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Introduction to System Engineering ISE 102 Spring 2007 Notes

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Title: Introduction to System Engineering ISE 102 Spring 2007 Notes


1
Introduction to System Engineering ISE 102
Spring 2007 Notes Course Materials
Asst. Prof. Dr. Mahmut Ali GOKCE ISE Dept.
Faculty of Computer Sciences
2
This Lecture
  • Review of Week 1
  • Productivity
  • Modelling
  • Forecasting

3
Review Business Organizations
  • Business organizations are devoted to producing
    good and/or providing services.
  • Operations, Finance and Marketing are key
    functions of business organizations.
  • The operation function consist of all activities
    directly related to producing good and services.
  • Manufacturing and Service systems have many
    operational decisions in common.
  • Forecasting
  • Locations selection
  • Scheduling
  • etc.
  • Hence we dont limit our selves to only
    manufacturing systems.

4
Our Job
  • The design, operation, and improvement of the
    production systems that create the firms
    products or services.

5
Recall Decision Making
  • System Design
  • Capacity
  • Location
  • Arrangement of departments
  • Product and Service Planning
  • Acquisition and planning of equipment
  • System Operation
  • Personnel
  • Inventory
  • Scheduling
  • Project Management
  • Quality Assurance

System Improvement!
6
Review Value Adding Process
Inputs
Outputs
Material
Product
Workforce
Value Adding (Transformation) Process
Capital
Service
Knowledge
7
Added Value at Operational Level
  • The aim of the business organization should be
    to add value at each component of the production
    system. All non-value adding operations need to
    be carefully screened and eliminated. A non-value
    adding operation is an operation that does not
    add value directly transferable to the customer,
    i.e., if it is eliminated, the benefit accrued by
    the customer from the product does not diminish.
  • How do we measure the performance of the system?
  • One of the measures is productivity.

8
Some Definitions Productivity
  • Productivity is a measure of the effective use of
    resources, defined as the ratio of output to
    input.
  • Kinds of Productivity
  • Factor productivity (output is related to one or
    more of the resources of production, such as
    labour, capital, land, raw material, etc.)
  • Total factor productivity (an overall measure
    expressing the contribution of the resources of
    production to the efficiency attained by a firm.)
  • Both types of productivity can be expressed as
    physical productivity with output being measured
    in physical units and as well as value
    productivity with output being measured in
    monetary units.

9
Productivity
  • Factor productivity
  • Partial measures
  • output/(single input)
  • Multi-factor measures
  • output/(multiple inputs)
  • Total factor productivity
  • Total measure
  • output/(total inputs)

10
Measures of Productivity
11
Examples of Partial Productivity Measures
12
How to use Productivity?
  • Productivity measures can be used to track
    performance over time. This allows managers to
    judge performance and and to decide where
    improvements are needed.
  • If productivity has slipped in a certain area
    examine the factors and determine the reasons
  • Productivity also can be used to benchmark the
    companies standing with respect to competitors.
  • How to position the company with respect to the
    best in the classroom. Determine the areas the
    company is behind and take actions accordingly.

13
Example Productivity
14
Example Labor Productivity
  • 10,000 units/500hrs 20 units/hour or we can
    arrive at a unitless figure
  • (10,000 unit 10/unit)/(500hrs 9/hr) 22.22

15
Example Multifactor Productivity
MFP Output Labor Materials
MFP (10,000 units)(10) (500)(9)
(5000) (25000)
MFP 2.90
16
From Idea to Product
  • Decision problems
  • Forecasting
  • Product and service design
  • Capacity Planning
  • Facilities Layout
  • Location
  • Transportation/assignment
  • Inventory
  • Aggregate Planning
  • Scheduling
  • Project Management

17
From Idea to Product
  • Methods
  • L.P. modelling and graphical solution
  • Special algorithms tailored for certain problems
  • Simulation
  • Stochastic processes
  • IP/NLP
  • Statistics
  • DP

18
Problem Solving Approach of OR
Problem Definition
Generation of Alternatives
Evaluation of Alternatives
Selection of an Alternative
Implementation of the Alternative
19
What Is A Model ?
  • A model is the selected abstract representation
    of a real situation or behaviour with suitable
    language or expression.
  • Since a model is an explicit representation of
    reality, it is generally less complex than
    reality.
  • The level of abstraction depends on the subject,
    the purpose, and the environment of modelling.
  • It is important that it is sufficiently complete
    to approximate those aspects of reality to be
    investigated.

20
Real World - Model World
f
Real World
Model
f-1
21
Types of Models
  • Physical models (e.g., molecular structures, ship
    models - scaling and relative positioning are
    important)
  • Conceptual models (e.g., organizational charts,
    maps, circuit diagrams, relationship charts -
    relations among entities are important)
  • Mathematical models (e.g., optimization models,
    Hookes law - range of validity is important)
  • Simulation models (computer programs or physical
    models-simulators to represent reality)

22
Purposes of Modelling
  • To understand better the subject of modelling.
  • To describe the subject of modelling.
  • To create a means to exchange views on the
    subject.
  • To predict and control the behaviour of the
    subject.

23
Advantages of modeling a Business System
  • Definition of business objectives, practices,
    structure, and constraints
  • Definition and establishment of business
    parameters and costs
  • Systematic evaluation of alternative system
    alternatives
  • Quick response through sensitivity analysis

24
Tradeoffs in Modeling
  • Realism vs. Solvability
  • Decision Support vs. Decision Making

25
Operations Research Model Types
  • Descriptive Models (Decision support)
  • Statistics
  • Simulation
  • Queuing
  • Prescriptive Models (Decision making)
  • Optimization
  • Linear Programming
  • Nonlinear Programming
  • Network Flows

26
Algorithms to Solve Models
  • An algorithm is a recipe to solve a problem.
  • A step-by-step problem-solving procedure,
    especially an established, recursive
    computational procedure for solving a problem in
    a finite number of steps. ( http//www.dictionary
    .com )
  • Efficient vs. Effective
  • Optimal vs. Heuristic
  • Primal vs. Dual
  • Construction vs. Improvement
  • Alternative Generating vs. Alternative Selecting

27
FORECASTING
28
Introduction
  • Forecasting is to predict the future by analysis
    of relevant data.
  • Forecasts are the basis (input) for a wide range
    of decisions in operations management and
    control.
  • Forecasts are typically developed by the
    Marketing function, but Operations function
    is usually called on to assist in its
    development.
  • Furthermore, Operations is the major user of
    forecasts.
  • One can forecast anything. We will focus on
    demand forecast. But techniques are there!

29
Why Do We Forecast?
Accounting Cost/profit estimates for new products
Finance Timing and amount of cash flow and funding
Human Resources Hiring/recruiting/training activities
Marketing Pricing, promotion, strategy
MIS IT/IS systems, services
Operations Schedules, MRP,inventory planning, make-or-buy decisions
Product/service design Design of new products and services
30
Keep in Mind
  • Assumes causal system past gt future
  • Forecasts are always wrong!
  • Forecasts more accurate for groups vs.
    individuals canceling effect
  • Forecast accuracy decreases as time horizon
    increases

He who lives by the crystal ball ends up eating
glass. An old Klingon proverb
31
Types of Forecasts
  • Judgmental - uses subjective input such as market
    surveys, expert opinion, etc.
  • Time series - uses historical data assuming the
    future will be like the past
  • Associative models (casual models) - uses
    explanatory variables to predict the future,
    demand for paint might be related to variables
    such as price, quality, etc.

32
Judgmental Forecasts
  • There may not be enough time to gather data and
    analyze quantitative data or no data at all.
  • Expert Judgment managers(marketing,operations,fi
    nance,etc.)
  • Be careful about who you call an expert
  • Sales force composite
  • Recent experience may influence their perceptions
  • Consumer surveys
  • Requires considerable amount of knowledge and
    skill
  • Opinions of managers and staff
  • Delphi method a series of questionnaire,
    responses are kept anonymous, new questionnaires
    are developed based on earlier results Rand
    corporation (1948)

33
Time Series Model Building
  • A time-series is a time ordered sequence of
    observations taken at regular intervals over a
    period of time.
  • The data may be demand, earnings, profit,
    accidents, consumer price index,etc.
  • The assumption is future values of the series can
    be estimated from past values
  • One need to identify the underlying behavior of
    the series - pattern of the data

34
Some Behaviors Typically Observed
  • Trend
  • E.g., population shifts, change in income.
    Usually a long-term movement in data
  • Seasonality
  • Fairly regular variations, e.g., Friday nights in
    restaurants, new year in shopping malls, rush
    hour traffic., etc.
  • Cycles
  • Wavelike variations lasting more than a year,
    e.g. economic recessions, etc.
  • Irregular variations
  • Caused by unusual circumstances, e.g., strikes,
    weather conditions, etc.
  • Random variations
  • Residual variations after all other behaviors are
    accounted for. Caused by chance

35
Forecast Variations
36
Types of Time Series Models
  • We will cover the following techniques in this
    section
  • Naïve
  • Techniques for averaging
  • Moving average
  • Weighted moving average
  • Exponential smoothing
  • Techniques for trend
  • Linear equations
  • Trend adjusted exponential smoothing
  • Techniques for seasonality
  • Techniques for Cycles

37
Naive Forecasts
38
Naïve Forecasts
  • Simple and widely used technique.
  • A single previous value of a time series as the
    basis for forecast.
  • Virtually no cost.
  • Data analysis is nonexistent, easily
    understandable
  • Cannot provide high accuracy, may be used as a
    standard for accuracy.
  • Can be used in case of,
  • Stable series
  • Series with seasonality
  • Series with trend

39
Uses for Naïve Forecasts
  • Ai Actual value in period i
  • Ft Forecast for time period t
  • Stable time series data last data becomes the
    forecast for the next period
  • Ft A(t-1)
  • Seasonal variations forecast for this season
    will be the value of last season.
  • Ft A(t-1)
  • Data with trends forecast is last value plus or
    minus the difference between the last two values
    of the series.
  • Ft A(t-1) (A(t-1) A(t-2))

40
Random Variations
Actual
Demand
Naïve Forecast
Smoothing may reduce the errors!
t
Average
t
41
Techniques for Averaging
  • Inherent in the data taken over time is some form
    of random variation. There exist methods for
    reducing of cancelling the effect due to random
    variation. An often-used technique in industry is
    "smoothing". This technique, when properly
    applied, reveals more clearly the underlying
    trend, seasonal and cyclic components.
  • Moving average
  • Weighted moving average
  • Exponential smoothing

42
Simple Moving Average
  • A moving average forecast uses number of the most
    recent actual data values in generating a
    forecast.
  • Ft average(At-n , At-n1 , , At-1) where n is
    the window size (number of data points used in
    the moving average.
  • Example
  • Suppose monthly sales data for the past 5 months
    was 42 40 43 40 41. What would be your
    forecast for the 6th month sales by using MA with
    n3 ?
  • F6 average(A6-3,A6-31, A6-1)average(A3,A4,A5)
    (434041)/3 41.33

What would your estimate be if you used naïve
approach?
43
Simple Moving Average - Example
  • Consider the following data,
  • Starting from 4th period one can start
    forecasting by using MA3. Same is true for MA5
    after the 6th period.
  • Actual versus predicted(forecasted) graphs are as
    follows

44
Simple Moving Average - Example
Actual
MA5
MA3
45
Weighted Moving Average
  • A weighted moving average forecast is a weighted
    average of a number of the most recent actual
    data values.
  • Ft w1At-n w2 At-n1 wn At-1 ,where n is
    the window size and w1 w2 wn1
  • Good thing is you can give more importance to
    more recent data. Problem is identifying the
    weights, which is usually achieved by trial and
    error.
  • Suppose monthly sales data for the past 5 months
    was 42 40 43 40 41. What would be your
    forecast for the 6th month sales by using WMA
    with n3 and w10.2, w20.3, w30.5
  • F6 0.2430.3400.541 41.1

46
Exponential Smoothing
  • Exponential smoothing is a sophisticated
    weighted average. Each new forecast is based on
    the previous forecast plus a percentage of the
    difference between that forecast and the actual
    value of the series at that point.
  • It is similar to a feedback controller.
  • Next forecast Previous forecast ?(Actual
    -Previous forecast )
  • Ft Ft-1 ?(At-1- Ft-1) where ? is the
    smoothing constant.
  • Suppose monthly sales data for the past 5 months
    was 42 40 43 40 41. What would be your
    forecast for the 2nd month sales by using ES with
    ?0.1 ? What about 3th month?
  • F2 42 no data available. Check the actual. Its
    40. Difference is -2.
  • F3 F2 0.1 -2 41.8.

47
Example of Exponential Smoothing
48
Picking a Smoothing Constant
Lower values of ??are preferred when the
underlying trend is stable and higher values of
??are preferred when it is susceptible to change.
Note that if ??is low your next forecast highly
depends on your previous ones and feedback is
less effective.
49
Techniques For Trends
  • Develop an equation that will suitably describe
    the trend.
  • Trend may be linear or it may not.
  • We will focus on linear trends.
  • Some common nonlinear trends.

50
Linear Trend Equation - Notation
A linear trend equation has the form Yt a
bt
  • b is similar to the slope. However, since it is
    calculated with the variability of the data in
    mind, its formulation is not as straight-forward
    as our usual notion of slope.

yt Forecast for period t, a value of yt at t0
and b is the slope of the line.
51
Insights For Calculating a and b
  • Suppose that you think that there is a linear
    relation between the height (ft.) and weight
    (pounds) of humans. You collected data and want
    to fit a linear line to this data.
  • Weight a b Height
  • How do you estimate a and b?

For further information refer to http//www.stat.p
su.edu/bart/0515.doc or any statistics book!
52
More Insights For Calculating a and b
  • Demand observed for the past 11 weeks are given.
  • We want to fit a linear line (DabT) and
    determine a and b that minimizes the sum of the
    squared deviations. (Why squared?)

A little bit calculus, take the partial
derivatives and set it equal to 0 and solve for a
and b!
53
Linear Trend Equation Example
54
Linear Trend Calculation
If we fit a line to the observed sales of the
last five months,
Question is forecasting the sales for the 6th
period. What do you think it will be?
55
Linear Trend Calculation
812
-
6.3(15)
a




143.5

5
y 143.5 6.3t
y 143.5 6.36 181.5
56
Trends Adjusted Exponential Smoothing
  • A variation of simple Exponential Smoothing can
    be used when trend is observed in historical
    data.
  • It is also referred as double smoothing.
  • Note that if a series has a trend and simple
    smoothing is used the forecasts will all lag the
    trend. If data are increasing each forecast will
    be low! When trend exists we may improve the
    model by adjusting for this trend. (C.C. Holt)
  • Trend Adjusted Forecasts (TAF) is composed of two
    elements a smoothed error and a trend factor
  • TAFt1 St Tt where
  • St smoothed forecast TAFt ?(At TAFt)
  • Tt current trend estimate Tt-1 b(TAFt
    TAFt-1 Tt-1)

57
Insights TAES
  • TAFt1 St Tt where
  • St smoothed forecast TAFt ?(At TAFt)
  • Tt current trend estimate Tt-1 b(TAFt TAFt-1
    Tt-1) (1-b) Tt-1 b(TAFt TAFt-1 )
    Weighted average of last trend and last forecast
    error.
  • ? and b are smoothing constants to be selected
    by the modeler.
  • St is same with original ES feedback for the
    forecast error is added to previous forecast with
    a percentage of ?
  • If there is trend ES will have a lag. We must
    also include this lag to our model. Hence Tt is
    added where
  • Tt is the trend and updated each period.

58
Associative Forecasting
  • Time is not the only factor for future demand!
  • We have to identify the related variables that
    can be used to predict values of the variable of
    interest.
  • Sales of beef may be related to price and the
    prices of substitutes such as fish, chicken and
    lamb.
  • Predictor variables - used to predict values of
    variable interest
  • Simple Linear Regression - technique for fitting
    a line to a set of points. Simplest and widely
    used form of regression.
  • Least squares line - minimizes sum of squared
    deviations around the line

59
Time Series vs. Associative(Causal) Models
  • Time Series Models

Sales2003 Sales2002 Sales2001
Time Series Model
Year 2004 Sales
Casual Models
Price Population Advertising
Causal Model
Year 2004 Sales
60
Linear Model Seems Reasonable
61
Comments on Linear Regression
  • Assumptions
  • Variations around the line are random no trend
    or seasonality or cycles.
  • Deviations around the line is normally
    distributed.
  • Predictions are being made only within the range
    of observations.
  • To obtain the best results
  • Always plot the data verify that linear
    relationship is appropriate.
  • If data is time-dependent prefer time series
    analysis.
  • Identify the all necessary predictors might use
    correlation as an indicator of relations.

62
Measures of Forecast Accuracy
  • Error - difference between actual value and
    predicted value
  • Mean absolute deviation (MAD)
  • Average absolute error
  • Mean squared error (MSE)
  • Average of squared error
  • Tracking signal
  • Ratio of cumulative error and MAD

63
MAD MSE
64
Tracking Signal
65
Example Improving the Accuracy
Months Week 1 Week 2 Week 3 Week 4 Average
1 7 7 5 9 7
2 3 3 6 7 4.75
3 9 3 6 6 6
4 9 9 9 6 8.25
5 6 4 5 8 5.75
6 8 3 9 4 6
7 6 3 6 8 5.75
8 7 7 5 7 6.50
66
Example Improving the Accuracy
Time versus sales plot of 32 weeks for the cars
sold. Suppose we were at week 28 and would like
to forecast the sales for 29 30 31 and
32. Lets use ES with ? 0.1 Recall Ft Ft-1
?(At-1- Ft-1)
67
Example Improving the Accuracy
We applied the formulas and predicted for weeks
29 30 31 and 32. The accuracy of the
forecast in terms of MAD 0.93 and MSE1.23
68
Example Improving the Accuracy
Months Average
1 7
2 4.75
3 6
4 8.25
5 5.75
6 6
7 5.75
8 6.5
Aggregated Sales
69
Example Improving the Accuracy
Aggregated Sales
We can now predict the 8th month demand given the
previous 7 months and weekly forecasts may be
monthly averages!
70
Example Improving the Accuracy
ES forecasts 6.58 average sales for the 8th
month. In this case error in terms of MAD and MSE
would be as follows
71
Example Improving the Accuracy
MAD 0.75 and MSE1.06 Note that it was MAD
0.93 and MSE1.23 without aggregation.
72
Exponential Smoothing
T3-2
73
Linear Trend Equation
T3-3
74
Trend Adjusted Exponential Smoothing
T3-4
75
Simple Linear Regression
T3-5
76
Which Forecasting Approach to Take?
http//129.128.94.195/mgtsc352/web_notes/forecasti
ng/2_02.asp2.2.3
77
Resources
  • Textbooks!
  • http//129.128.94.195/mgtsc352/web_notes/forecasti
    ng/toc.asp (MGTSC 352)
  • http//www.itl.nist.gov/div898/handbook/pmc/sectio
    n4/pmc4.htm
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