Forecasting

Forecasting

August 29, WednesdayAugust 29, Wednesday

Introduction

Operations Strategy & Competitiveness Quality Management

Strategic Decisions (some) Design

of Produc

tsand Servic

es

Process Selectionand Design

Capacity and Facility Decisions

Tactical & Operational Decisions

CourseStructure

Forecasting

Forecasting

Predict the next number in the pattern:

a) 3.7, 3.7, 3.7, 3.7, 3.7, ?

b) 2.5, 4.5, 6.5, 8.5, 10.5, ?

c) 5.0, 7.5, 6.0, 4.5, 7.0, 9.5, 8.0, 6.5, ?

Forecasting

Predict the next number in the pattern:

a) 3.7, 3.7, 3.7, 3.7, 3.7,

b) 2.5, 4.5, 6.5, 8.5, 10.5,

c) 5.0, 7.5, 6.0, 4.5, 7.0, 9.5, 8.0, 6.5,

3.7

12.5

9.0

Outline

What is forecasting? Types of forecasts Time-Series forecasting

Naïve

Moving Average

Exponential Smoothing

Regression

Good forecasts

What is Forecasting?

Process of predicting a future event based on historical data

Educated Guessing

Underlying basis of all business decisions

Production Inventory Personnel Facilities

In general, forecasts are almost always wrong. So,

Why do we need to forecast?

Throughout the day we forecast very different things such as weather, traffic, stock market, state

of our company from different perspectives.

Virtually every business attempt is based on forecasting. Not all of them are derived from

sophisticated methods. However, “Best" educated guesses about future are more valuable for

purpose of Planning than no forecasts and hence no planning.

Departments throughout the organization depend on forecasts to formulate and execute their plans.

Finance needs forecasts to project cash flows and capital requirements.

Human resources need forecasts to anticipate hiring needs.

Production needs forecasts to plan production levels, workforce, material requirements,

inventories, etc.

Importance of Forecasting in OM

Demand is not the only variable of interest to forecasters.

Manufacturers also forecast worker absenteeism, machine availability, material costs, transportation and production lead

times, etc.

Besides demand, service providers are also interested in forecasts of population, of other

demographic variables, of weather, etc.

Importance of Forecasting in OM

Short-range forecast Usually < 3 months

Job scheduling, worker assignments

Medium-range forecast 3 months to 2 years

Sales/production planning

Long-range forecast > 2 years

New product planning

Types of Forecasts by Time Horizon

Designof system

Detailed use ofsystem

Quantitative

methods

QualitativeMethods

Forecasting During the Life Cycle

Introduction Growth Maturity Decline

Sales

Time

Quantitative models

- Time series analysis- Regression analysis

Qualitative models- Executive judgment

- Market research-Survey of sales force

-Delphi method

Qualitative Forecasting Methods

QualitativeForecasting

ModelsMarket

Research/Survey

SalesForce

Composite

Executive Judgement

DelphiMethod

Smoothing

Briefly, the qualitative methods are:

Executive Judgment: Opinion of a group of high level experts or managers is pooled

Sales Force Composite: Each regional salesperson provides his/her sales estimates. Those forecasts are then

reviewed to make sure they are realistic. All regional forecasts are then pooled at the district and national levels

to obtain an overall forecast.

Market Research/Survey: Solicits input from customers pertaining to their future purchasing plans. It involves the use of questionnaires, consumer panels and tests of new

products and services.

.

Qualitative Methods

Delphi Method: As opposed to regular panels where the individuals involved are in direct communication, this method eliminates the effects of group potential dominance of the most vocal members. The group involves individuals from inside as well as outside the

organization.

Typically, the procedure consists of the following steps:Each expert in the group makes his/her own forecasts in form of statements

The coordinator collects all group statements and summarizes themThe coordinator provides this summary and gives another set of questions to each group member including feedback as to the input of other experts.The above steps are repeated until a consensus is reached.

.

Qualitative Methods

Quantitative Forecasting Methods

QuantitativeForecasting

RegressionModels

2. MovingAverage

1. Naive

Time SeriesModels

3. ExponentialSmoothing

a) simpleb) weighted

a) levelb) trend

c) seasonality



RegressionModels

2. MovingAverage

1. Naive

Time SeriesModels



a) levelb) trend

c) seasonality

Time Series Models

Try to predict the future based on past data

Assume that factors influencing the past will continue to influence the future

RandomRandom

SeasonalSeasonal

TrendTrend

CompositeComposite

Time Series Models: Components

Product Demand over Time

Year1

Year2

Year3

Year4

Dem

and

for p

rodu

ct o

r ser

vice

Product Demand over Time

Year1

Year2

Year3

Year4

Dem

and

for p

rodu

ct o

r ser

vice

Trend component

Actual demand line

Seasonal peaks

Random variation

Now let’s look at some time series approaches to forecasting…Borrowed from Heizer/Render - Principles of Operations Management, 5e, and Operations Management, 7e


Quantitative

Models

2. MovingAverage

1. Naive

Time SeriesModels



a) levelb) trend

c) seasonality

1. Naive Approach

Demand in next period is the same as demand in most recent period

May sales = 48 →

Usually not good

June forecast = 48

2a. Simple Moving Average

n

A+...+A +A +A =F 1n-t2-t1-tt

1t

n

A+...+A +A +A =F 1n-t2-t1-tt

1t

Assumes an average is a good estimator of future behavior

Used if little or no trend

Used for smoothing

Ft+1 = Forecast for the upcoming period, t+1n = Number of periods to be averaged

A t = Actual occurrence in period t


You’re manager in Amazon’s electronics department. You want to forecast ipod sales for months 4-6 using a 3-period moving average.

n

A+...+A +A +A =F 1n-t2-t1-tt

1t

n

A+...+A +A +A =F 1n-t2-t1-tt

1t

MonthSales(000)

1 42 63 54 ?5 ?6 ?


MonthSales(000)

Moving Average(n=3)

1 4 NA2 6 NA3 5 NA4 ?5 ?

(4+6+5)/3=5

6 ?

n

A+...+A +A +A =F 1n-t2-t1-tt

1t

n

A+...+A +A +A =F 1n-t2-t1-tt

1t

You’re manager in Amazon’s electronics department. You want to forecast ipod sales for months 4-6 using a 3-period moving average.

What if ipod sales were actually 3 in month 4

MonthSales(000)

Moving Average(n=3)

1 4 NA2 6 NA3 5 NA4 35 ?

5

6 ?


?

Forecast for Month 5?

MonthSales(000)

Moving Average(n=3)

1 4 NA2 6 NA3 5 NA4 35 ?

5

6 ?(6+5+3)/3=4.667


Actual Demand for Month 5 = 7

MonthSales(000)

Moving Average(n=3)

1 4 NA2 6 NA3 5 NA4 35 7

5

6 ? 4.667


?

Forecast for Month 6?

MonthSales(000)

Moving Average(n=3)

1 4 NA2 6 NA3 5 NA4 35 7

5

6 ? 4.667(5+3+7)/3=5


Gives more emphasis to recent data

Weights decrease for older data sum to 1.0

2b. Weighted Moving Average

1n-tn2-t31-t2t11t Aw+...+Aw+A w+A w=F 1n-tn2-t31-t2t11t Aw+...+Aw+A w+A w=F

Simple movingaverage models

weight all previousperiods equally

Simple movingaverage models

weight all previousperiods equally

2b. Weighted Moving Average: 3/6, 2/6, 1/6

Month WeightedMoving Average

1 4 NA2 6 NA3 5 NA4 31/6 = 5.16756 ?

??


Sales(000)

2b. Weighted Moving Average: 3/6, 2/6, 1/6

Month Sales(000)

WeightedMoving Average

1 4 NA2 6 NA3 5 NA4 3 31/6 = 5.1675 76

25/6 = 4.16732/6 = 5.333


3a. Exponential Smoothing

Assumes the most recent observations have the highest predictive value gives more weight to recent time periods

Ft+1 = Ft + (At - Ft)Ft+1 = Ft + (At - Ft)et

Ft+1 = Forecast value for time t+1

At = Actual value at time t

= Smoothing constant

Need initial

forecast Ft

to start.

Need initial

forecast Ft

to start.

3a. Exponential Smoothing – Example 1

Week Demand1 8202 7753 6804 6555 7506 8027 7988 6899 775

10

Given the weekly demand data what are the exponentialsmoothing forecasts for periods 2-10 using =0.10?

Assume F1=D1

Given the weekly demand data what are the exponentialsmoothing forecasts for periods 2-10 using =0.10?

Assume F1=D1

Ft+1 = Ft + (At - Ft)Ft+1 = Ft + (At - Ft)i Ai

Week Demand 0.1 0.61 820 820.00 820.002 775 820.00 820.003 680 815.50 793.004 655 801.95 725.205 750 787.26 683.086 802 783.53 723.237 798 785.38 770.498 689 786.64 787.009 775 776.88 728.20

10 776.69 756.28

Ft+1 = Ft + (At - Ft)Ft+1 = Ft + (At - Ft)3a. Exponential Smoothing – Example 1

=

F2 = F1+ (A1–F1) =820+(820–820)

=820

i Ai Fi

Week Demand 0.1 0.61 820 820.00 820.002 775 820.00 820.003 680 815.50 793.004 655 801.95 725.205 750 787.26 683.086 802 783.53 723.237 798 785.38 770.498 689 786.64 787.009 775 776.88 728.20

10 776.69 756.28

Ft+1 = Ft + (At - Ft)Ft+1 = Ft + (At - Ft)3a. Exponential Smoothing – Example 1

=

F3 = F2+ (A2–F2) =820+(775–820)

=815.5

i Ai Fi

Week Demand 0.1 0.61 820 820.00 820.002 775 820.00 820.003 680 815.50 793.004 655 801.95 725.205 750 787.26 683.086 802 783.53 723.237 798 785.38 770.498 689 786.64 787.009 775 776.88 728.20

10 776.69 756.28

Ft+1 = Ft + (At - Ft)Ft+1 = Ft + (At - Ft)

This process continues

through week 10


=i Ai Fi

Week Demand 0.1 0.61 820 820.00 820.002 775 820.00 820.003 680 815.50 793.004 655 801.95 725.205 750 787.26 683.086 802 783.53 723.237 798 785.38 770.498 689 786.64 787.009 775 776.88 728.20

10 776.69 756.28


What if the constant equals 0.6


= =i Ai Fi

Month Demand 0.3 0.6January 120 100.00 100.00February 90 106.00 112.00March 101 101.20 98.80April 91 101.14 100.12May 115 98.10 94.65June 83 103.17 106.86July 97.12 92.54AugustSeptember




= =i Ai Fi

Company A, a personal computer producer purchases generic parts and assembles them to final product. Even though most of the orders

require customization, they have many common components. Thus, managers of Company A need

a good forecast of demand so that they can purchase computer parts accordingly to minimize inventory cost while meeting acceptable service

level. Demand data for its computers for the past 5

months is given in the following table.

Company A, a personal computer producer purchases generic parts and assembles them to final product. Even though most of the orders

require customization, they have many common components. Thus, managers of Company A need

a good forecast of demand so that they can purchase computer parts accordingly to minimize inventory cost while meeting acceptable service

level. Demand data for its computers for the past 5

months is given in the following table.


Month Demand 0.3 0.5January 80 84.00 84.00February 84 82.80 82.00March 82 83.16 83.00April 85 82.81 82.50May 89 83.47 83.75June 85.13 86.38July ?? ??




= =i Ai Fi

How to choose αα depends on the emphasis you want to place depends on the emphasis you want to place

on the most recent dataon the most recent data

Increasing αα makes forecast more sensitive to recent data

3a. Exponential Smoothing

Ft+1 = At + (1- ) At - 1 + (1- )2At - 2 + ...

Forecast Effects ofSmoothing Constant

Weights

Prior Period

2 periods ago

(1 - )

3 periods ago

(1 - )2

=

= 0.10

= 0.90

10% 9% 8.1%

90% 9% 0.9%

Ft+1 = Ft + (At - Ft)or

w1 w2 w3

Collect historical data

Select a model Moving average methods

Select n (number of periods) For weighted moving average: select weights

Exponential smoothing Select

Selections should produce a good forecast

To Use a Forecasting Method

…but what is a good forecast?

A Good Forecast

Has a small error Error = Demand - Forecast

Measures of Forecast Error

b. MSE = Mean Squared Error

n

F-A =MSE

n

1=t

2tt

n

F-A =MSE

n

1=t

2tt

MAD = A - F

n

t tt=1

n

MAD =

A - F

n

t tt=1

n

et

Ideal values =0 (i.e., no forecasting error)

MSE =RMSE MSE =RMSEc. RMSE = Root Mean Squared Error

a. MAD = Mean Absolute Deviation

MAD Example

Month Sales Forecast1 220 n/a2 250 2553 210 2054 300 3205 325 315

What is the MAD value given the forecast values in the table below?

What is the MAD value given the forecast values in the table below?

MAD = A - F

n

t tt=1

n

MAD =

A - F

n

t tt=1

n

55

2010

|At – Ft|FtAt

= 40

= 40 4

=10

MSE/RMSE Example

Month Sales Forecast1 220 n/a2 250 2553 210 2054 300 3205 325 315

What is the MSE value?What is the MSE value?

55

2010

|At – Ft|FtAt

= 550 4

=137.5

(At – Ft)2

2525

400100

= 550

n

F-A =MSE

n

1=t

2tt

n

F-A =MSE

n

1=t

2tt

RMSE = √137.5

=11.73

Measures of Error

t At Ft et |et| et2

Jan 120 100 20 20 400

Feb 90 106 256

Mar 101 102

April 91 101

May 115 98

June 83 103

1. Mean Absolute Deviation (MAD)n

eMAD

n

t 1

2a. Mean Squared

Error (MSE)

MSE

e

n

t

n

2

1

2b. Root Mean

Squared Error (RMSE)

RMSE MSE

-16 16

-1 1

-10

17

-20

10

17

20

1

100

289

400

-10 84 1,446

846

= 14

1,4466

= 241

= SQRT(241)=15.52

An accurate forecasting system will have small MAD, MSE and RMSE; ideally equal to zero. A large error may indicate that either the forecasting method used or the

parameters such as α used in the method are wrong.

Note: In the above, n is the number of periods, which is 6 in our example

deviation absoluteMean

)(=

MAD

RSFE=TS

t

tt forecastactual

30

How can we tell if a forecast has a positive or negative bias?

TS = Tracking Signal Good tracking signal has low values

Forecast Bias

MAD



RegressionModels

2. MovingAverage

1. Naive

Time SeriesModels



a) levelb) trend

c) seasonality

We looked at using exponential smoothing to forecast demand with only random variations

Exponential Smoothing (continued)

Ft+1 = Ft + (At - Ft)

Ft+1 = Ft + At – Ft

Ft+1 = At + (1-) Ft

Exponential Smoothing (continued)

We looked at using exponential smoothing to forecast demand with only random variations

What if demand varies due to randomness and trend?

What if we have trend and seasonality in the data?

Regression Analysis as a Method for Forecasting

Regression analysis takes advantage of the relationship between two variables. Demand is then forecasted based on the knowledge of this relationship and for the given value of the related variable.

Ex: Sale of Tires (Y), Sale of Autos (X) are obviously related

If we analyze the past data of these two variables and establish a relationship between them, we may use that relationship to forecast the sales of tires given the sales of automobiles.

The simplest form of the relationship is, of course, linear, hence it is referred to as a regression line.

Sales of Autos (100,000)

Formulas

xbya

22 xnx

yxnxyb

x

y

xy

y = a + b x

where,

y = a + b x

where,

MonthAdvertising Sales X2 XYJanuary 3 1 9.00 3.00February 4 2 16.00 8.00March 2 1 4.00 2.00April 5 3 25.00 15.00May 4 2 16.00 8.00June 2 1 4.00 2.00July

TOTAL 20 10 74 38

y = a + b Xy = a + b X Regression – Example

22 xnx

yxnxyb xbya

General Guiding Principles for Forecasting

1. Forecasts are more accurate for larger groups of items. 2. Forecasts are more accurate for shorter periods of time.3. Every forecast should include an estimate of error.4. Before applying any forecasting method, the total system

should be understood.5. Before applying any forecasting method, the method should

be tested and evaluated.6. Be aware of people; they can prove you wrong very easily

in forecasting

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