Moving Average 1Ardavan Asef-Vaziri 6/4/2009 Forecasting -1 Chapter 7 Demand Forecasting in a Supply...

Moving Average 1Ardavan Asef-Vaziri 6/4/2009

Forecasting -1

Chapter 7Demand Forecastingin a Supply Chain

“Those who do not remember the past

are condemned to repeat it”

George Santayana (1863-1952)

Spanish philosopher, essayist, poet and novelist


Forecasting -1


Forecasting -1Moving Average

Ardavan Asef-Vaziri

Based on Operations management: Stevenson

Operations Management: Jacobs, Chase, and AquilanoSupply Chain Management: Chopra and MeindlUSC Marshall School of Business Lecture Notes


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Accounting Cost/Profit Estimates

Finance Cash Flow and Funding

Human Resources Hiring/Recruiting/Training

Marketing Pricing, Promotion

MIS IT/IS Systems, Services

Operations Production Planning, MRP

Product/Service Design New Products and Services

Uses of Forecasts

Forecast: a prediction of the future value of a variable of interest, such as demand.


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Types of Forecasting

Qualitative Techniques Delphi

Quantitative Techniques Time Series Analysis - Analyzing data by time

periods to determine if trends or patterns exist.Moving AverageExponential Smoothing

Causal Relationship Forecasting - Relating demand to an underlying factor other than time. Linear - Single and Multi VariablesNonlinear - Single and Multi Variables

Measures of Accuracy Mean Absolute Deviation, Tracking Signal


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Four Characteristics of Forecasts

Forecasts are usually (always) inaccurate (wrong). Forecasts should be accompanied by a measure of

forecast error. Forecasts for aggregate items are more accurate

than individual forecasts. Aggregate forecasts reduce the amount of variability – relative to the aggregate mean demand. Standard Deviation of sum of two variables is less than sum of the Standard Deviation of the two variables.

Long-range forecasts are less accurate than short-range forecasts. Forecasts further into the future tends to be less accurate than those of more imminent events. As time passes, we get better information, and make better prediction.


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Container Handling 2007: World Total 450 MTEUs

RANK PORT (Country) Million TEUs

1 Singapore (Singapore) 27.9

2 Shanghai (China) 26.2

3 Hong Kong (China) 24

4 Shenzhen (China) 21.1

5 Los Angeles & Long Beach (US) 15.7

6 Yingkou/Liaonian (China) 13.7

7 Busan (South Korea) 13.3

8 Rotterdam (Netherlands) 10.8

9 Dubai Ports (UAE) 10.7

10 Kaohsiung (Taiwan) 10.3

11 Hamburg (Germany) 9.9

12 Qingdao (China) 9.4

13 Ningbo (China) 9.3

14 Guangzhou (China) 9.2

15 Antwerp (Belgium) 8.2

16 Port Kelang (Malaysia) 7.1

17 Tianjin (China) 7.1

18 Tanjung Pelepas (Malaysia) 5.5

19 New York / New Jersey (US) 5.3

20 Bremen (Germany) 4.9


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More than 50% of containers coming to US pass through SPB ports. More than 1/3 of the containerized product consumed in all other states pass through SPB ports.

The total value of trade using the southern California trade infrastructure network is around $300 billion, creating around $30 billion in state and local taxes and around 3 million jobs or full time equivalents.

SPB ports need to retain their competing

edges.


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US-China Alternative Routes

Narvik, Norway

Vostochny, Russia

Hong Kong, China

Singapore

Rotterdam, Netherlands

Savannah

NorfolkNew York

Prince Rupert, Canada

Savannah

NorfolkNew York

Los Angeles

Colima, Mexico

Ensenada, Mexico


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Competing Edges of SPB Ports

Deep-water facilities for 8,000+ container ships.

State-of-the-art on-dock facilities between ship and train.

Intermodal transfer – Ship-train-truck.Consolidation and distribution facilities for

trans-loading- from 20’ and 40’ to 56’.The last two Characteristics of all Forecasting

Techniques


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Strategic Positioning and Smooth Flow

2 Weeks

3 Weeks

4 Weeks


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Strategic Positioning and Smooth Flow

14 days

3-4 days2-3 days


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Qualitative Methods - Delphi

Non-quantitative forecasting techniques based on expert opinions and intuition. Typically used when there are no data available.

Delphi MethodSubjective, judgmentalBased on intuition, estimates, and opinions

Expert Opinions Market Research Historical Analogies


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Find a relationship between demand and time.

Demand

Time

Time Series Forecasts


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Components of an Observation

Observed variable (O) =Systematic component (S) + Random component (R)

Level (current deseasonalized )

Trend (growth or decline)

Seasonality (predictable seasonal fluctuation)

Systematic component: Expected value of the variable Random component: The part of the forecast that deviates

from the systematic component Forecast error: difference between forecast and actual

demand


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Naive Forecast

Moving Average

Exponential Smoothing

Time Series Techniques


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We sold 250 wheels last week.... Now, next week we should sell.…

At : Actual demand in period t

F(t+1) : Forecast of demand for period t+1

F(t+1) = At

Naive Forecast

250 wheels

The naive forecast can also serve as an accuracy standard for other techniques.


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Moving Average

Three period moving average in period 7 is the average of:

MAt10 = (At+ At-1+ At-2 +At-3+ ….+ At-9 )/10

MA73 = (A7+ A6+ A5 )/3

Three period moving average in period t is the average of:

MAt3 = (At+ At-1+ At-2 )/3

Ten period moving average in period t is the average of:


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Forecast Using Moving Average

Forecast for period t+1 is equal to moving average for period t

Ft+1 =MAtn

n period moving average in period t is the average of:

MAtn = (At+ At-1+ At-2 +At-3+ ….+ At-n+1 )/n

Ft+1 =MAtn = (At+ At-1+ At-2 +At-3+ ….+ At-n+1 )/n


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An example for comparison of two Moving Averages

Let’s develop 3-week and 6-week moving average forecasts for demand in week 13.

t At1 11282 18663 11824 14345 18906 13387 11048 17169 165010 169211 132012 1758

13


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3-Period and 6-Period Moving Average

(1300+1356+1442)/3 (1300+1356+1442+1576+1716+1832)/6

Week Demand3-week

MA Forecast1 13002 13563 1442 13664 1576 1458 13665 1716 1578 14586 1832 1708 15787 1996 1848 17088 2028 1952 18489 2048 2024 195210 2200 2092 202411 2214 2154 209212 2420 2278 2154

Week Demand6-week

MA Forecast1 13002 13563 14424 15765 17166 1832 15377 1996 1653 15378 2028 1765 16539 2048 1866 176510 2200 1970 186611 2214 2053 197012 2420 2151 2053


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MAD to Compare Two or More Methods

t At 3-P-MA Forecast1 13682 17583 1020 13824 1470 1416 13825 1008 1166 14166 1530 1336 11667 1572 1370 13368 1488 1530 13709 1704 1588 153010 1566 1586 158811 1548 1606 158612 1236 1450 1606


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How do we measure errors?

MADDeviation AbsoluteMean

Standard Deviation of Error = 1.25MAD

Error is assumed to be normally distributed A MEAN (AVERAGE) = 0 STANDARD DEVIATION = 1.25MAD

Therefore, our forecast is also normally distributed A MEAN (AVERAGE) = Ft STANDARD DEVIATION = 1.25MAD

periodsofNumber

FA tt ||

Error = At - Ft


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MAD for One Method

But. Compare two or more forecasting techniques only over a period when data is available for all techniques.

t At 3-P-MA Forecast Deviation AD 1 13682 17583 1020 13824 1470 1416 1382 88 885 1008 1166 1416 -408 4086 1530 1336 1166 364 3647 1572 1370 1336 236 2368 1488 1530 1370 118 1189 1704 1588 1530 174 17410 1566 1586 1588 -22 2211 1548 1606 1586 -38 3812 1236 1450 1606 -370 370

MAD 20213 Forecast 1450


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Compare Two Methods

t At 3-P-MA Forecast Error AD 6-P-MA Forecast Error AD 1 13682 17583 1020 13824 1470 1416 1382 88 885 1008 1166 1416 -408 4086 1530 1336 1166 364 364 13597 1572 1370 1336 236 236 1393 1359 213 2138 1488 1530 1370 118 118 1348 1393 95 959 1704 1588 1530 174 174 1462 1348 356 35610 1566 1586 1588 -22 22 1478 1462 104 10411 1548 1606 1586 -38 38 1568 1478 70 7012 1236 1450 1606 -370 370 1519 1568 -332 332

MAD 159.7 195.013 Forecast 1450 1519


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Moving Average Comparison

How many periods should we use for forecasting? 6-week forecast is 1519 and MAD is 195 3-week forecast is 1450 and MAD is almost 160 3-week MAD is lower than 6-week MAD

Seems we prefer 3-week to 6-week. So … should we use as many periods as possible?


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Check a Second Example

t At 3-P-MA Forecast Error AD 6-P-MA Forecast Error AD 1 11282 18663 1182 13924 1434 1494 1392 42 425 1890 1502 1494 396 3966 1338 1554 1502 -164 164 14737 1104 1444 1554 -450 450 1469 1473 -369 3698 1716 1386 1444 272 272 1444 1469 247 2479 1650 1490 1386 264 264 1522 1444 206 20610 1692 1686 1490 202 202 1565 1522 170 17011 1320 1554 1686 -366 366 1470 1565 -245 24512 1758 1590 1554 204 204 1540 1470 288 288

MAD 293.0 254.213 Forecast 1590 1540


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MA comparison

Note that MAD is now lower for the 6-week than for the 3-week MA. 3-week MAD is 293 6-week MAD is almost 254

What is going on?


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Moving Average: Observations

A large number of periods will cause the moving average to respond slowly to changes. A smooth curve.

A small number of periods will be more reactive. Response to the most current changes.

Long term investors stay with larger number of periods. Day-trades, with smaller number of periods.

Try many different time window sizes, and choose the one with the lowest MAD.


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Moving Average: Microsoft


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Tracking Signal

MAD

ForecastActualTS

)(

||

)( periods) of (#

ForecastActual

ForecastActualTS

t At Ft |At-Ft| SUM|At-Ft| MAD At-Ft SUM(At-Ft) TS

1 690

2 680 690 10.0 10.0 10.0 -10.0 -10.0 -1.0

3 720 685.0 35.0 45.0 22.5 35.0 25.0 1.1

4 680 702.5 22.5 67.5 22.5 -22.5 2.5 0.1

5 740 691.3 48.8 116.3 29.1 48.8 51.3 1.8

6 670 715.6 45.6 161.9 32.4 -45.6 5.6 0.2

7 660 692.8 32.8 194.7 32.4 -32.8 -27.2 -0.8

8 710 676.4 33.6 228.3 32.6 33.6 6.4 0.2

9 660 693.2 33.2 261.5 32.7 -33.2 -26.8 -0.8


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Tracking Signal

Tracking Signal

UCL

LCL

Time

Are our observations within UCL and LCL?Is there any systematic error?

MAD

ForecastActualTS

)(


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UCL

LCL

Time

Tracking Signal

Tracking Signal

MAD

ForecastActualTS

)(


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Basic Applications of MAD and TS

MAD To select the most appropriate forecasting

method among two or more candidate methods To estimate the Standard Deviation of forecast

TS To check if TS is between ULC and LCL To check if TS does not show any systematic

pattern

In practice UCL=5, LCL = -5


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Predictions are usually difficult,

especially about the future.

Yogi Berra

The former New York Yankees Catcher

Moving Average 1Ardavan Asef-Vaziri 6/4/2009 Forecasting -1 Chapter 7 Demand Forecasting in a Supply...

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