 180

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Actual Trend

Estimating slope and intercept

 Slope and intercept can be estimated from historical data

Linear Trend Equation Example

Exercise: Calculate b and a by using the sums on the left

Period (t) Sales (Yt) t*Yt t^2

5958

10

2

2 2

n

Y t

5 996

Y

Techniques for Seasonality

Seasonality – regularly repeating movements in series values that can be tied to

Seasonality is expressed as a quantity that gets added to or subtracted from the time-series

average in order to incorporate seasonality

Multiplicative

Seasonality is expressed as a percentage of the average (or trend) amount which is then used to

multiply the value of a series in order to incorporate seasonality

Models of Seasonality

Seasonal relatives

 The seasonal percentage used in the multiplicative seasonally adjusted forecasting model

Using seasonal relatives

To deseasonalize data

Done in order to get a clearer picture of the nonseasonal (e.g., trend) components of the data series

Divide each data point by its seasonal relative

To incorporate seasonality in a forecast

1. Obtain trend estimates for desired periods using a trend equation

2. Add seasonality by multiplying these trend estimates by the corresponding seasonal

relative

Seasonal Relatives

Techniques for Cycles

Cycles are similar to seasonal variations but are of longer duration

Explanatory approach

 Search for another variable that relates to, and leads, the variable of interest

Housing starts precede demand for products and services directly related to construction of

new homes

If a high correlation can be established with a leading variable, an equation can be

developed that describes the relationship, enabling forecasts to be made

Associative Forecasting Techniques

 Associative techniques are based on the development of an equation

that summarizes the effects of predictor variables

Predictor variables - variables that can be used to predict values of the

variable of interest

Home values may be related to such factors as home and property size, location,

number of bedrooms, and number of bathrooms

Simple Linear Regression

 Regression - a technique for fitting a line to a set of data points

Simple linear regression - the simplest form of regression that involves a linear

relationship between two variables

The object of simple linear regression is to obtain an equation of a straight line that

minimizes the sum of squared vertical deviations from the line (i.e., the least squares

criterion)

Least Squares Line

( ) ( )( )

( ) ( )

ns observatio paired

of Number

the of height the

(i.e., 0

when of

Value

line the

of Slope

variable nt)

(independe Predictor

variable )

(dependent Predicted

where

2 2

y n

x b

y a

x x

n

y x

xy

n b

y x

y a

b x y

bx a

y

c c

c

 Standard error of estimate

A measure of the scatter of points around a regression line

If the standard error is relatively small, the predictions using the linear equation

will tend to be more accurate than if the standard error is larger

Standard Error

( )

points data

of number

point data

each of

value

estimate of

error standard

where

n

y

y S

e

c e

Correlation, r

 A measure of the strength and direction of relationship between two variables

 Ranges between -1.00 and +1.00

r2, square of the correlation coefficient

 A measure of the percentage of variability in the values of y that is “explained” by the independent variable

 Ranges between 0 and 1.00

n x

x n

y x

xy n

r

Simple Linear Regression Assumptions

1 Variations around the line are random

2 Deviations around the average value (the line) should be normally distributed

3 Predictions are made only within the range of observed values

Forecast Accuracy and Control

 Forecasters want to minimize forecast errors

It is nearly impossible to correctly forecast real-world variable values on a regular

basis

So, it is important to provide an indication of the extent to which the forecast

might deviate from the value of the variable that actually occurs

 Forecast accuracy should be an important forecasting technique selection

criterion

Error = Actual – Forecast

If errors fall beyond acceptable bounds, corrective action may be necessary

Forecast Accuracy Metrics

MAD weights all errors evenly

MSE weights errors according to their squared values

MAPE weights errors according to relative error

Forecast Actual

MAPE t

tt

1

Forecast

Actual MSE

−

−

n

Issues to consider:

 Always plot the line to verify that a linear relationship is appropriate

 The data may be time-dependent.

If they are

use analysis of time series

use time as an independent variable in a multiple regression analysis

 A small correlation may indicate that other variables are important

Monitoring the Forecast

Tracking forecast errors and analyzing them can provide useful insight into whether forecasts are

performing satisfactorily

Sources of forecast errors

The model may be inadequate

Irregular variations may have occurred

The forecasting technique has been incorrectly applied

Random variation

Control charts are useful for identifying the presence of non-random error in forecasts

Tracking signals can be used to detect forecast bias

Choosing a Forecasting Technique

 Factors to consider

Cost

Availability of historical data

Availability of forecasting software

Time needed to gather and analyze data and prepare a forecast

Forecast horizon

Using Forecast Information

Reactive approach

 View forecasts as probable future demand

 React to meet that demand

The better forecasts are, the more able organizations will be to take advantage of

future opportunities and reduce potential risks

 A worthwhile strategy is to work to improve short-term forecasts

Accurate up-to-date information can have a significant effect on forecast accuracy:

Prices

Demand

Other important variables

 Reduce the time horizon forecasts have to cover

 Sharing forecasts or demand data through the

supply chain can improve forecast quality

Operations Strategy