Operations Management

3-1

Forecasting

Operations Management

William J. Stevenson

8th edition

3-2

Forecasting

CHAPTER

3

Forecasting

McGraw-Hill/Irwin

3-3

Operations Management, Eighth Edition, by William J. Stevenson Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecasting

FORECAST: •

•

A statement about the future value of a variable of interest such as demand. Forecasts affect decisions and activities throughout an organization • Accounting, finance • Human resources • Marketing • MIS • Operations • Product / service design

3-4

Forecasting

Uses of Forecasts

3-5

3-6

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

Forecasting

•

Assumes causal system past ==> future

•

Forecasts rarely perfect because of randomness

•

Forecasts more accurate for groups vs. individuals

•

Forecast accuracy decreases as time horizon increases

I see that you will get an A this semester.

Forecasting

Elements of a Good Forecast

Timely

Reliable

M

l fu ng i n ea

Accurate

Written

sy Ea

to

e us

3-7

Forecasting

Steps in the Forecasting Process

“The forecast”

Step 6 Monitor the forecast Step 5 Prepare the forecast Step 4 Gather and analyze data Step 3 Select a forecasting technique Step 2 Establish a time horizon Step 1 Determine purpose of forecast

3-8

Forecasting

Types of Forecasts

3-9

•

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

Forecasting

Judgmental Forecasts •

Executive opinions

•

Sales force opinions

•

Consumer surveys

•

Outside opinion

• Delphi

method

•

Opinions of managers and staff

•

Achieves a consensus forecast

3-10 Forecasting

Time Series Forecasts Trend - long-term movement in data • Seasonality - short-term regular variations in data • Cycle – wavelike variations of more than one year’s duration • Irregular variations - caused by unusual circumstances • Random variations - caused by chance •

3-11 Forecasting

Forecast Variations Figure 3.1 Irregular variation

Trend

Cycles 90 89 88 Seasonal variations

3-12 Forecasting

Naive Forecasts

Uh, give me a minute.... We sold 250 wheels last week.... Now, next week we should sell.... The forecast for any period equals the previous period’s actual value.

3-13 Forecasting

Naïve Forecasts Simple to use Virtually no cost • Quick and easy to prepare • Data analysis is nonexistent • Easily understandable • Cannot provide high accuracy • Can be a standard for accuracy • •

3-14 Forecasting

Uses for Naïve Forecasts •

Stable time series data •

F(t) = A(t-1)

•

Seasonal variations

•

Data with trends

•

•

F(t) = A(t-n) F(t) = A(t-1) + (A(t-1) – A(t-2))

3-15 Forecasting

Techniques for Averaging •

Moving average

•

Weighted moving average

•

Exponential smoothing

3-16 Forecasting

Moving Averages •

Moving average – A technique that averages a number of recent actual values, updated as new values become available. n

Ai ∑ i=1

MAn = •

n

Weighted moving average – More recent values in a series are given more weight in computing the forecast.

3-17 Forecasting

Simple Moving Average Actual

47 45

MA5

43 41 39 37 35

MA3

1

2

3

4

5

6

7

8

9

10 11 12

n

MAn =

Ai ∑ i=1 n

3-18 Forecasting

Exponential Smoothing

Ft = Ft-1 + α(At-1 - Ft-1) • 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.

3-19 Forecasting

Exponential Smoothing

Ft = Ft-1 + α(At-1 - Ft-1) Weighted averaging method based on previous forecast plus a percentage of the forecast error • A-F is the error term, α is the % feedback •

3-20 Forecasting

Example 3 - Exponential Smoothing Period

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

Alpha = 0.1 Error 42 40 43 40 41 39 46 44 45 38 40

42 41.8 41.92 41.73 41.66 41.39 41.85 42.07 42.36 41.92 41.73

Alpha = 0.4 Error -2.00 1.20 -1.92 -0.73 -2.66 4.61 2.15 2.93 -4.36 -1.92

42 41.2 41.92 41.15 41.09 40.25 42.55 43.13 43.88 41.53 40.92

-2 1.8 -1.92 -0.15 -2.09 5.75 1.45 1.87 -5.88 -1.53

3-21 Forecasting

Picking a Smoothing Constant Actual

50 Dem and

α = .4 α = .1

45 40 35 1

2

3

4

5

6

7

Period

8

9 10 11 12

3-22 Forecasting

Common Nonlinear Trends Figure 3.5

Parabolic

Exponential

Growth

3-23 Forecasting

Linear Trend Equation Ft

Ft = a + bt • • • •

0 1 2 Ft = Forecast for period t t = Specified number of time periods a = Value of Ft at t = 0 b = Slope of the line

3 4 5

3-24 Forecasting

Calculating a and b

b =

n ∑ (ty) - ∑ t ∑ y n∑ t 2 - ( ∑ t) 2

a =

∑ y - b∑ t n

t

3-25 Forecasting

Linear Trend Equation Example t Week 1 2 3 4 5

2

t 1 4 9 16 25 2

Σ t = 15 Σ t = 55 2 (Σ t) = 225

y Sales 150 157 162 166 177

ty 150 314 486 664 885

Σ y = 812 Σ ty = 2499

3-26 Forecasting

Linear Trend Calculation b =

5 (2499) - 15(812) 12495-12180 = = 6.3 5(55) - 225 275 -225

a =

812 - 6.3(15) = 143.5 5

y = 143.5 + 6.3t

3-27 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

3-28 Forecasting

Linear Model Seems Reasonable X 7 2 6 4 14 15 16 12 14 20 15 7

Y 15 10 13 15 25 27 24 20 27 44 34 17

Computed relationship 50 40 30 20 10 0 0

5

10

15

20

25

A straight line is fitted to a set of sample points.

3-29 Forecasting

Forecast Accuracy •

Error - difference between actual value and predicted value

•

Mean Absolute Deviation (MAD) •

•

Mean Squared Error (MSE) •

•

Average absolute error

Average of squared error

Mean Absolute Percent Error (MAPE) •

Average absolute percent error

3-30 Forecasting

MAD, MSE, and MAPE

MAD

=

∑ Actual

− forecast n

MSE

=

∑ ( Actual

− forecast)

2

n -1

MAPE =

∑( Actual

− forecast / Actual*100) n

3-31 Forecasting

Example 10 Period 1 2 3 4 5 6 7 8

Actual 217 213 216 210 213 219 216 212

Forecast 215 216 215 214 211 214 217 216

(A-F) 2 -3 1 -4 2 5 -1 -4 -2

|A-F| 2 3 1 4 2 5 1 4 22

(A-F)^2 4 9 1 16 4 25 1 16 76

(|A-F|/Actual)*100 0.92 1.41 0.46 1.90 0.94 2.28 0.46 1.89 10.26

2.75 10.86 1.28

MAD= MSE= MAPE=

3-32 Forecasting

Controlling the Forecast •

Control chart • •

•

A visual tool for monitoring forecast errors Used to detect non-randomness in errors

Forecasting errors are in control if All errors are within the control limits • No patterns, such as trends or cycles, are present •

3-33 Forecasting

Sources of Forecast errors Model may be inadequate Irregular variations • Incorrect use of forecasting technique • •

3-34 Forecasting

Tracking Signal •Tracking signal –Ratio of cumulative error to MAD

Tracking signal =

∑(Actual-forecast) MAD

Bias – Persistent tendency for forecasts to be Greater or less than actual values.

3-35 Forecasting

Choosing a Forecasting Technique • •

No single technique works in every situation Two most important factors • •

•

Cost Accuracy

Other factors include the availability of: Historical data Computers • Time needed to gather and analyze the data • Forecast horizon •

•

3-36 Forecasting

Exponential Smoothing

3-37 Forecasting

Linear Trend Equation

3-38 Forecasting

Simple Linear Regression

3-39 Forecasting

Workload/Scheduling

SSU9 United Airlines example