# 5 Forecasting

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PRODUCTION AND OPERATIONS MANAGEMENTCh. 5: Forecasting

POM - J. Galvn

1

Learning Objectives

Understand techniques to foresee the future

POM - J. Galvn

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What is Forecasting? Process of predicting a future event Underlying basis of all business decisionsProduction Inventory Personnel FacilitiesPOM - J. Galvn 3

Sales will be $200 Million!

Types of Forecasts by Time Horizon

ShortShort-range forecast Up

to 1 year; usually < 3 months Job scheduling, worker assignments3

MediumMedium-range forecastmonths to 3 years Sales & production planning, budgeting

LongLong-range forecast 3+

years New product planning, facility locationPOM - J. Galvn 4

Short-term vs. Longer-term ShortLongerForecasting

Medium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes. ShortShort-term forecasting usually employs different methodologies than longerlongerterm forecasting ShortShort-term forecasts tend to be more accurate than longer-term forecasts. longerPOM - J. Galvn 5

Influence of Product Life Cycle

Stages of introduction & growth require longer forecasts than maturity and decline Forecasts useful in projectingstaffing levels, inventory levels, and factory capacity

as product passes through stagesPOM - J. Galvn 6

Types of Forecasts

Economic forecasts Address

business cycle e.g., inflation rate, money supply etc.

Technological forecasts Predict

technological change Predict new product sales

Demand forecasts Predict

existing product salesPOM - J. Galvn 7

Seven Steps in Forecasting

Determine the use of the forecast Select the items to be forecast Determine the time horizon of the forecast Select the forecasting model(s) Gather the data Make the forecast Validate and implement resultsPOM - J. Galvn 8

Realities of Forecasting

Forecasts are seldom perfect Most forecasting methods assume that there is some underlying stability in the system Both product family and aggregated product forecasts are more accurate than individual product forecastsPOM - J. Galvn 9

Forecasting ApproachesQualitative Methods Quantitative Methods Used when situation is Used when situation vague & little data is stable & historical exist data exist New products Existing products New technology Current technology Involves intuition, Involves mathematical experience techniques e.g., forecasting sales e.g., forecasting sales on Internet of color televisionsPOM - J. Galvn 10

Overview of Qualitative Methods

Jury of executive opinion Pool opinions of high-level executives, sometimes highaugment by statistical models Sales force composite estimates from individual salespersons are reviewed for reasonableness, then aggregated Delphi method Panel of experts, queried iteratively Consumer Market Survey Ask the customer

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Jury of Executive Opinion Involves small group of high-level managers

Group estimates demand by working together

Combines managerial experience with statistical models Relatively quick Group-think disadvantagePOM - J. Galvn 12

1995 Corel Corp.

Sales Force Composite Each salesperson projects their sales Combined at district & national levels Sales reps know customers wants Tends to be overly optimisticPOM - J. Galvn

Sales

1995 Corel Corp.

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Delphi Method

Iterative group process 3 types of Staff people (What Decision Staff Respondents

Decision Makers(Sales?) (Sales will be 50!)

makers will salesbe? survey)

Reduces groupgroupthinkPOM - J. Galvn

Respondents(Sales will be 45, 50, 55)14

Consumer Market Survey Ask customers about purchasing plans What consumers say, and what they actually do are often different Sometimes difficult to answerHow many hours will you use the Internet next week?

1995 Corel Corp.

POM - J. Galvn

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Overview of Quantitative Approaches

Nave approach Moving averages Exponential smoothing Trend projection Linear regressionPOM - J. Galvn

Time-series Models

Causal models16

5-22

Quantitative Forecasting Methods(Non(Non-Naive)Quantitative Forecasting Time Series Models Causal Models

Moving Average

Exponential Smoothing

Trend Projection

Linear Regression

POM - J. Galvn

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What is a 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, present, & future will continue Example Year: 1993 1994 1995 1996 1997 Sales: 78.7 63.5 89.7 93.2 92.1

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Time Series Components

Trend

Cyclical

SeasonalPOM - J. Galvn

Random19

Trend Component

Persistent, overall upward or downward pattern Due to population, technology etc. Several years durationResponse

Mo., Qtr., Yr.POM - J. Galvn

1984-1994 T/Maker Co. 20

Cyclical Component

Repeating up & down movements Due to interactions of factors influencing economy Usually 2-10 years duration 2Cycle Response

Mo., Qtr., Yr.POM - J. Galvn 21

B

Seasonal Component

Regular pattern of up & down fluctuations Due to weather, customs etc. Occurs within 1 yearSummer Response 1984-1994 T/Maker Co.

POM - J. Galvn Mo., Qtr.

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Random Component

Erratic, unsystematic, residual fluctuations Due to random variation or unforeseen eventsstrike Tornado Union

Short duration & nonrepeatingPOM - J. Galvn 23

General Time Series Models

Any observed value in a time series is the product (or sum) of time series components Multiplicative model Yi = Ti Si Ci Ri (if quarterly or mo. data) Additive model Yi = Ti + Si + Ci + Ri (if quarterly or mo. data)

POM - J. Galvn

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Naive Approach Assumes demand in next period is the same as demand in most recent period e.g., If May sales were 48, then June sales will be 48 Sometimes cost effective & efficient 1995 Corel Corp.POM - J. Galvn 25

Moving Average Method

MA is a series of arithmetic means Used if little or no trend Used often for smoothing

Provides overall impression of data over time

Equation Demand in Previous n Periods MA ! nPOM - J. Galvn 26

Moving Average GraphSales 8 6 4 2 0 93Actual

Forecast

94

95 96 YearPOM - J. Galvn

97

9827

Disadvantages of Moving Average Method

Increasing n makes forecast less sensitive to changes Do not forecast trend well Require much historical data 1984-1994 T/Maker Co.

POM - J. Galvn

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Linear Trend Projection

Used for forecasting linear trend line Assumes relationship between response variable, Y, and time, X, is a linear function Yi ! a bX i Estimated by least squares method

Minimizes sum of squared errorsPOM - J. Galvn 29

Linear Trend Projection Model Yi !abX iYa b0

Scatter DiagramSales 4 3 2 1 0 92Sales vs. Time

93

94

95

96

TimePOM - J. Galvn 31

Least Squares EquationsEquation: Yi ! a bx in

Slope:

b ! i ! n x i n x

i !

x i y i nx y

Y-Intercept:

a ! y bxPOM - J. Galvn 32

Multiplicative Seasonal Model

Find average historical demand for each season by summing the demand for that season in each year, and dividing by the number of years for which you have data. Compute the average demand over all seasons by dividing the total average annual demand by the number of seasons. Compute a seasonal index by dividing that seasons historical demand (from step 1) by the average demand over all seasons. Estimate next years total demand Divide this estimate of total demand by the number of seasons then multiply it by the seasonal index for that season. This provides the seasonal forecast. 33 forecast. POM - J. Galvn

Linear Regression Model

Shows linear relationship between dependent & explanatory variables Example:

Sales & advertising (not time) (notSlope

Y-intercept

^ Yi = a + b X iDependent (response) variablePOM - J. Galvn

Independent (explanatory) variable34

Linear Regression ModelYYi = a + b X i + ErrorError Regression line

^ =a +b X Yi i

XObserved valuePOM - J. Galvn 35

Linear Regression EquationsEquation: Yi ! a bx in

Slope:

b ! i ! n x i n x

i !

x i y i nx y

Y-Intercept:

a ! y bxPOM - J. Galvn 36

Interpretation of Coefficients

Slope (b) (b Estimated If

Y changes by b for each 1 unit increase in Xb = 2, then sales (Y) is expected to (Y increase by 2 for each 1 unit increase in advertising (X) (X

Y-intercept (a) (a Average If

value of Y when X = 0

a = 4, then average sales (Y) is expected (Y to be 4 when advertising (X) is 0 (XPOM - J. Galvn 37

Correlation

Answers: how strong is the linear how relationship between the variables? Coefficient of correlation Sample correlation coefficient denoted r

Values range from -1 to +1 Measures degree of association

Used mainly for understandingPOM - J. Galvn 38

Coefficient of Correlation ValuesPerfect Negative Correlation No Correlation Perfect Positive Correlation

-1.0

-.5

0

+.5

+1.0

Increasing degree of negative c