chapter 7 demand forecasting in a supply chain

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

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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


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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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Forecasting Objectives

Introduce the basic concepts of forecasting and its importance within an organization.

Identify several of the more common forecasting methods

Measure and assess the errors that exist in all forecasts


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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 TechniquesTime Series Analysis Causal Relationship Forecasting


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Qualitative Methods

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

Subjective, judgmentalBased on intuition, estimates, and opinions

Expert Opinions Market Research Historical Analogies


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Time Series Methods

Analyzing data by time periods to determine if trends or patterns occur. Moving average Exponential smoothing More sophisticated techniques available


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Causal Relationship Methods

Relating demand to an underlying factor other than time. (Regression) (Number of socks sold depends on number of running shoes sold.)

Multiple Regression Models


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Forecasts are rarely perfect because of randomness.

Beside the average, we also need a measure of variation, which is called standard deviation

Forecasts are more accurate for groups of items than for individuals.

Forecast accuracy decreases as the time horizon increases.

I see that you willget an A this semester.

Four Basic Characteristics of Forecasts


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Time Series Models

Models for short term decisionsInventory decisions

Stock levels of Gameboys Production planning decisions

Staffing decisions Call center scheduling Fast food chain


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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

Week Demand1 3582 9523 6234 1865 7146 537 8938 4259 535

10 4711 95612 257

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


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Week Demand 3-week MA Forecast1 3582 9523 623 644.334 186 587.00 644.335 714 507.67 587.006 53 317.67 507.677 893 553.33 317.678 425 457.00 553.339 535 617.67 457.0010 47 335.67 617.6711 956 512.67 335.6712 257 420.00 512.6713 420.0

3-Period and 6-Period Moving Average

(358+952+623)/3 (358+952+623+186+714+53)/6

Week Demand 6-week MA Forecast1 3582 9523 6234 1865 7146 53 481.007 893 570.17 481.008 425 482.33 570.179 535 467.67 482.3310 47 444.50 467.6711 956 484.83 444.5012 257 518.83 484.8313 518.8


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Graphical Comparison

0

200

400

600

800

1000

1200

Week

Demand

3-week MA

6-week MA

6-week MA is smoother than 3-week MA, which appears to result in better predictions.

How do we measure which one is doing better?


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How do we measure errors?

MADDeviation AbsoluteMean

Standard Deviation of Error = 1.25 MAD

Error is assumed to NORMALLY DISTRIBUTED with A MEAN (AVERAGE) = 0 STANDARD DEVIATION = 1.25* MAD

periodsofNumberFA tt ||


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MAD for One Method

Week Demand 3-week MA Forecast AD 1 3582 9523 623 644.334 186 587.00 644.33 458.335 714 507.67 587.00 127.006 53 317.67 507.67 454.677 893 553.33 317.67 575.338 425 457.00 553.33 128.339 535 617.67 457.00 78.0010 47 335.67 617.67 570.6711 956 512.67 335.67 620.3312 257 420.00 512.67 255.67

MAD 363.113 Forecast 420.0

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


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MAD to Compare Two or More Methods

Week Demand 3-week MA Forecast AD 6-week MA Forecast AD 1 3582 9523 623 644.334 186 587.00 644.33 458.335 714 507.67 587.00 127.006 53 317.67 507.67 454.67 481.007 893 553.33 317.67 575.33 570.17 481.00 412.008 425 457.00 553.33 128.33 482.33 570.17 145.179 535 617.67 457.00 78.00 467.67 482.33 52.6710 47 335.67 617.67 570.67 444.50 467.67 420.6711 956 512.67 335.67 620.33 484.83 444.50 511.5012 257 420.00 512.67 255.67 518.83 484.83 227.83

MAD 371.4 295.013 Forecast 420.0 518.8


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Moving Average Comparison

How many periods should we use for forecasting? 6-week forecast is 518.8 and MAD is 295 3-week forecast is 420 and MAD is 371.4 6-week MAD is lower than 3-week MAD

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

possible?


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Check a Second Example

Week Demand 3-week MA Forecast AD 6-week MA Forecast AD 1 6502 6783 720 682.674 785 727.67 682.67 102.335 859 788.00 727.67 131.336 920 854.67 788.00 132.00 768.677 1000 926.33 854.67 145.33 827.00 768.67 231.338 1015 978.33 926.33 88.67 883.17 827.00 188.009 1025 1013.33 978.33 46.67 934.00 883.17 141.8310 1100 1046.67 1013.33 86.67 986.50 934.00 166.0011 1109 1078.00 1046.67 62.33 1028.17 986.50 122.5012 1210 1139.67 1078.00 132.00 1076.50 1028.17 181.83

MAD 93.6 171.913 Forecast 1139.7 1076.5


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MA comparison

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

3-week MAD is 93.6 6-week MAD is 171.9What is going on?

0

200

400

600

800

1000

1200

1400

1 2 3 4 5 6 7 8 9 10 11 12

3-week MA

6-week MA

Demand


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Moving Average: Observations

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

When there is a obvious current trend in the data, using larger number of periods results in a forecast with larger error.

In general, there is a trade-off between using more periods to smooth out random variations and using less periods to more closely follow trends.

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


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Tracking Signal

MADForecastActual

TS

)(

||)(

periods) of (#ForecastActualForecastActual

TS

t At Ft |At-Ft| SUM|At-Ft| MAD At-Ft SUM(At-Ft) TS1 7002 724 700

3 710 712.0 2.0 2.0 2.0 -2.0 -2.0 -1.04 715 711.0 4.0 6.0 3.0 4.0 2.0 0.75 710 713.0 3.0 9.0 3.0 -3.0 -1.0 -0.36 710 711.5 1.5 10.5 2.6 -1.5 -2.5 -1.07 715 710.8 4.3 14.8 3.0 4.3 1.8 0.68 710 712.9 2.9 17.6 2.9 -2.9 -1.1 -0.49 720 711.4 8.6 26.2 3.7 8.6 7.4 2.0


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Tracking Signal

Tracking Signal

UCL

LCL

Time

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


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UCL

LCL

Time

Tracking Signal

Tracking Signal


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Predictions are usually difficult, especially about the future.

Yogi BerraThe former New York Yankees Catcher

chapter 7 demand forecasting in a supply chain

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