Rachmat A. AnggaraPMBS, BOPR 5301, Session 4

Operation Management

Forecasting

Why we have to forecast??

??

Forecast Reduces CostUnder forecast the condition when capacity is

below actual demandOver forecast the condition where capacity is

above actual demand

Increase Competitive advantageEconomic ForecastTechnological forecastsDemand forecasts

FORECASTING

Process of predicting a future eventForecasting Time Horizons

Short-range ForecastMedium-range ForecastLong-range Forecast

Forecasting Approach

Intuitive Decision Making

movie

Forecasting Approach

Qualitative MethodsJury of executive

opinionSales force composite

Quantitative Method

Consumer Market Survey

Delphi method

1. Naive approach

2. Moving averages

3. Exponential smoothing

4. Trend projection

5. Linear regression

Time-Series Models

Associative Model

Qualitative Method

Used when situation is vague and little data exist New products New technology

Involves intuition, experience e.g., forecasting sales on Internet

Quantitative Method

Used when situation is vague and little data exist New products New technology

Involves intuition, experience e.g., forecasting sales on Internet

Quantitative Method

1. TIME SERIES

Set of evenly spaced numerical data Obtained by observing response

variable at regular time periods Forecast based only on past values

Assumes that factors influencing past and present will continue influence in future

Quantitative Method

TIME SERIES COMPONENT

Trend

Seasonal

Cyclical

Random

Component of DemandD

eman

d fo

r pr

oduc

t or

ser

vice

| | | |1 2 3 4

Year

Average demand over four years

Seasonal peaks

Trend component

Actual demand

Random variation

Steps of ForecastingDetermine the use of

the forecast

Select the items to be forecasted

Determine the time horizon of the

forecast

Select the forecasting model(s)

Gather the data

Make the forecast

Validate and implement results

1. Moving Average

Moving average =∑ demand in previous n periods

n

January 10February 12March 13April 16May 19June 23July 26

Actual 3-MonthMonth Shed Sales Moving Average

(12 + 13 + 16)/3 = 13 2/3

(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1/3

101213

(10 + 12 + 13)/3 = 11 2/3

TIME SERIES METHOD

2. Weighted Moving Average

January 10February 12March 13April 16May 19June 23July 26

Actual 3-Month WeightedMonth Shed Sales Moving Average

[(3 x 16) + (2 x 13) + (12)]/6 = 141/3

[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 201/2

101213

[(3 x 13) + (2 x 12) + (10)]/6 = 121/6

Weights Applied Period3 Last month2 Two months ago1 Three months ago

TIME SERIES METHOD

Graph of Moving Averages

30 –

25 –

20 –

15 –

10 –

5 –

Sa

les

de

man

d

| | | | | | | | | | | |

J F M A M J J A S O N D

Actual sales

Moving average

Weighted moving average

TIME SERIES METHOD

3. Exponential SmoothingFt = Ft – 1 + a(At – 1 - Ft – 1)

where Ft = new forecast At – 1 = previous Actual Demand

Ft – 1 = previous forecasta = smoothing (or weighting) constant

(0 a 1)

Example – Ford Mustangs :Predicted demand = 142Actual demand = 153Smoothing constant a = .20Next Period Forecast = …

TIME SERIES METHOD

Measuring Forecast ErrorRounded Absolute (Error)2 Absolute

Actual Forecast Deviation PercentageTonnage with for Error

Quarter Unloaded a = .10 a = .10

1 180 175 5 52=25 2.78%2 168 176 8 64 4.76%3 159 175 16 256 10.06%4 175 173 2 4 1.14%5 190 173 17 289 8.95%6 205 175 30 900 14.63%7 180 178 2 4 1.11%8 182 178 4 16 2.20%

84 1,558 45.63%MAD =

∑ |actual - forecast|

n

MSE =∑ (forecast errors)2

nMAPE =

100 ∑ |actuali - forecasti|/actuali

n

n

i = 1

TIME SERIES METHOD

Calculate MAPE, α = 0.50Rounded Absolute Rounded Absolute

Actual Forecast Deviation Forecast DeviationTonnage with for with for

Quarter Unloaded a = .10 a = .10 a = .50 a = .50

1 180 175 5 175 52 168 176 8 178 103 159 175 16 173 144 175 173 2 166 95 190 173 17 170 206 205 175 30 180 257 180 178 2 193 138 182 178 4 186 4

84 100

TIME SERIES METHOD

4. Exponential Smoothing with Trend Adjustment

When a trend is present, exponential smoothing must be modified

Forecast including (FITt) = trend

exponentially exponentiallysmoothed (Ft) + (Tt) smoothedforecast trend

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

Tt = b(Ft - Ft - 1) + (1 - b)Tt - 1

Step 1: Compute Ft

Step 2: Compute Tt

Step 3: Calculate the forecast FITt = Ft + Tt

TIME SERIES METHOD

Gambar perbandingan (xls)

ExponentialActual Smoothing

Tonnage Ft Tt with TrendQuarter Unloaded a = 0.10 β = .20 Adjustment

1 180 175 2 1772 168 177 2 179.43 159 178 2 180.14 175 178 1 179.45 190 179 1 180.36 205 181 2 182.77 180 185 2 186.98 182 186 2 188.1

TIME SERIES METHOD

Graphics

TIME SERIES METHOD

Fitting a trend line to historical data points to project into the medium-to-long-range

Linear trends can be found using the least squares technique

y = a + bx^

where y = computed value of the variable to be predicted (dependent variable)a = y-axis interceptb = slope of the regression linex = the independent variable

^

5. Trend Projections

TIME SERIES METHOD

Least Squares Method

Time period

Va

lue

s o

f D

ep

end

en

t V

ari

able

Figure 4.4

Deviation1

Deviation5

Deviation7

Deviation2

Deviation6

Deviation4

Deviation3

Actual observation (y value)

Trend line, y = a + bx^

TIME SERIES METHOD

Least Squares MethodEquations to calculate the regression variables

b =Sxy - nxy

Sx2 - nx2

y = a + bx^

a = y - bx

TIME SERIES METHOD

Least Squares Example

b = = = 10.54∑xy - nxy

∑x2 - nx2

3,063 - (7)(4)(98.86)

140 - (7)(42)a = y - bx = 98.86 - 10.54(4) = 56.70

Time Electrical Power Year Period (x) Demand x2 xy

1999 1 74 1 742000 2 79 4 1582001 3 80 9 2402002 4 90 16 3602003 5 105 25 5252004 6 142 36 8522005 7 122 49 854

∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063x = 4 y = 98.86

TIME SERIES METHOD

Least Squares Example

| | | | | | | | |1999 2000 2001 2002 2003 2004 2005 2006 2007

160 –150 –140 –130 –120 –110 –100 –90 –80 –70 –60 –50 –

Year

Po

wer

dem

and

Trend line,y = 56.70 + 10.54x^

TIME SERIES METHOD

Associative Forecasting• Forecasting an outcome based on

predictor variables.• Methods:

1. Regression Analysis

2. Correlation Coefficients

3. Standard Error of the Estimate.

4. Multiple Regression Analysis.

ASSOCIATIVE METHOD

Regression Analysis

Sales Local Payroll($000,000), y ($000,000,000), x

2.0 13.0 32.5 42.0 22.0 13.5 7

y = a + bx^

where y = computed value of the variable to be predicted (dependent variable)a = y-axis interceptb = slope of the regression linex = the independent variable though to predict the value of the dependent variable

^

Example:

ASSOCIATIVE METHOD

4.0 –

3.0 –

2.0 –

1.0 –

| | | | | | |0 1 2 3 4 5 6 7

Sal

es

Area payroll

y = 1.75 + .25x^

Sales = 1.75 + .25(payroll)

Sales = 1.75 + .25(6)Sales = $325,000

3.25

If payroll next year is estimated to be $600

million, then:

ASSOCIATIVE METHOD

Correlation Coefficient

r = nSxy - SxSy

[nSx2 - (Sx)2][nSy2 - (Sy)2]

How strong is the linear relationship between the variables?

Correlation does not necessarily imply causality!

Coefficient of correlation, r, measures degree of association Values range from -1 to +1

ASSOCIATIVE METHOD

Multiple RegressionIf more than one independent variable is to be

used in the model, linear regression can be extended to multiple regression to accommodate

several independent variables

y = a + b1x1 + b2x2 …^

Computationally, this is quite complex and generally done on the computer

ASSOCIATIVE METHOD

Questions?