OM3-1 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights

OM3-1

McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

Chapter 3

Forecasting

OM3-2


Forecasting

FORECAST:

• A statement about the future

• Used to help managers– Plan the system– Plan the use of the system

OM3-3


Forecasting

Accounting Cost/profit estimates

Finance Cash flow and funding

Human Resources Hiring/recruiting/training

Marketing Pricing, promotion, strategy

MIS IT/IS systems, services

Operations Schedules, MRP, workloads

Product/service design New products and services

Uses of Forecasts

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Forecasting

• Assumes causal systempast ==> future

• Forecasts rarely perfect because of randomness

• Forecasts more accurate forgroups vs. individuals

• Forecast accuracy decreases as time horizon increases

I see that you willget an A this semester.

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Forecasting

Elements of a Good Forecast

Timely

AccurateReliable

Mea

ningfu

l

Written

Easy

to u

se

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Forecasting

Steps in the Forecasting Process

Step 1 Determine purpose of forecast

Step 2 Establish a time horizon

Step 3 Select a forecasting technique

Step 4 Gather and analyze data

Step 5 Prepare the forecast

Step 6 Monitor the forecast

“The forecast”

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Forecasting

Forecast Accuracy

• Error - difference between actual value and predicted value

• Average Error (BIAS) – Any Problems!• Mean absolute deviation (MAD)

– Average absolute error

• Mean Absolute Percentage Error (MAPE)• Mean squared error (MSE)

– Average of squared error

• Tracking signal– Ratio of cumulative error and MAD

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Forecasting

BIAS & MSE

BIAS = Actual forecast)n

(

MSE = Actual forecast)

-1

2n

(

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Forecasting

MAD & MAPE

MAD = Actual forecastn

MAPE = |Actual - Forecast|)/Actualn

(

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Forecasting

Types of Forecasts

• Judgmental - uses subjective inputs

• Time series - uses historical data assuming the future will be like the past

• Associative models - uses explanatory variables to predict the future

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Forecasting

Judgmental Forecasts

• Executive opinions

• Sales force composite

• Consumer surveys

• Focus Groups

• Outside opinion

• Opinions of managers and staff– Delphi technique

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Forecasting

Time Series Forecasts

• Trend - long-term movement in data

• Seasonality - short-term regular variations in data

• Irregular variations - caused by unusual circumstances

• Random variations - caused by chance

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Forecasting

Forecast Variations

Trend

Irregularvariation

Cycles

Seasonal variations

908988

Figure 3-1

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Forecasting

• Simple to use

• Virtually no cost

• Data analysis is nonexistent

• Easily understandable

• Cannot provide high accuracy

• Can be a standard for accuracy

Naïve Forecasts

OM3-15


Forecasting

Techniques for Averaging

• Naïve forecasts

• Arithmetic Mean

• Moving Averages

• Weighted Moving Averages

• Exponential Smoothing

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Forecasting

Definitions

• At = Actual Demand in period t

• Ft = Forecast Demand in period t

• n = Number of past Observations

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Forecasting

• Stable time series data– F(t) = A(t-1)

• Seasonal variations– F(t) = A(t-n)

• Data with trends– F(t) = A(t-1) + (A(t-1) – A(t-2))

Uses for Naïve Forecasts

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Forecasting

Naive Forecasts

Uh, give me a minute.... We sold 250 wheels lastweek.... Now, next week we should sell....

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Forecasting

Arithmetic Average

Ft+1 = n

Aii = 1n

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Forecasting

Techniques for Averaging

• Moving average

• Weighted moving average

• Exponential smoothing

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Forecasting

Simple Moving Average

600

700

800

900

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

Actual

MA3

MA5

Ft+1 = k

Aii = 1k

Figure 3-4

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Forecasting

Weighted Moving Average

• Ft+1 = At*wt + At-1*wt-1 + At-2*wt-2 + ….+ At-

k*wt-k

where: wi = 1

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Forecasting

Exponential Smoothing

Premise--The most recent observations might have the highest predictive value.

– Therefore, we should give more weight to the more recent time periods when forecasting.

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

Ft+1 = At + (1-Ft

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Forecasting

Example 1

• A laundry has experienced the following past demand pattern for garment cleaning.

Period Annual Demand (kgs)

1 15

2 20

3 10

4 20

5 10

6 15

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Forecasting

Example 1 (cont.)

Forecast demand for period seven using:

a) Last period demand

b) The arithmetic average

c) Three period moving average

d) Weighted moving average with the weights as .2, .3, and .5

e) Exponential smoothing with = 0.1

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Forecasting

Period Actual Alpha = 0.1 Error Alpha = 0.4 Error1 422 40 42 -2.00 42 -23 43 41.8 1.20 41.2 1.84 40 41.92 -1.92 41.92 -1.925 41 41.73 -0.73 41.15 -0.156 39 41.66 -2.66 41.09 -2.097 46 41.39 4.61 40.25 5.758 44 41.85 2.15 42.55 1.459 45 42.07 2.93 43.13 1.87

10 38 42.36 -4.36 43.88 -5.8811 40 41.92 -1.92 41.53 -1.5312 41.73 40.92

Example of Picking a Smoothing Constant

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Forecasting

Picking a Smoothing Constant

35

40

45

50

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

Period

Dem

and .1

.4

Actual

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Forecasting

Common Nonlinear Trends

Parabolic

Exponential

Growth

Figure 3-5

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Forecasting

Linear Trend Equation

• b is similar to the slope. However, since it is calculated with the variability of the data in mind, its formulation is not as straight-forward as our usual notion of slope.

Yt = a + bt

0 1 2 3 4 5 t

Y

OM3-30


Forecasting

Calculating a and b

b = n (ty) - t y

n t2 - ( t)2

a = y - b t

n

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Forecasting

Linear Trend Equation Example

t yW e e k t 2 S a l e s t y

1 1 1 5 0 1 5 02 4 1 5 7 3 1 43 9 1 6 2 4 8 64 1 6 1 6 6 6 6 45 2 5 1 7 7 8 8 5

t = 1 5 t 2 = 5 5 y = 8 1 2 t y = 2 4 9 9( t ) 2 = 2 2 5

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Forecasting

Linear Trend Calculation

y = 143.5 + 6.3t

a = 812 - 6.3(15)

5 =

b = 5 (2499) - 15(812)

5(55) - 225 =

12495-12180

275 -225 = 6.3

143.5

OM3-33


Forecasting

Forecasting: Trend Adjustment

Example 22 (a). Using the data below, develop a linear regression line to capture the trend component and predict for quarter numbers 15, 16 and 17. 2 (b) Then, predict for the same periods using both the trend and seasonal components.

Quarter Number

t

Demand Y

Quarter Number

t

Demand Y

1 3.5 8 16 2 8 9 15.5 3 5.5 10 20 4 10 11 17.5 5 9.5 12 22 6 14 13 21.5 7 11.5 14 26

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Forecasting

Solution Example 2 (a) - Trend Equation

• Using Excel, the following can be obtained as the best fit line for Example 2 (a).

Y = 2.725 + 1.546t

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Forecasting

Forecasting: Seasonal Adjustments

• Seasonal Variations are regularly repeating upward or downward movements in series values that can be tied to recurring events.

• Examples include winter and summer clothing, ski equipment, rush hour traffic, restaurants, and customer service assistance.

•Additive vs. Multiplicative Models

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Forecasting


•Use multiplicative method known as Ratio-to-Trend Method

Actual Observation

Trend Value

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Forecasting


• Use the linear regression model to capture the trend component and forecast each past period.• Divide the actual observation by the trend value to obtain a ratio.• Average ratios of similar periods to obtain seasonal factors.• Multiply the trend forecasted value by the appropriate seasonal factors to obtain seasonally adjusted forecasts.• See example 2 (b)

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Forecasting

Associative Forecasting

• Predictor variables - used to predict values of variable interest

• Regression - technique for fitting a line to a set of points

• Least squares line - minimizes sum of squared deviations around the line

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Forecasting


• Again, the least squares line equation is used:

y = a + b(x)

where,

y = Predicted (dependent) variable

x = Predictor (independent) variable

b = Slope of the line

a = Value of y, when x=0 (or the y intercept)

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Forecasting


Then,

22 xxn

yxxynb

)()(

))(()(

and

n

xbya

)(

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Forecasting


• Coefficient of Correlation (r): The coefficient of correlation r is a relative measure of such a relationship between two variables.

• Coefficient of Determination (r2)

• It is a statistic that indicates how well a regression line explains or fits the observed data.

• -1 < r < +1

• r > 0 implies positive correlation

• r < 0 implies negative correlation

OM3-42


Forecasting


• -1 < r < +1

• r > 0 implies positive correlation

• r < 0 implies negative correlation

• R can be calculated by using the following equation:

2222 yynxxn

yxxynr

)()(.)()(

))(()(

OM3-43


Forecasting


• Control Limits on the Forecast Value

Upper Limit = Forecast Value + z (Syx)

Lower Limit = Forecast Value – z (Syx)

where, z is the standard normal deviate and

2n

xybyayS

2

yx

)()(

OM3-44


Forecasting

Linear Model Seems Reasonable

0

10

20

30

40

50

0 5 10 15 20 25

X Y7 152 106 134 15

14 2515 2716 2412 2014 2720 4415 347 17

Computedrelationship

OM3-45


Forecasting

Tracking Signal

• Tracking Signal is a measurement that indicates whether the forecast average is keeping pace with any genuine upward or downward changes in demand

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Forecasting

Tracking Signal

Tracking signal = (Actual-forecast)

MAD

Tracking signal = (Actual-forecast)Actual-forecast

n

OM3-47


Forecasting

Tracking Signal

• ExampleWeek Forecast Actual Deviation

(Actual – Forecast)

Running Sum of (Actual-

Forecast)

Absolute Deviation

Sum of Absolute Deviation

MAD TS

1 100 95 -5 -5 5 5 5 -12 102 105 3 -2 3 8 4 -0.53 98 110 12 10 12 20 6.66666667 1.54 96 94 -2 8 2 22 5.5 1.454545455 101 106 5 13 5 27 5.4 2.407407416 100 107 7 20 7 34 5.66666667 3.52941176

Documents

OM3-1 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights