Title: Introduction to System Engineering ISE 102 Spring 2007 Notes
1Introduction to System Engineering ISE 102
Spring 2007 Notes Course Materials
Asst. Prof. Dr. Mahmut Ali GOKCE ISE Dept.
Faculty of Computer Sciences
2This Lecture
 Review of Week 1
 Productivity
 Modelling
 Forecasting
3Review 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.
4Our Job

 The design, operation, and improvement of the
production systems that create the firms
products or services.
5Recall 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!
6Review Value Adding Process
Inputs
Outputs
Material
Product
Workforce
Value Adding (Transformation) Process
Capital
Service
Knowledge
7Added Value at Operational Level
 The aim of the business organization should be
to add value at each component of the production
system. All nonvalue adding operations need to
be carefully screened and eliminated. A nonvalue
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.
8Some 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.
9Productivity
 Factor productivity
 Partial measures
 output/(single input)
 Multifactor measures
 output/(multiple inputs)
 Total factor productivity
 Total measure
 output/(total inputs)
10Measures of Productivity
11Examples of Partial Productivity Measures
12How 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.
13Example Productivity
14Example 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
15Example Multifactor Productivity
MFP Output Labor Materials
MFP (10,000 units)(10) (500)(9)
(5000) (25000)
MFP 2.90
16From Idea to Product
 Decision problems
 Forecasting
 Product and service design
 Capacity Planning
 Facilities Layout
 Location
 Transportation/assignment
 Inventory
 Aggregate Planning
 Scheduling
 Project Management
17From Idea to Product
 Methods
 L.P. modelling and graphical solution
 Special algorithms tailored for certain problems
 Simulation
 Stochastic processes
 IP/NLP
 Statistics
 DP
18Problem Solving Approach of OR
Problem Definition
Generation of Alternatives
Evaluation of Alternatives
Selection of an Alternative
Implementation of the Alternative
19What 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.
20Real World  Model World
f
Real World
Model
f1
21Types 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
modelssimulators to represent reality)
22Purposes 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.
23Advantages 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
24Tradeoffs 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
26Algorithms to Solve Models
 An algorithm is a recipe to solve a problem.
 A stepbystep problemsolving 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
27FORECASTING
28Introduction
 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!
29Why 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, makeorbuy decisions
Product/service design Design of new products and services
30Keep 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
31Types 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.
32Judgmental 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)
33Time Series Model Building
 A timeseries 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
34Some Behaviors Typically Observed
 Trend
 E.g., population shifts, change in income.
Usually a longterm 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
35Forecast Variations
36Types 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
37Naive Forecasts
38Naïve 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
39Uses 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(t1)
 Seasonal variations forecast for this season
will be the value of last season.  Ft A(t1)
 Data with trends forecast is last value plus or
minus the difference between the last two values
of the series.  Ft A(t1) (A(t1) A(t2))
40Random Variations
Actual
Demand
Naïve Forecast
Smoothing may reduce the errors!
t
Average
t
41Techniques 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 oftenused 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
42Simple Moving Average
 A moving average forecast uses number of the most
recent actual data values in generating a
forecast.  Ft average(Atn , Atn1 , , At1) 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(A63,A631, A61)average(A3,A4,A5)
(434041)/3 41.33
What would your estimate be if you used naïve
approach?
43Simple 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
44Simple Moving Average  Example
Actual
MA5
MA3
45Weighted Moving Average
 A weighted moving average forecast is a weighted
average of a number of the most recent actual
data values.  Ft w1Atn w2 Atn1 wn At1 ,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
46Exponential 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 Ft1 ?(At1 Ft1) 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.
47Example of Exponential Smoothing
48Picking 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.
49Techniques 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.
50Linear 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 straightforward
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.
51Insights 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!
53Linear Trend Equation Example
54Linear 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?
55Linear Trend Calculation
812

6.3(15)
a
143.5
5
y 143.5 6.3t
y 143.5 6.36 181.5
56Trends 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 Tt1 b(TAFt
TAFt1 Tt1)
57Insights TAES
 TAFt1 St Tt where
 St smoothed forecast TAFt ?(At TAFt)
 Tt current trend estimate Tt1 b(TAFt TAFt1
Tt1) (1b) Tt1 b(TAFt TAFt1 )
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.
58Associative 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
59Time Series vs. Associative(Causal) Models
Sales2003 Sales2002 Sales2001
Time Series Model
Year 2004 Sales
Casual Models
Price Population Advertising
Causal Model
Year 2004 Sales
60Linear Model Seems Reasonable
61Comments 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 timedependent prefer time series
analysis.  Identify the all necessary predictors might use
correlation as an indicator of relations.
62Measures 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
63MAD MSE
64Tracking Signal
65Example 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
66Example 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 Ft1
?(At1 Ft1)
67Example 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
68Example 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
69Example 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!
70Example 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
71Example Improving the Accuracy
MAD 0.75 and MSE1.06 Note that it was MAD
0.93 and MSE1.23 without aggregation.
72Exponential Smoothing
T32
73Linear Trend Equation
T33
74Trend Adjusted Exponential Smoothing
T34
75Simple Linear Regression
T35
76Which Forecasting Approach to Take?
http//129.128.94.195/mgtsc352/web_notes/forecasti
ng/2_02.asp2.2.3
77Resources
 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