Opration management chapter 3 forecasting

Forecasting at Disney WorldKong, Paris, Tokyo, Orlando, and Anaheim many visitors and how they spend their money the forecast and actual attendance at each park... Forecasting at Disney

Operations

Management

Session 3 –

Forecasting

Learning Objectives

When you complete this chapter you

should be able to :

which models apply for each use

qualitative models

exponential smoothing, and trend methods

analysis

Forecasting at Disney World

Kong, Paris, Tokyo, Orlando, and Anaheim

many visitors and how they spend their money

the forecast and actual attendance at each park

Forecasting at Disney World

annual, and 5-year forecasts

maintenance, operations, finance, and park scheduling

rides, shows, staffing levels, and guests admitted

Forecasting at Disney World

USA

domestic product, cross-exchange rates, arrivals into the USA

survey 1 million park guests, employees, and travel professionals each year

Forecasting at Disney World

airline specials, Federal Reserve policies, Wall Street trends,

vacation/holiday schedules for 3,000 school districts around the world

forecast is 5%

forecasts is between 0% and 3%

What is Forecasting?

 Process of

predicting a future event

 Underlying basis of

all business decisions

 Short-range forecast

 Up to 1 year, generally less than 3 months

 Purchasing, job scheduling, workforce

levels, job assignments, production levels

 New product planning, facility location,

research and development

Forecasting Time Horizons

Distinguishing Differences

 Medium/long range Medium/long range forecasts deal with

more comprehensive issues and support management decisions regarding

planning and products, plants and processes

 Short-term Short-term forecasting usually employs

different methodologies than longer-term forecasting

 Short-term Short-term forecasts tend to be more

accurate than longer-term forecasts

Types of Forecasts

 Address business cycle – inflation rate,

money supply, housing starts, etc.

 Predict rate of technological progress

 Impacts development of new products

 Predict sales of existing products and

services

Seven Steps in Forecasting

forecast

The Realities!

 Forecasts are seldom perfect

 Most techniques assume an

underlying stability in the system

 Product family and aggregated

forecasts are more accurate than individual product forecasts

Forecasting Approaches

 Used when situation is vague Used when situation is vague

and little data exist

 New products New products

 New technology New technology

 Involves intuition, experience Involves intuition, experience

 e.g., forecasting sales on Internet e.g., forecasting sales on Internet

Qualitative Methods

Forecasting Approaches

 Used when situation is ‘stable’ and

historical data exist

 Involves mathematical techniques

televisions

Quantitative Methods

Overview of Qualitative

Methods

 Jury of executive opinion

sometimes augment by statistical models

 Delphi method

Overview of Qualitative

Methods

 Sales force composite

salespersons are reviewed for reasonableness, then aggregated

 Consumer Market Survey

 Involves small group of high-level experts

Sales Force Composite

 Each salesperson projects his or

her sales

 Combined at district and national

levels

 Sales reps know customers’ wants

 Tends to be overly optimistic

Decision Makers

(Evaluate responses and make decisions)

Respondents (People who can make valuable judgments)

Consumer Market Survey

 Ask customers about purchasing

plans

 What consumers say, and what

they actually do are often different

 Sometimes difficult to answer

Associative

Model

 Set of evenly spaced numerical data

variable at regular time periods

 Forecast based only on past values,

no other variables important

past and present will continue influence in future

Time Series Forecasting

Seasonal peaks

Trend component

Actual demand

Random variation

Figure 4.1

 Persistent, overall upward or

downward pattern

 Changes due to population,

technology, age, culture, etc.

 Typically several years

duration

Trend Component

 Regular pattern of up and

down fluctuations

 Due to weather, customs, etc.

 Occurs within a single year

Seasonal Component

Number of Period Length Seasons

 Repeating up and down movements

 Affected by business cycle,

political, and economic factors

 Multiple years duration

 Often causal or

associative relationships

Cyclical Component

0 5 10 15 20

 Erratic, unsystematic, ‘residual’

Naive Approach

 Assumes demand in next

period is the same as demand in most recent period

February sales will be 68

 Sometimes cost effective and

efficient

 Can be good starting point

 MA is a series of arithmetic means

 Used if little or no trend

 Used often for smoothing

over time

Moving Average Method

Moving average = ∑ demand in previous n periods n

Moving Average Example

10 12 13

(

(10 10 + 12 + 12 + 13 + 13 )/3 = 11 2 / 3

Graph of Moving Average

Moving Average Forecast

 Used when trend is present

 Weights based on experience and

intuition

Weighted Moving Average

Weighted moving average =

∑ (weight for period n)

x (demand in period n)

∑ weights

[(3 x

[(3 x 13 13 ) + (2 x 12 ) + (2 x 12 ) + (10 ) + ( 10 )]/6 = 12 1 / 6

 Increasing n smooths the forecast

but makes it less sensitive to changes

 Do not forecast trends well

 Require extensive historical data

Potential Problems With

Moving Average

Moving Average And Weighted Moving Average

Moving average

Weighted moving average

Figure 4.2

 Form of weighted moving average

 Requires smoothing constant ( α )

Exponential Smoothing

– Last period’s forecast)

when underlying average

is likely to change

when underlying average

is stable

Forecast error = Actual demand - Forecast value

= A t - F t

Common Measures of Error

Mean Absolute Deviation ( MAD )

n

Mean Squared Error ( MSE )

2

n

Common Measures of Error

Mean Absolute Percent Error ( MAPE )

MAPE = ∑100|Actual i - Forecast i |/Actual i

n

n

i = 1

Comparison of Forecast

Error

Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded α = 10 α = 10 α = 50 α = 50

Comparison of Forecast

Error

Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded α = 10 α = 10 α = 50 α = 50

Comparison of Forecast

Error

Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded α = 10 α = 10 α = 50 α = 50

Comparison of Forecast

Error

Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded α = 10 α = 10 α = 50 α = 50

Comparison of Forecast

Error

Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded α = 10 α = 10 α = 50 α = 50

Exponential Smoothing with

Exponential Smoothing with

Exponential Smoothing with

Trend Adjustment Example

Forecast Actual Smoothed Smoothed Including Month(t) Demand (A t) Forecast, F t Trend, T t Trend, FIT t

Exponential Smoothing with

Trend Adjustment Example

Forecast Actual Smoothed Smoothed Including Month(t) Demand (A t) Forecast, F t Trend, T t Trend, FIT t

Exponential Smoothing with

Trend Adjustment Example

Forecast Actual Smoothed Smoothed Including Month(t) Demand (A t) Forecast, F t Trend, T t Trend, FIT t

Exponential Smoothing with

Trend Adjustment Example

Forecast Actual Smoothed Smoothed Including Month(t) Demand (A t) Forecast, F t Trend, T t Trend, FIT t

Exponential Smoothing with

Trend Adjustment Example

Forecast Actual Smoothed Smoothed Including Month(t) Demand (A t) Forecast, F t Trend, T t Trend, FIT t

Exponential Smoothing with

Trend Adjustment Example

Trend Projections

Fitting a trend line to historical data points

to project into the medium to long-range

Linear trends can be found using the least

Least Squares Method

Least Squares Method

Least Squares Method

Equations to calculate the regression variables

Σx2 - nx2

y ^ = a + bx

a = y - bx

Least Squares Example

Least Squares Example

Least Squares Example

Seasonal Variations In Data

The multiplicative

seasonal model

can adjust trend

data for seasonal

variations in

demand

Seasonal Variations In Data

1 Find average historical demand for each

season

2 Compute the average demand over all

seasons

3 Compute a seasonal index for each season

4 Estimate next year’s total demand

5 Divide this estimate of total demand by the

number of seasons, then multiply it by the seasonal index for that season

Steps in the process:

Seasonal Index Example

Seasonal Index Example

Seasonal index = average 2005-2007 monthly demand

average monthly demand

= 90/94 = 957

Seasonal Index Example

Seasonal Index Example

Seasonal Index Example

San Diego Hospital

San Diego Hospital

San Diego Hospital

Associative Forecasting

Used when changes in one or more independent variables can be used to predict

the changes in the dependent variable

Most common technique is linear

regression analysis

We apply this technique just as we did

in the time series example

Associative Forecasting

Forecasting an outcome based on predictor

variables using the least squares technique

b = slope of the regression line

x = the independent variable though to predict the value of the dependent variable

^

Associative Forecasting

Example

4.0 – 3.0 – 2.0 – 1.0 –

Standard Error of the

Figure 4.9

4.0 – 3.0 – 2.0 – 1.0 –

Standard Error of the

Estimate

point

y c = computed value of the dependent variable, from the regression equation

points

S y,x = ∑(y - y c) 2

n - 2

Standard Error of the

Estimate

Computationally, this equation is

considerably easier to use

We use the standard error to set up prediction intervals around the

point estimate

S y,x = ∑y2 - a∑y - b∑xy

n - 2

Standard Error of the

Estimate

4.0 – 3.0 – 2.0 – 1.0 –

 How strong is the linear

relationship between the variables?

 Correlation does not necessarily

imply causality!

 Coefficient of correlation, r,

measures degree of association

Correlation

Correlation Coefficient

[nΣx2 - (Σx) 2 ][nΣy2 - (Σy) 2 ]

r = -1

 Coefficient of Determination, r2,

measures the percent of change in

y predicted by the change in x

 Values range from 0 to 1

Multiple Regression

Analysis

If more than one independent variable is to be

used in the model, linear regression can be

extended to multiple regression to accommodate several independent variables

y ^ = a + b1x1 + b2x2 …

Computationally, this is quite complex and generally done on the

computer

An improved correlation coefficient of r = 96

means this model does a better job of predicting

the change in construction sales

Sales = 1.80 + 30(6) - 5.0(.12) = 3.00

Sales = $3,000,000

 Measures how well the forecast is

predicting actual values

(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 and Controlling

Forecasts

Tracking Signal

Monitoring and Controlling

in period i)

(∑|Actual - Forecast|/n)

Tracking Signal

Tracking signal +

0 MADs

–

Upper control limit

Lower control limit

Time

Signal exceeding limit

Acceptable range

Tracking Signal Example

Cumulative Absolute Absolute Actual Forecast Forecast Forecast Qtr Demand Demand Error RSFE Error Error MAD

Cumulative Absolute Absolute Actual Forecast Forecast Forecast Qtr Demand Demand Error RSFE Error Error MAD

-10/10 = -1 -15/7.5 = -2 0/10 = 0 -10/10 = -1 +5/11 = +0.5 +35/14.2 = +2.5

The variation of the tracking signal between -2.0 and +2.5 is within acceptable limits

Adaptive Forecasting

It’s possible to use the computer to

continually monitor forecast error and

adjust the values of the α and β

coefficients used in exponential

smoothing to continually minimize

forecast error

This technique is called adaptive

smoothing

Focus Forecasting

Developed at American Hardware Supply,

focus forecasting is based on two principles:

1 Sophisticated forecasting models are not always better than simple ones

2 There is no single technique that should

be used for all products or services

This approach uses historical data to test

multiple forecasting models for individual items

The forecasting model with the lowest error is

then used to forecast the next demand

Forecasting in the Service

Sector

 Presents unusual challenges

industry and product

Fast Food Restaurant

FedEx Call Center Forecast