Session 10 Forecasting

8/9/2019 Session 10 Forecasting

1/20

PRODUCTION & OPERATIONS

MANAGEMENTDr. Partha Priya Datta

Associate Professor of Operations Management

Chair, Visionary Leadership in Manufacturing

[email protected]

Office: M-202, NAB,

Tel: 765

mailto:[email protected]:[email protected]


2/20

Principles of Forecasting

Many types of forecasting models that differ in complexity

and amount of data & way they generate forecasts:

1. Forecasts are rarely perfect

2. Forecasts are more accurate for grouped data than for individualitems

3. Forecast are more accurate for shorter than longer time periods

214 January 2015 Session 10 (Ch.18): Forecasting (Partha P. Datta)


3/20

Three Building Blocks

3

Source: PRTM.com



4/20

• Qualitative

– Sales force composite / Grass Roots

– Market Research / Consumer market surveys & interviews

– Jury of Executive Opinion / Panel Consensus – Delphi Method

– Historical Analogy - DVDs like VCRs

– Naïve approach

• Quantitative

– Time Series Analysis

– Causal Relationships

– Simulation

Types of Forecasts



5/20

Selection of Forecasting Methods

Method Data Requirements Applications Relative

Cost

Moving

Averages

At least two years of data Short-range

forecasts

Low

ExponentialSmoothing Well adapted to computerapplications, at least two

years of data

Short-rangeforecasts Low

Decomposition Aggregate data, at least

two years of data

Medium-range

forecasts

Medium

Causal

Forecasting

Large volume of data Short to medium

range

Medium

to High

Qualitative

Forecasting

Large volume of expert

judgments, surveys, Not

enough quantitative data

Long range

forecasts

Medium

to High



6/20

6

Time Series Patterns



7/20

Time Series Models

14 January 2015 Session 10 (Ch.18): Forecasting (Partha P. Datta) 7

• Simple Mean:• The average of all available data - good for level patterns

• Moving Average:• The average value over a set time period

(e.g.: the last four weeks)

• Each new forecast drops the oldest data point & adds a new observation• More responsive to a trend but still lags behind actual data

F t = Forecast for the coming period

n = Number of periods to be averaged

At-i = Actual occurrence in the past period for up to “n” periods

n

A A A F

nt t t

t

...

21


8/208

Time Series Models contd..

• Weighted Moving Average:

• All weights must add to 100% or 1.00

e.g. Ct .5, Ct-1 .3, Ct-2 .2 (weights add to 1.0)

• Allows emphasizing one period over others; above indicates

more weight on recent data (Ct=.5)

• Differs from the simple moving average that weighs all periodsequally - more responsive to trends

tt1t ACF



9/209

Time Series Models contd..

Exponential Smoothing:

• Most frequently used time series method because of ease of

use and minimal amount of data needed

• Need just three pieces of data to start:

• Last period’s forecast (Ft)

• Last periods actual value ( At)

• Select value of smoothing coefficient, a ,between 0 and 1.0

• If no last period forecast is available, average the last few

periods or use naive method

• Higher a values (e.g. .7 or .8) may place too much weight on

last period’s random variation

tt1t Fα1αAF



10/20

Compare MAF and ESF

Period

20 21 22 23 24 25 26 27 28

5-period MAF

weights

0% 0% 0% 20% 20% 20% 20% 20% ----

ESF weights(a.3 2% 4% 5% 7% 10% 15% 21% 30% ----

Ft = aAt-1 + (1-aFt-1

F28 = 0.3xA27 + 0.7xF27

F27 = 0.3xA26 + 0.7xF26

F28 = 0.3xA27 + 0.7x(0.3xA26 + 0.7xF26



11/2011

Seasonality problem: a university must develop forecasts for the next year’s quarterly

enrollments. It has collected quarterly enrollments for the past two years. It has also

forecast total enrollment for next year to be 90,000 students. What is the forecast for

each quarter of next year?

Quarter Year 1 SeasonalIndex

Year2

SeasonalIndex

Avg.Index

Year3

Fall24000 ? 26000 ? ? 27450

Winter 23000 ? 22000 ? ? ?

Spring 19000 ? 19000 ? ? ?

Summer 14000 ? 17000 ? ? ?

Total 80000 ? 84000 ? ? ?

Average ? ? ?



12/2012

Seasonality problem: a university must develop forecasts for the next year’s quarterly enrollments. It

has collected quarterly enrollments for the past two years. It has also forecast total enrollment for

next year to be 90,000 students. What is the forecast for each quarter of next year?

Quarter Year 1 SeasonalIndex

Year2

SeasonalIndex

Avg.Index

Year3

Fall24000 1.2 26000 1.23 1.22 27450

Winter 23000 1.15 22000 1.05 1.1 24750

Spring 19000 0.95 19000 0.91 0.93 20925

Summer 14000 0.7 17000 0.81 0.75 16875

Total 80000 4 84000 4 4 90000

Average 20000 21000 22500



13/20

Problem 1

Qtr Yr1-

Q1

Yr1-

Q2

Yr1-

Q3

Yr1-

Q4

Yr2-

Q1

Yr2-

Q2

Yr2-

Q3

Yr2-

Q4

Actual 525 605 755 675 580 675 850 740

Trend 628.2 641.8 655.4 668.9 682.5 696.1 709.7 723.3


Given the following quarterly demand data and trend values, what is the seasonal factor

for quarter II?


14/20

Problem 2The following equation summarizes the trend portion of quarterly sales ofwardrobes over a long cycle. Sales also exhibit seasonal variations.

F t = 40 – 6 .5t + 2t 2

Where

F t =Unit Sales

t=0 at the 1st quarter of 2004

The seasonal indexes for each quarter are given belowQuarter Index

1 1.1

2 1.0

3 0.6

4 1.3

Using the information given, select the forecast of sales (rounded to the nextinteger) for the first quarter of 2008 from the choices given.

a) 192;

b) 493;

c) 432;

d) 336;

e) none of the above



15/20

Problem 3

A shoe manufacturer, using exponential smoothing with a =

0.1, has developed a January forecast of 400 units for a

ladies’ shoe. This brand has seasonal indexes of 0.80,

0.90, and 1.20, respectively, for the first 3 months of the

year. Assuming that actual sales were 344 units in Januaryand 414 units in February, what would be the seasonalized

March forecast? Assume a multiplicative time series model.



16/20

Problem 4

Month

Jan

Feb

Mar

Apr

May

Jun

July

Aug

Sep

Oct

Nov

Dec

S.I.

0.86

0.96

1.2

1.44

1.22

1.06

0.99

0.93

0.89

1.1

3


Using seasonal indices Apple’s Citrus Fruit Farm ships boxed fruits anywhere in the

world. Using the following information, forecast shipments for the first five months of

next year .

However, for the first two months the S.I. data is misplaced and you only have actual

shipment data for January for last 3 years, which are 300, 400 and 500. Also you know

that the average actual monthly shipment is 500 over the last 3 years. For February youdo not have any information on actual shipments. The trend portion of the demand is

projected using monthly forecast equation: Ft=402+3t, where t=0 for January of last

year and Ft is the number of shipments.

17


17/20

The Bias Statistic to Determine Forecasting Error

• The ideal Bias/Mean Error is zero which would meanthere is no forecasting error

• Positive Bias means on average under-forecasting

• Bias indicates compensation actions

n

)F(A

=Bias

n

1=t

tt


1814 J 201 S i 10 (Ch 18) F i (P h P D )


18/20

The MAD Statistic to Determine Forecasting Error

• The ideal MAD is zero which would mean there is noforecasting error

• The larger the MAD, the less the accurate the resultingmodel

• Gives us the size of compensation

MAD =

A - F

n

t tt=1

n


1914 J 2015 S i 10 (Ch 18) F ti (P th P D tt )


19/20

Tracking Signal

• The Tracking Signal or TS is a measure that

measures whether forecasting model is working• If >4 or


20/20

MAD, RSFE and TSMont

h

Demand

Forecast

Actua

l

Deviatio

n

RSFE Abs

Dev

Sum

of Abs

Dev

MAD TS

1 1000 950 -50 -50 50 50 50 -1

2 1000 1070 70 20 70 120 60 .33

3 1000 1100 100 120 100 220 73.3 1.64

4 1000 960 -40 80 40 260 65 1.2

5 1000 1090 90 170 90 350 70 2.46 1000 1050 50 220 50 400 66.7 3.3


Session 10 Forecasting

Documents

Transcript of Session 10 Forecasting