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Chapter 8 - Forecasting

Operations Management 6th Edition

R. Dan Reid & Nada R. Sanders

Learning Objectives

 Identify principles of forecasting.

 Explain the steps involved in the forecasting process.

 Identify types of forecasting methods and their characteristics.

 Describe time series models.

Learning Objectives - cont'd

 Describe causal modeling using linear regression.

 Compute forecast accuracy.

 Explain the factors that should be considered when selecting a forecasting model.

 Explain the nine-step process of CPFR.

Forecasting - Defined

 Predicting future events  One of the most important business functions as

decisions are based on a forecast of the future  Goal: Generate good forecasts on the average over

time and keep errors low  Forecasting is an ongoing process

Principles of Forecasting

Many types of forecasting models differ in complexity and amount of data & way they generate forecasts.

Common features include: 1. Forecasts are rarely perfect 2. Forecasts are more accurate for grouped data than

for individual items 3. Forecast are more accurate for shorter than longer

time periods

Steps in the Forecasting Process

 Decide what needs to be forecast  Level of detail, units of analysis & time horizon required

 Evaluate and analyze appropriate data  Identify needed data & whether it’s available

 Select and test the forecasting model  Cost, ease of use & accuracy

 Generate the forecast  Monitor forecast accuracy over time

Types of Forecasting Methods – cont’d

Classified into two groups:

Types of Forecasting Models

 Qualitative methods – judgmental methods  Forecasts generated subjectively by the forecaster

 Educated guesses

 Quantitative methods – based on mathematical modeling:  Forecasts generated through mathematical modeling

Qualitative Methods 9

Quantitative Methods

 Time Series Models:  Assumes information needed

to generate a forecast is contained in a time series of data

 Assumes the future will follow same patterns as the past

 Causal Models or Associative Models  Explores cause-and-effect

relationships

 Uses leading indicators to predict the future

 Housing starts and appliance sales

Time Series Models

 Forecaster looks for data patterns as

 Data = historic pattern + random variation

 Historic pattern to be forecasted:

 Level (long-term average) – data fluctuates around a constant mean

 Trend – data exhibits an increasing or decreasing pattern

 Seasonality – any pattern that regularly repeats itself and is of a constant

length

 Cycle – patterns created by economic fluctuations

 Random Variation cannot be predicted

Time Series Patterns 12

Time Series Models

 Naive:  The forecast is equal to the actual value observed during the last

period – good for level patterns

 Simple Mean:  The average of all available data - good for level patterns

 Simple Moving Average:  The average value over a set time period

(e.g.: the last four weeks)  Each new forecast drops the oldest data point & adds a new

observation  More responsive to a trend but still lags behind actual data - good for

level patterns; trend + level = bad forecast

tA 1t

n/AF t1t 

Time Series Models cont'd

 Weighted Moving Average:  Method in which “n” of the most recent observations are

averaged and past observations may be weighted differently

 All weights must add to 100% or 1.00

e.g. Ct .5, Ct-1 .3, Ct-2 .2 (weights add to 1.0)

 Allows emphasizing one period over others; above indicates more weight on recent data (Ct=.5)

 Differs from the simple moving average that weighs all periods equally - more responsive to trends

 tt1t ACF

Time Series Models cont'd

 Exponential Smoothing:  Most frequently used time series method because of ease of

use and minimal amount of data needed

 Need just three pieces of data to start:  Last period’s forecast (Ft)

 Last periods actual value (At)

 Select value of smoothing coefficient, ,between 0 and 1.0

 If no last period forecast is available, average the last few periods or use naive method

 Higher values (e.g. .7 or .8) place a lot of weight on current periods actual demand and influenced by random variation

  tt1t

Fα1αAF  



Time Series Problem

 Determine forecast for periods 7 & 8

 2-period moving average

 4-period moving average

 2-period weighted moving average with t-

1 weighted 0.6 and t-2 weighted 0.4

 Exponential smoothing with alpha=0.2

and the period 6 forecast being 375

Period Actual

1 300

2 315

3 290

4 345

5 320

6 360

7 375

Time Series Problem Solution

Period Actual 2-Period 4-Period 2-Per.Wgted.

Exponential

Smoothing

1 300

2 315

3 290

4 345

5 320

6 360

7 375 340.0 328.8 344.0 372.0

8 367.5 350.0 369.0 372.6

Forecasting Trend

 Basic forecasting models for trends compensate for the lagging that would otherwise occur

 One model, trend-adjusted exponential smoothing uses a three step process  Step 1 - Smoothing the level of the series

 Step 2 – Smoothing the trend

 Step 3 - Forecast including the trend

)Tα)(S(1αAS 1t1ttt 



1t1ttt β)T(1)Sβ(ST

 

tt1t TSFIT 



Forecasting trend problem: a company uses exponential smoothing with trend to forecast usage of its lawn care products. At the end of July the company wishes to forecast sales for August. July demand was 62. The trend through June has been

15 additional gallons of product sold per month. Average sales have been 57 gallons per month. The company uses alpha+0.2 and beta +0.10. Forecast for August.

 Smooth the level of the series:

 Smooth the trend:

 Forecast including trend:

      7015570.8620.2)Tα)(S(1αAS 1t1ttJuly

 

      14.8150.957700.1β)T(1)Sβ(ST 1t1ttJuly

 

gallons 84.814.870TSFIT ttAugust



Linear Trend Line

 A time series technique that computes a forecast with trend by drawing a straight line through a set of data using this formula:

Y = a + bx where

Y = forecast for period X X = the number of time periods from X = 0 A = value of y at X = 0 (Y intercept) B = slope of the line

Forecasting Seasonality

 Remember it is a regularly repeating pattern

 Examples:  University enrollment varies between quarters or semesters; higher in the

fall than in the summer

 Seasonal Index:  Percentage amount by which data for each season are above

or below the mean.

Forecasting Seasonality Steps

1. Calculate the average demand per season  E.g.: average quarterly demand

2. Calculate a seasonal index for each season of each year:

 Divide the actual demand of each season by the average demand per season for that year

3. Average the indexes by season  E.g.: take the average of all Spring indexes, then of all

Summer indexes, ...

Forecasting Seasonality Steps - cont'd

4. Forecast demand for the next year & divide by the number of seasons

 Use regular forecasting method & divide by four for average quarterly demand

5. Multiply next year’s average seasonal demand by each average seasonal index

 Result is a forecast of demand for each season of next year

Seasonality problem: a university must develop forecasts for the next year’s quarterly enrollments. It has collected quarterly enrollments for the past two years. It has also forecast total enrollment for next year to

be 90,000 students. What is the forecast for each quarter of next year?

Quarter Year 1 Seasonal Index

Year 2

Seasonal Index

Avg. Index

Year3

Fall 24000 1.2 26000 1.238 1.22 27450

Winter 23000 22000

Spring 19000 19000

Summer 14000 17000

Total 80000 84000 90000

Average 20000 21000 22500

Causal Models

 Often, leading indicators can help to predict changes in future demand e.g. housing starts

 Causal models establish a cause-and-effect relationship between independent and dependent variables

 A common tool of causal modeling is linear regression:

 Additional related variables may require multiple regression modeling

bxaY 

Linear Regression

      

  

 

XXX

YXXY b

XbYa 

 Identify dependent (y) and independent (x) variables

 Solve for the slope of the line

 Solve for the y intercept

 Develop your equation for the trend line

Y=a + bX



 

 

2 2

XnX

YXnXY b

Linear Regression Problem: A maker of golf shirts has been tracking the relationship between sales and advertising dollars. Use linear regression to find out what sales might be if

the company invested $53,000 in advertising next year.

    

 

  153.85531.1592.9Y 1.15X92.9bXaY

92.9a

47.251.15147.25XbYa

1.15 47.2549253

147.2547.25428202 b









 

 

Sales $ (Y)

Adv.$ (X)

XY X^2 Y^2

1 130 32 4160 2304 16,900

2 151 52 7852 2704 22,801

3 150 50 7500 2500 22,500

4 158 55 8690 3025 24964

5 153.85 53

Tot 589 189 28202 9253 87165

Avg 147.25 47.2 5



 

 

2 2

XnX

YXnXY b

Correlation Coefficient- How Good is the Fit?

 Correlation coefficient (r) measures the direction and strength of the linear relationship between two variables. The closer the r value is to 1.0 the better the regression line fits the data points.

 Coefficient of determination ( ) measures the amount of variation in the dependent variable about its mean that is explained by the regression line. Values of ( ) close to 1.0 are desirable.

    

           

   

  .964.982r

.992 58987,1654*(189)-4(9253)

58918928,2024 r

YYn*XXn

YXXYn r

2 2



 

 



 



2 r

Multiple Regression

 An extension of linear regression but:  Multiple regression develops a relationship between a

dependent variable and multiple independent variables. The general formula is:

Measuring Forecast Accuracy

 Forecasts are never perfect  Need to measure over time  Need to know how much we should rely on our

chosen forecasting method  Measuring forecast error:

 Note that over-forecasts = negative errors and under- forecasts = positive errors

ttt FAE 

Measuring Forecasting Accuracy

 Mean Absolute Deviation (MAD)  measures the total error in a forecast

without regard to sign

 Cumulative Forecast Error (CFE)  Measures any bias in the forecast

 Mean Square Error (MSE)  Penalizes larger errors

 Tracking Signal  Measures if your model is working;

quality

 

forecast - actual MSE

 

MAD

CFE TS 

forecastactual MAD

  

   forecastactualCFE

Accuracy & Tracking Signal Problem: A company is comparing the accuracy of two forecasting methods. Forecasts using both methods are shown below along with the actual values for January through May. The company also uses a tracking

signal with ±4 limits to decide when a forecast should be reviewed. Which forecasting method is best?

Month Actual sales

Method A Method B

F’cast Error Cum.

Error

Tracking Signal

F’cast Error Cum. Error

Tracking Signal

Jan. 30 28 2 2 2 27 2 2 1

Feb. 26 25 1 3 3 25 1 3 1.5

March 32 32 0 3 3 29 3 6 3

April 29 30 -1 2 2 27 2 8 4

May 31 30 1 3 3 29 2 10 5

MAD 1 2

MSE 1.4 4.4

Selecting the Right Forecasting Model

1. The amount & type of available data  Some methods require more data than others

2. Degree of accuracy required  Increasing accuracy means more data

3. Length of forecast horizon  Different models for 3 month vs. 10 years

4. Presence of data patterns  Lagging will occur when a forecasting model meant for a

level pattern is applied with a trend

Forecasting Software

 Spreadsheets  Microsoft Excel, Quattro Pro, Lotus 1-2-3

 Limited statistical analysis of forecast data

 Statistical packages  SPSS, SAS, NCSS, Minitab

 Forecasting plus statistical and graphics

 Specialty forecasting packages  Forecast Master, Forecast Pro, Autobox, SCA

 Extensive range of forecasting capability

Guidelines for Selecting Software

 Does the package have the features you want?  What platform is the package available for?  How easy is the package to learn and use?  Is it possible to implement new methods?  Do you require interactive or repetitive forecasting?  Do you have any large data sets?  Is there local support and training available?  Does the package give the right answers?  What is the cost of the package?  Is it compatible with our existing software

Collaborative Planning Forecasting & Replenishment(CPFR)

 Establish collaborative relationships between buyers and sellers  Create a joint business plan  Create a sales forecast  Identify exceptions for sales forecast  Resolve/collaborate on exception items  Create order forecast  Identify exceptions for order forecast  Resolve/collaborate on exception items  Generate order

CPFR is an iterative process.

Forecasting Within OM: How It All Fits Together

 Forecasts impact not only other business functions but all other operations decisions. Operations managers make many forecasts, such as the expected demand for a company’s products.

 These forecasts are then used to determine: Product designs that are expected to sell (Ch 2) The quantity of product to produce (Chs 5 and 6) The amount of needed supplies and materials (Ch 12) Future space requirements (Ch 10) Capacity and location needs (Ch 9) The amount of labor needed (Ch 11)

Forecasting within OM - cont'd

 Forecasts drive strategic operations decisions, such as: Choice of competitive priorities, changes in processes, and large technology purchases (Ch 3) Forecast decisions serve as the basis for tactical planning; developing worker schedules (Ch 11)

Virtually all operations management decisions are based on a forecast of the future.

Forecasting Across the Organization

 Forecasting is critical to management of all organizational functional areas  Marketing relies on forecasting to predict demand and future

sales  Finance forecasts stock prices, financial performance, capital

investment needs..  Information systems provides ability to share databases and

information  Human resources forecasts future hiring requirements

Chapter 8 Highlights

 Three basic principles of forecasting are: forecasts are rarely perfect, are more accurate for groups than individual items, and are more accurate in the shorter term than longer time horizons.

 The forecasting process involves five steps: decide what to forecast, evaluate and analyze appropriate data, select and test model, generate forecast, and monitor accuracy.

 Forecasting methods can be classified into two groups: Qualitative methods are based on subjective opinion of forecaster and quantitative methods are based on mathematical modeling.

Chapter 8 Highlights - cont'd

 Time series models are based on the assumption that all information needed is contained in the time series of data. Causal models assume that the variable being forecast is related to other variables in the environment.

 There are four basic patterns of data: level or horizontal, trend, seasonality, and cycles. In addition, data usually contain random variation. Some forecast models used to forecast the level of a time series are: naïve, simple mean, simple moving average, weighted moving average, and exponential smoothing. Separate models are used to forecast trends and seasonality.

Chapter 8 Highlights - cont'd

 A simple causal model is linear regression in which a straight-line relationship is modeled between the variable we are forecasting and another variable in the environment. The correlation measures the strength of the linear relationship between these two variables.

 Three useful measures of forecast error are mean absolute deviation (MAD), mean square error (MSE) and tracking signal.

 There are four factors when selecting a model: amount and type of data available, degree of accuracy required, length of forecast horizon, and patterns present in the data.