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Forecasting. BUS255. Goals. By the end of this chapter, you should know: Importance of Forecasting Various Forecasting Techniques Choosing a Forecasting Method. Forecasting. Forecasts are done to predict future events for planning

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By the end of this chapter, you should know:

  • Importance of Forecasting

  • Various Forecasting Techniques

  • Choosing a Forecasting Method



  • Forecasts are done to predict future events for planning

  • Finance, human resources, marketing, operations, and supply chain managers need forecasts to plan

  • Forecasts are made on many different variables

  • Forecasts are important to managing both processes and managing supply chains

Key decisions in forecasting

Key Decisions in Forecasting

  • Deciding what to forecast

    • Level of aggregation

    • Units of measurement

  • Choosing a forecasting system

  • Choosing a forecasting technique

Qualitative judgment methods

Qualitative (Judgment) methods

  • Salesforce estimates

  • Executive opinion

  • Market Research

  • The Delphi Method

Case study

Case Study

Case study questions

Case study questions

  • What information system is used by UNILEVER to manage forecasts?

  • What does UNILEVER do when statistical information is not useful for forecasting?

  • What types of qualitative methods are used by UNILEVER?

  • What were some suggestions provided to improve forecasting?

Causal methods linear regression

Causal methods – Linear Regression

  • A dependent variable is related to one or more independent variables by a linear equation

  • The independent variables are assumed to “cause” the results observed in the past

  • Simple linear regression model assumes a straight line relationship

Causal methods linear regression1

Causal methods – Linear Regression

Y = a + bX


Y= dependent variable

X= independent variable

a= Y-intercept of the line

b= slope of the line

Causal methods linear regression2

Causal methods – Linear Regression

  • Fit of the regression model

    • Coefficient of determination

    • Standard error of the estimate

  • Please go to in-class exercise sheet

Time series

Time Series

  • A time series is the repeated observations of demand for a service or product in their order of occurrence

  • There are five basic time series patterns

    • Horizontal

    • Trend

    • Seasonal

    • Cyclical

    • Random

Demand patterns



Demand Patterns

(a) Horizontal: Data cluster about a horizontal line

Demand patterns1



Demand Patterns

(b) Trend: Data consistently increase or decrease

Demand patterns2

Year 1


Year 2




Demand Patterns

(c) Seasonal: Data consistently show peaks and valleys

Demand patterns3





Demand Patterns

(d) Cyclical: Data reveal gradual increases and decreases over extended periods

Demand patterns4

Demand Patterns

  • Four of the patterns – horizontal, trend, seasonal, and cyclical – combine in varying degrees to define the underlying time pattern

  • Fifth pattern

    • Random variation: Results from chance causes and cannot be predicted

    • Random variation is what makes every forecast ultimately wrong

Time series methods

Time-Series methods

  • Use only historical information rather than independent variables (as used by Regression)

  • Assumption is that past pattern continues in future

  • In a naive forecast the forecast for the next period equals the demand for the current period (Forecast = Dt)

Time series methods1

Time-Series methods

  • This section considers time-series methods with demand that has no trend, seasonal, or cyclical patterns

  • All variation in time series is due to random variation, so the following techniques are appropriate:

    • Simple moving average

    • Weighted moving average

    • Exponential smoothing

Simple moving average

Sum of last n demands


Dt+ Dt-1 + Dt-2 + … + Dt-n+1


Ft+1 = =

Simple Moving Average

  • The forecast for period t + 1 can be calculated at the end of period t (after the actual demand for period t is known) as


Dt= actual demand in periodt

n= total number of periods in the average

Ft+1= forecast for period t + 1

Forecast error

Forecast error

  • For any forecasting method, it is important to measure the accuracy of its forecasts. Forecast error is simply the difference found by subtracting the forecast from actual demand for a given period, or

Et = Dt– Ft


Et= forecast error for period t

Dt= actual demand in periodt

Ft= forecast for period t

Simple moving average1

Simple Moving Average

Please refer to problem in the in-class exercise

Weighted moving average

Weighted Moving Average

Using this method, each historical demand in the average can have its own weight, provided that the sum of the weights equals 1.0.

Ft+1 = W1D1 + W2D2 + … + WnDt-n+1

A three-period weighted moving average model with the most recent period weight of 0.50, the second most recent weight of 0.30, and the third most recent might be weight of 0.20

Ft+1 = 0.50Dt+ 0.30Dt–1 + 0.20Dt–2

Weighted moving average1

Weighted Moving Average

Please refer to problem in the in-class exercise

Exponential smoothing

Exponential Smoothing

  • A sophisticated weighted moving average that calculates the average of a time series by giving recent demands more weight than earlier demands

  • Requires only three items of data

    • The last period’s forecast

    • The demand for this period

    • A smoothing parameter, alpha (α), where 0 ≤ α ≤ 1.0

  • The equation for the forecast is

Ft+1= α(Demand this period) + (1 – α)(Forecast calculated last period)

= αDt+ (1 – α)Ft

or the equivalent

Ft+1 = Ft+ α(Dt– Ft)

Exponential smoothing1

Exponential Smoothing

Please refer to problem in the in-class exercise

Exponential smoothing2

Exponential Smoothing

  • The emphasis given to the most recent demand levels can be adjusted by changing the smoothing parameter

  • Larger α values emphasize recent levels of demand and result in forecasts more responsive to changes in the underlying average

  • Smaller α values treat past demand more uniformly and result in more stable forecasts

  • Exponential smoothing is simple and requires minimal data

  • When the underlying average is showing some trend, different model is needed

Choosing a time series method

Choosing a Time-Series Method

  • Forecast performance is determined by forecast errors

  • Forecast errors detect when something is going wrong with the forecasting system

  • Forecast errors can be classified as either bias errors or random errors

  • Bias errors (or systematic errors) are the result of consistent mistakes

  • Random error results from unpredictable factors that cause the forecast to deviate from the actual demand

So what do we mean by systematic error

So, what do we mean by systematic error?

Measures of forecast error

Measures of Forecast Error

  • Forecast Error = Demand value – Forecast Value

  • Mean absolute deviation (MAD)

  • Mean signed deviation (MSD)

  • Tracking signal (TS)

  • Mean squared error (MSE)

  • Mean absolute percentage error (MAPE)

Et = Dt– Ft

Mean absolute deviation mad




Mean Absolute Deviation (MAD)

  • MAD is the average of the absolute values of the errors.

  • Stated in the same units as the forecast

  • Captures the magnitude of the forecasting error

  • Compute MAD for the example problem in Excel sheet (tab 2) and interpret the results

Mean sign deviation msd

 Et



Mean Sign Deviation (MSD)

  • MSD is the average of the errors

  • Stated in the same units as the forecast

  • Signs (+/-) of the error terms tend to cancel each other out

  • A large value (+/-) indicates systematic forecast error

  • Compute MSD for the example problem in Excel sheet (tab 2) and interpret the results

Tracking signal ts



TS =

Tracking Signal (TS)

  • Tracking Signal (TS) measures systematic error

  • TS is unitless and is between -1 and 1

  • Think of it as percentage of forecast error that is systematic

Tracking signal ts1

Tracking Signal (TS)

Interpreting tracking signal ts

Interpreting Tracking Signal (TS)

Interpreting tracking signal ts1

Interpreting Tracking Signal (TS)

  • Calculate TS for the example problem and interpret it

Mean squared error mse

 Et2



Mean Squared Error(MSE)

  • MSE is the average of the square errors

  • It is a measure of dispersion of forecast error

  • Smaller values indicate that forecast is typically close to actual demand

  • Compute MSE for the example problem in Excel sheet (tab 2) and interpret the results

Mean absolute percentage error mape

 (|Et|/Dt)(100)



Mean Absolute Percentage Error(MAPE)

  • MAPE takes the absolute error of each forecast, and divides it by the value of the demand, multiply that quantity with 100 to get the error as a percentage of the demand, and then averages these percentage errors.

  • Very useful for comparisons between time series for different SKUs

  • Compute MAPE for the example problem in Excel sheet (tab 2) and interpret the results

Criteria for selecting methods

Criteria for Selecting Methods

  • Criteria to use in making forecast method and parameter choices include

    • Minimizing bias

    • Minimizing MAPE, MAD, or MSE

    • Meeting managerial expectations of changes in the components of demand

    • Minimizing the forecast error last period

  • Statistical performance measures can be used

    • For projections of more stable demand patterns, use lower αvalues or larger n values

    • For projections of more dynamic demand patterns try higher αor smaller n values

Forecasting as a process

Adjust history file


Consensus meetings and collaboration


Prepare initial forecasts


Review by Operating Committee



and communicate


Revise forecasts


Forecasting as a Process

  • Forecasting is not a stand-alone activity, but part of a larger process

Remember forecasting is like fortune telling

Remember, forecasting is like fortune telling…

You’re right only by accident!



  • Krajewski, Ritzman, Malhotra. (2010). Operations Management: Processes and Supply Chains, Ninth Edition. Pearson Prentice Hall.

  • Dr. Gary Mitchell, Class Notes

  • Dr. Min Yu, Class Notes

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