# Chap003 - Forecasting

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3-1

Forecasting

Operations Management

William J. Stevenson

8th edition

3-2

Forecasting

CHAPTER

3

Forecasting

McGraw-Hill/Irwin

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

3-3

Forecasting

FORECAST:y y

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

3-4

Forecasting

Uses of ForecastsAccounting Finance Human Resources Marketing MIS Operations Product/service design Cost/profit estimates Cash flow and funding Hiring/recruiting/training Pricing, promotion, strategy IT/IS systems, services Schedules, MRP, workloads New products and services

3-5

Forecasting

y

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

y

y

y

I see that you will get an A this semester.

3-6

Forecasting

Elements of a Good Forecast

Timely

Reliable

Accurate

Written

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 Forecastsy y

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

y

3-9

Forecasting

Judgmental Forecastsy y y y

Executive opinions Sales force opinions Consumer surveys Outside opinion Delphi methody y

y

Opinions of managers and staff Achieves a consensus forecast

3-10 Forecasting

Time Series ForecastsTrend - long-term movement in data y Seasonality - short-term regular variations in data y Cycle wavelike variations of more than one years duration y Irregular variations - caused by unusual circumstances y Random variations - caused by chancey

3-11 Forecasting

Forecast VariationsFigure 3.1Irregular variatio n

Trend

Cycles90 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 periods actual value.

3-13 Forecasting

Nave ForecastsSimple to use y Virtually no cost y Quick and easy to prepare y Data analysis is nonexistent y Easily understandable y Cannot provide high accuracy y Can be a standard for accuracyy

3-14 Forecasting

Uses for Nave Forecastsy

Stable time series datay

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

y

Seasonal variationsy

y

Data with trendsy

3-15 Forecasting

Techniques for Averagingy y y

Moving average Weighted moving average Exponential smoothing

3-16 Forecasting

Moving Averagesy

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

MAn =y

1 Ai i=n

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

3-17 Forecasting

Simple Moving AverageActual 47 45 43 41 39 37 35 1 2 3 4 5 6 7n

MA5

MA3 8 9 10 11 12

MAn =

1 Ai i=n

3-18 Forecasting

Exponential Smoothing

Ft = Ft-1 + E(At-1 - Ft-1) Premise--The most recent observations might have the highest predictive value.y Therefore,

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

3-19 Forecasting

Exponential Smoothing

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

3-20 Forecasting

Example 3 - Exponential SmoothingPeriod 1 2 3 4 5 6 7 8 9 10 11 12 Actual 42 40 43 40 41 39 46 44 45 38 40 Alpha = 0.1 Error 42 41.8 41.92 41.73 41.66 41.39 41.85 42.07 42.36 41.92 41.73 -2.00 1.20 -1.92 -0.73 -2.66 4.61 2.15 2.93 -4.36 -1.92 Alpha = 0.4 Error 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 ConstantActual

50E!.4

Demand

45 40 35 1 2 3 4 5 6 7 8

E !.1

9 10 11 12

Period

3-22 Forecasting

Common Nonlinear TrendsFigure 3.5

Parabolic

Exponential

Growth

3-23 Forecasting

Linear Trend EquationFt

Ft = a + bty y y y0 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 t

3-24 Forecasting

Calculating a and bn (ty) - t y b = n t 2 - ( t) 2

y - b t a = n

3-25 Forecasting

Linear Trend Equation Examplet W eek 1 2 3 4 5 t 1 4 9 16 252 2

y Sales 150 157 162 166 177

ty 150 314 486 664 885

7 t = 15 7t = 55 2 (7t) = 225

7 y = 812 7 ty = 2499

3-26 Forecasting

Linear Trend Calculation5 (2499) - 15(812) 12495-12180 b = = = 6.3 5(55) - 225 275 -225

812 - 6.3(15) a = = 143.5 5

y = 143.5 + 6.3t

3-27 Forecasting

Associative Forecastingy

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

y

y

3-28 Forecasting

Linear Model Seems ReasonableX 7 2 4 14 15 1 12 14 20 15 7 Y 15 10 13 15 25 27 24 20 27 44 34 17

Computed relationship50 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 Accuracyy

Error - difference between actual value and predicted value Mean Absolute Deviation (MAD)y

y

Average absolute error

y

Mean Squared Error (MSE)y

Average of squared error Average absolute percent error

y

Mean Absolute Percent Error (MAPE)y

3-30 Forecasting

MAD, MSE, and MAPEMAD = Actual forecast n MSE = ( Actual forecast) n -1 Actual forecas t n / Actual*100)2

MAPE =

3-31 Forecasting

Example 10Period 1 2 3 4 5 6 7 8 Actu 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 ^ 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

MAD= MSE= MAPE=

2.75 10.86 1.28

3-32 Forecasting

Controlling the Forecasty

Control chartA visual tool for monitoring forecast errors y Used to detect non-randomness in errorsy

y

Forecasting errors are in control ifAll errors are within the control limits y No patterns, such as trends or cycles, are presenty

3-33 Forecasting

Sources of Forecast errorsModel may be inadequate y Irregular variations y Incorrect use of forecasting techniquey

3-34 Forecasting

Tracking SignalTracking signalRatio of cumulative error to MAD

(Actual-forecast) Tracking signal =MADBias Persistent tendency for forecasts to be Greater or less than actual values.

3-35 Forecasting

Choosing a Forecasting TechniqueNo single technique works in every situation y Two most important factorsy

Cost y Accuracyy

y

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

3-36 Forecasting

Exponential Smoothing

3-37 Forecasting

Linear Trend Equation

3-38 Forecasting

Simple Linear Regression