Chapter 04 Forecasting 8th Ed 2011 - Faculty Websites 04... · 4 Forecasting. Outline • Global ... • Consumer market survey ... (Weight for period n) (Demand in period n)

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4 Forecasting

Outline

• Global Company Profile: Disney World• What is Forecasting?• Types of Forecasts• Forecasting Approaches

– Overview of Qualitative & Quantitative Methods• Time-Series Forecasting• Monitoring and Controlling Forecasts

Famous Forecasting Quotes

"Those who have knowledge, don't predict. Those who predict, don't have knowledge. "

-- Lao Tzu, 6th Century BC Chinese Poet

"It is often said there are two types of forecasts ... lucky or wrong!!!! "

-- "Control" magazine (Inst. of Ops. Mgmt.)

(http://www.met.rdg.ac.uk/cag/forecasting/quotes.html)


Forecasting at Disney World

• Global portfolio includes parks in Hong Kong, Paris, Tokyo, Orlando, and Anaheim

• Revenues are derived from people – how many visitors and how they spend their money

• Daily management report contains only the forecast and actual attendance at each park

• Disney generates daily, weekly, monthly, annual, and 5-year forecasts

• Forecast used by labor management, maintenance, operations, finance, and park scheduling

• Forecast used to adjust opening times, rides, shows, staffing levels, and guests admitted


Forecasting at Disney World

• 20% of customers come from outside the USA• Economic model includes gross domestic product,

cross-exchange rates, arrivals into the USA• A staff of 35 analysts and 70 field people survey 1

million park guests, employees, and travel professionals each year

• Inputs to the forecasting model include airline specials, Federal Reserve policies, Wall Street trends, vacation/holiday schedules for 3,000 school districts around the world

• Average forecast error for the 5-year forecast is 5%• Average forecast error for annual forecasts is between

0% and 3%


• Process of predicting a future event

• Underlying basis of all business decisions– Production– Inventory– Personnel– Facilities

Sales will be $200 Million!

What is Forecasting?


• Short-range forecast• Up to 1 year, generally less than 3 months• Purchasing, job scheduling, workforce levels, job

assignments, production levels• Medium-range forecast

• 3 months to 3 years• Sales and production planning, budgeting

• Long-range forecast• 3+ years• New product planning, facility location, research

and development

Forecasting Time Horizons


Types of Forecasts

• Economic forecasts– Address business cycle, e.g., inflation rate, money

supply, housing starts, etc.• Technological forecasts

– Predict rate of technological progress– Impacts development of new products

• Demand forecasts– Predict sales of existing products and services


Strategic Importance of Forecasting

• Human Resources – Hiring, training, laying off workers

• Capacity – Capacity shortages can result in undependable delivery, loss of customers, loss of market share

• Supply Chain Management – Good supplier relations and price advantages


Used when situation is stable & historical data exist

Existing productsCurrent technology

Involves mathematical techniques

e.g., forecasting sales of color televisions

Quantitative MethodsUsed when situation is vague & little data exist

New productsNew technology

Involves intuition, experience

e.g., forecasting sales on Internet

Qualitative Methods

Forecasting Approaches


Overview of Qualitative Methods

• Jury of executive opinion– Pool opinions of high-level executives, sometimes

augment by statistical models– ‘Group-think’ disadvantage

• Sales force composite– Estimates from individual salespersons are

reviewed for reasonableness, then aggregated– Sales reps know customers’ wants

• Delphi method– Panel of experts, queried iteratively

• Consumer market survey– Ask the customer


1. Naive approach

2. Moving averages

3. Exponential smoothing

4. Trend projection

5. Linear regression

Time-Series Models

Associative Model

Quantitative Approaches


Time Series Forecasting

• Set of evenly spaced numerical data• Obtained by observing response variable at

regular time periods• Forecast based only on past values, no other

variables important• Assumes that factors influencing past and present

will continue influence in future


Trend

Seasonal

Cyclical

Random

Time Series Forecasting


Dem

and

for p

rodu

ct o

r ser

vice

| | | |1 2 3 4

Time (years)

Average demand over 4 years

Trend component

Actual demand line

Random variation

Seasonal peaks

Components of Demand


Naive Approach

• Assumes demand in next period is the same as demand in most recent period– If May sales were 48, then June sales will be 48

• Sometimes can be cost effective and efficient• Can be good starting point


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

Moving average =∑ demand in previous n periods

n


Potential Problems With MA

• Increasing n smooths the forecast but makes it less sensitive to changes

• Do not forecast trends well• Require extensive historical data


(12 + 14 + 16)/3 = 14(14 + 16 + 18)/3 = 16(16 + 18 + 23)/3 = 19

JanuaryFebruaryMarchApril 16May 18June 23July 26

Actual 3-MonthMonth Shed Sales Moving Average

101214

Moving Average Example

(10 + 12 + 14)/3 = 12


• Used when trend is present – Older data usually less important

• Weights based on intuition– Ranges between 0 & 1, & sum to 1.0

• Equation

WMA = Σ(Weight for period n) (Demand in period n)

ΣWeights

Weighted Moving Average Method


(12*0.2 + 14*0.3 + 16*0.5) = 14.6(14*0.2 + 16*0.3 + 18*0.5) = 16.6(16*0.2 + 18*0.3 + 23*0.5) = 20.1

JanuaryFebruaryMarchApril 16May 18June 23July 26

Actual 3-MonthMonth Shed Sales Moving Average

101214

Weighted Moving Average Example

Weights: heaviest weights applied to most recent month – 0.5, 0.3, 0.2

(10*0.2 + 12*0.3 + 14*0.5) = 12.6


Exponential Smoothing Method

• Form of weighted moving average– Weights decline exponentially– Most recent data weighted most

• Requires smoothing constant (α)– Ranges from 0 to 1– Select the value of α that gives us the lowest

forecast error (MAD or MSE)• Involves little record keeping of past data


• Ft = Ft-1 + α(At-1 - Ft-1)– Use for computing forecast

• Ft = αAt-1 + α(1-α)At-2 + α(1- α)2·At-3

+ α(1- α)3At-4 + ... + α(1- α)t-1·A0

– Ft = Forecast value – At = Actual value – α = Smoothing constant

• What happens when α = 1?

Exponential Smoothing Equations


Problem 4.6, Page 140

Month SalesJanuary 20February 21March 15April 14May 13June 16July 17August 18September 20

October 20November 21

December 23

(b) What is the forecast for January?

[iv] Exponential smoothing, α = 0.3FSep = 18FOct = 18 + 0.3(20-18) = 18.6FNov = 18.6 + 0.3(20-18.6) = 19.02FDec = 19.02 + 0.3(21-19.02) = 19.6FJan = 19.6 + 0.3(23-19.6) = 20.62


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

^

Trend Projections


Equations to calculate the regression variables

b =Σxy - nxyΣx2 - nx2

y = a + bx^

a = y - bx

Least Squares Method


• Example: Sales (y) & advertising (x)• Slope (b)

– Estimated y changes by b for each 1 unit increase in x• If b = 2, then sales (y) is expected to increase

by 2 for each 1 unit increase in advertising (x)• Y-intercept (a)

– Average value of y when x = 0• If a = 4, then average sales (y) is expected to

be 4 when advertising (x) is 0

Interpretation of Coefficients

^

^

^

^

^


• You want to achieve:– No pattern or direction in forecast error

• Error = (At - Ft) = (Actual - Forecast)• Seen in plots of errors over time

– Smallest forecast error• Mean square error (MSE)• Mean absolute deviation (MAD)

Selecting a Forecasting Model


Measuring Forecast Error

Mean Absolute Deviation (MAD)

MAD =∑ |actual - forecast|

n

Mean Squared Error (MSE)

MSE =∑ (forecast error)2

n


Comparison of Forecast Error

Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation

Tonnage using for using forQuarter Unloaded Model A Model A Model B Model B

1 180 179 1772 168 167 1713 159 160 1564 175 184 172


Forecast Error - MAD


Tonnage with for with forQuarter Unloaded Model A Model A Model B Model B

1 180 179 1 177 32 168 167 1 171 33 159 160 1 156 34 175 184 9 172 3

12 12

MAD =∑ |deviation|

n

= (1+1+1+9)/4= 12/4 = 3

For Model A

= (3+3+3+3)/4= 12/4 = 3

For Model B

Model A and Model B have the same MAD values.


Forecast Error - MSE


Tonnage with for with forQuarter Unloaded Model A Model A Model B Model B

1 180 179 1 177 32 168 167 1 171 33 159 160 1 156 34 175 184 9 172 3

12 12

= (1+1+1+81)/4= 84/4 = 21

For Model A

= (9+9+9+9)/4= 36/4 = 9

For Model B

MSE =∑ (forecast error)2

n

Model B has a smaller MSE (=9) than Model A (=21)


• Tracking signal• Measures how well the forecast is

predicting actual values• Ratio of running sum of forecast errors

(RSFE) to mean absolute deviation (MAD)• Good tracking signal has low values• If forecasts are continually high or low, the

forecast has a bias error

Monitoring & Controlling Forecasts


Tracking signal

RSFEMAD=

Tracking signal =

∑(actual demand in period i -

forecast demand in period i)

(∑|actual - forecast|/n)

Monitoring & Controlling Forecasts

What’s the interpretation of a positive or negative RSFE?


Tracking signal

Signal exceeding limit

+

0 MADs

–

Upper control limit

Lower control limit

Time

Acceptable range

Tracking Signal

Thank You

Questions? ?

Documents

Chapter 04 Forecasting 8th Ed 2011 - Faculty Websites 04... · 4 Forecasting. Outline • Global ... • Consumer market survey ... (Weight for period n) (Demand in period n)