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Forecasting for Operations Decisions

W S William

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Forecasting is the art and science of predictingfuture events.

Institute of Business Forecasting

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3-3

Elements of a Good Forecast

Timely

AccurateReliable

Written

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Key Issues in Forecasting

Choice of forecasting horizon (a week, a month etc.)

A forecasting method with desired accuracy.

The unit of forecasting ( gross sales, individual product

demand etc.)

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Forecast Horizon

Forecast horizon is the period for which forecast is prepared

Long-Range (years)

( e.g. Process selection, Capacity addition)

Medium-Range (months)

(e.g. Manpower planning, procurement of long lead time items)

Short-Range (weeks)

(e.g. Production schedules, overtimes etc.)

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Examples of Production Resource Forecasts

ForecastHorizon

Time Span Item Being Forecast Units ofMeasure

Long-Range Years

Product lines

Factory capacities

Planning for new products

Capital expenditures

Facility location or expansionR&D

Dollars, tons, etc.

Medium-

RangeMonths

Product groups

Department capacities

Sales planning

Production planning and budgeting

Dollars, tons, etc.

Short-Range Weeks

Specific product quantitiesMachine capacities

Planning

Purchasing

Scheduling

Workforce levels

Production levels

Job assignments

Physical units of

products

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Forecasting Methods

Broadly, forecasting methods fall under two categories:

Qualitative Methods : These are subjective in nature (ExecutiveOpinion, Market Research , Delphi Method)

Quantitative Methods: They use mathematical or simulationmethods base d on historical demand or relationshipsbetween variables.

Extrapolated or Time Series(Use past data to forecast future)

Explanatory or Causal Method (Establishes a relationshipbetween dependent and independent variables); y= f(x)

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Components of Demand

Horizontal Component

Trend Component

Seasonal Component

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Simple Moving Average

An averaging period (AP) is given or selected

The forecast for the next period is the

arithmetic average of the AP most recent

actual demands It is called a simple average because each

period used to compute the average is equally

weighted

. . . more

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It is called moving because as new demand

data becomes available, the oldest data is notused

By increasing the AP, the forecast is lessresponsive to fluctuations in demand (lowimpulse response)

By decreasing the AP, the forecast is moreresponsive to fluctuations in demand (highimpulse response)

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Week Demand

1 650

2 678

3 7204 785

5 859

6 920

7 850

8 7589 892

10 920

11 789

12 844

F = A + A + A +...+An

tt -1 t-2 t-3 t-n

Lets develop 3-week and6-week moving average

forecasts for demand.

Assume you only have 3weeks and 6 weeks of

actual demand data for the

respective forecasts

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Week Demand 3-Week 6-Week

1 650

2 678

3 720

4 785 682.67

5 859 727.67

6 920 788.00

7 850 854.67 768.67

8 758 876.33 802.009 892 842.67 815.33

10 920 833.33 844.00

11 789 856.67 866.50

12 844 867.00 854.83


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Weighted Moving Average

The weights must add to 1.0 and generally

decrease in value with the age of the data

The distribution of the weights determine

impulse response of the forecast

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Weighted Moving Average

F = w A + w A + w A +...+w At 1 t -1 2 t -2 3 t-3 n t - n

w = 1ii=1

n

Determine the 3-period

weighted moving average

forecast for period 4

Weights (adding up to 1.0):

t-1: .5

t-2: .3

t-3: .2

Week Demand

1 650

2 678

3 720

4

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Moving Average Method

Step1:Select the number of periods for which movingaverage will be computed, thus number N is called an order of

moving average

Step 2:Take the average demand for the most recent N

periods. This average demand then becomes the forecast for

the next period.

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Exponential Smoothing

Premise--The most recent observationsmight have the highest predictive value.

Therefore, we should give more weight to the

more recent time periods when forecasting.

Ft= Ft-1 + (At-1 - Ft-1)

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Simple Linear Regression

Relationship between one independent variable, X, and a

dependent variable, Y.

Assumed to be linear (a straight line)

Form: Y = a + bX

Y = dependent variable

X = independent variable

a = y-axis intercept

b = slope of regression line

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Simple Linear Regression Model

b is similar to the slope. However, since it

is calculated with the variability of the datain mind, its formulation is not as straight-

forward as our usual notion of slope

Yt= a + bx

0 1 2 3 4 5 x (weeks)

Y

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Calculating a and b

a = y - bx

b = xy - n(y)(x)

x -n(x2 2

)

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Regression Equation Example

Week Sales

1 150

2 1573 162

4 166

5 177

Develop a regression equation to predict sales

based on these five points.

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Week Week*Week Sales Week*Sales

1 1 150 150

2 4 157 314

3 9 162 486

4 16 166 6645 25 177 885

3 55 162.4 2499

Average Sum Average Sum

b =xy - n(y)(x)

x - n(x=

2499 - 5(162.4)(3)=

a = y - bx = 162.4 - (6.3)(3) =

2 2

) ( )55 5 9

63

10 6.3

143.5


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y = 143.5 + 6.3t

135

140

145

150

155

160

165

170

175

180

1 2 3 4 5Period

Sales

Sales

Forecast


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Forecast Accuracy

Accuracy is the typical criterion for judging the

performance of a forecasting approach

Accuracy is how well the forecasted values

match the actual values

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Monitoring Accuracy

Accuracy of a forecasting approach needs to be

monitored to assess the confidence you can have in

its forecasts and changes in the market may require

reevaluation of the approach

Accuracy can be measured in several ways

Mean absolute deviation (MAD)

Mean squared error (MSE)

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Mean Squared Error (MSE)

MSE = (Syx)2

Small value for Syxmeans data points tightlygrouped around the line and error range issmall. The smaller the standard error the

more accurate the forecast.

MSE = 1.25(MAD)

When the forecast errors are normally

distributed

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Solution

MAD =

A - F

n=

40

4= 10

t tt=1

n

Month Sales Forecast Abs Error

1 220 n/a

2 250 255 5

3 210 205 5

4 300 320 20

5 325 315 10

40

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Tracking Signal

Tracking signal = (Actual -forecast)MAD

Tracking signalRatio of cumulative error to MAD

BiasPersistent tendency for forecasts to be

Greater or less than actual values.

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Criteria for Selecting a Forecasting Method

Cost

Accuracy

Data available

Time span

Nature of products and services

Impulse response and noise dampening

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Reasons for Ineffective Forecasting

Not involving a broad cross section of people

Not recognizing that forecasting is integral to business

planning

Not recognizing that forecasts will always be wrong (think in

terms of interval rather than point forecasts)

Not forecasting the right things

(forecast independent demand only)

Not selecting an appropriate forecasting method

(use MAD to evaluate goodness of fit)

Not tracking the accuracy of the forecasting models

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Thank you

Documents

8721 Forecasting 2013