Www.izmirekonomi.edu.tr Mahmut Ali Gökçe 1 Introduction to System Engineering ISE 102 Spring 2007 Notes & Course Materials Asst. Prof. Dr. Mahmut Ali GOKCE

1www.izmirekonomi.edu.trMahmut Mahmut Ali GökçeAli Gökçe

Introduction to System Engineering ISE 102 Spring 2007Notes & Course Materials

Asst. Prof. Dr. Mahmut Ali GOKCE

ISE Dept. Faculty of Computer Sciences

www.izmirekonomi.edu.trMahmut Ali GökçeMahmut Ali Gökçe

This Lecture

Review of Week 1 Productivity Modelling Forecasting


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 don’t limit our selves to only manufacturing systems.


Our Job

The design, operation, and improvement of the production systems that create the firm’s products or services.


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!


Review: Value Adding Process

Value Adding (Transformation)

Process

Value Adding (Transformation)

Process

ProductProduct

ServiceService

WorkforceWorkforce

KnowledgeKnowledge

CapitalCapital

MaterialMaterial

InputsOutputs


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.


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.


Productivity

Factor productivity Partial measures

output/(single input) Multi-factor measures

output/(multiple inputs) Total factor productivity

Total measure output/(total inputs)

Productivity = Outputs

Inputs


Measures of Productivity

Partial Output Output Output Outputmeasures Labor Machine Capital Energy

Multifactor Output Outputmeasures Labor + Machine Labor + Capital + Energy

Total Goods or Services Producedmeasure All inputs used to produce them


Units of output per kilowatt-hourDollar value of output per kilowatt-hour

Energy Productivity

Units of output per dollar inputDollar value of output per dollar input

Capital Productivity

Units of output per machine hourmachine hour

Machine Productivity

Units of output per labor hourUnits of output per shiftValue-added per labor hour

Labor Productivity

Examples of Partial Productivity Measures


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.


Example: Productivity10,000 Units Produced

Sold for $10/unit

500 labor hours

Labor rate: $9/hr

Cost of raw material: $5,000

Cost of purchased material: $25,000

What is the 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

Example: Labor Productivity


Example: Multifactor Productivity

MFP = OutputLabor + Materials

MFP = (10,000 units)*($10)(500)*($9) + ($5000) + ($25000)

MFP = 2.90


From Idea to ProductDecision problems

Forecasting Product and service design Capacity Planning Facilities Layout Location Transportation/assignment Inventory Aggregate Planning Scheduling Project Management


From Idea to Product

Methods L.P. modelling and graphical solution Special algorithms tailored for certain problems Simulation Stochastic processes IP/NLP Statistics DP …


Problem Solving Approach of OR

Problem Definition

Generation of Alternatives

Evaluation of Alternatives

Selection of an Alternative

Implementation of the Alternative


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.


Real World - Model World

RealWorld

Model

f

f-1


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, Hooke’s law - range of validity is important)

Simulation models (computer programs or physical models-simulators to represent reality)


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.


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


Tradeoffs in Modeling

Realism vs. Solvability Decision Support vs. Decision Making


Operations Research :Model Types Descriptive Models (Decision support)

Statistics Simulation Queuing …

Prescriptive Models (Decision making) Optimization

Linear Programming Nonlinear Programming Network Flows

…


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

27www.izmirekonomi.edu.trMahmut Mahmut Ali GökçeAli Gökçe

FORECASTING


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!


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


Assumes causal systempast ==> future

Forecasts are always wrong!

Forecasts more accurate for groups vs. individuals – canceling effect

Forecast accuracy decreases as time horizon increases

I see that you willget an A this semester.

Keep in Mind…

‘He who lives by the crystal ball ends up eating glass.’

An old Klingon proverb


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.


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,finance,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)


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


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


Forecast Variations

Trend

Irregular variation

Seasonal variations

908988

Cycles

Trend with seasonal pattern


Types of Time Series ModelsWe 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


Naive Forecasts

Uh, give me a minute.... We sold 250 wheels lastweek.... Now, next week we should sell....


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

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))

Uses for Naïve Forecasts


Random Variations

Demand

t

Actual

Naïve Forecast

t

Average

Smoothing may reduce the errors!


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


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-n+1 , …, 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 n=3 ?

F6 = average(A6-3,A6-3+1, A6-1)=average(A3,A4,A5) =

(43+40+41)/3 = 41.33

What would your estimate be if you used naïve approach?


Simple Moving Average - Example

Period Actual MA3 MA5

1 42

2 40

3 43

4 40 41.7

5 41 41.0 6 39 41.3 41.27 46 40.0 40.68 44 42.0 41.89 45 43.0 42

10 38 45.0 4311 40 42.3 42.4

12 41.0 42.6

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;


Simple Moving Average - Example

35

37

39

41

43

45

47

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

Actual

MA3

MA5


Weighted Moving Average A weighted moving average forecast is a weighted

average of a number of the most recent actual data values. Ft = w1*At-n+ w2* At-n+1+ … wn* At-1 ,where n is the window

size and w1+ w2+ … + wn=1 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 n=3 and w1=0.2, w2=0.3, w3=0.5

F6 =0.2*43+0.3*40+0.5*41= 41.1


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. It’s 40. Difference is

-2. F3 = F2 +0.1* -2 = 41.8.


Period Actual Alpha = 0.1 Error Alpha = 0.4 Error1 422 40 42 -2.00 42 -23 43 41.8 1.20 41.2 1.84 40 41.92 -1.92 41.92 -1.925 41 41.73 -0.73 41.15 -0.156 39 41.66 -2.66 41.09 -2.097 46 41.39 4.61 40.25 5.758 44 41.85 2.15 42.55 1.459 45 42.07 2.93 43.13 1.87

Example of Exponential Smoothing


Picking a Smoothing Constant

35

40

45

50

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

Period

De

ma

nd

.1

.4

Actual

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.


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.

Parabolic

Exponential

Growth


Linear Trend Equation - Notation

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.

A linear trend equation has the form;

Yt = a + bt

0 1 2 3 4 5 t

Y

yt =Forecast for period t,

a= value of yt at t=0 and b is the slope of the line.


Insights For Calculating a and b

b = n (ty) - t y

n t 2 - ( t) 2

a = y - b t

n

Y = 28.011X - 11.598

100110120

130140150160

170180190

4.00 4.50 5.00 5.50 6.00 6.50 7.00

Height

Wei

gh

t

For further information refer tohttp://www.stat.psu.edu/~bart/0515.docor any statistics book!

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?


More Insights For Calculating a and bDemand observed for

the past 11 weeks are given.

We want to fit a linear line (D=a+bT) 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!


Linear Trend Equation Example

t yW e e k t 2 S a l e s t y

1 1 1 5 0 1 5 02 4 1 5 7 3 1 43 9 1 6 2 4 8 64 1 6 1 6 6 6 6 45 2 5 1 7 7 8 8 5

t = 1 5 t 2 = 5 5 y = 8 1 2 t y = 2 4 9 9( t ) 2 = 2 2 5


Linear Trend Calculation

140

150

160

170

180

190

0 2 4 6 8

Series1

Question is forecasting the sales for the 6th period. What do you think it will be?

If we fit a line to the observed sales of the last five months,


Linear Trend Calculation

y = 143.5 + 6.3t

a = 812 - 6.3(15)

5 =

b = 5 (2499) - 15(812)

5(55) - 225 =

12495 -12180

275 -225 = 6.3

143.5

y = 143.5 + 6.3*6= 181.5


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;

TAFt+1 = St + Tt where

St= smoothed forecast = TAFt + (At – TAFt)

Tt= current trend estimate= Tt-1 + (TAFt– TAFt-1 – Tt-1)


Insights: TAES TAFt+1 = St + Tt where

St= smoothed forecast = TAFt + (At – TAFt)

Tt= current trend estimate= Tt-1 + (TAFt– TAFt-1 – Tt-1)= (1-

Tt-1 + (TAFt– TAFt-1 ) Weighted average of last trend and

last forecast error. and 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.


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


Time Series vs. Associative(Causal) Models Time Series Models:

Causal Model

Year 2004 Sales

Price PopulationAdvertising

……

Casual Models:

Time Series Model

Year 2004Sales

Sales2003 Sales2002

Sales2001……


Linear Model Seems Reasonable

0

10

20

30

40

50

0 5 10 15 20 25

X Y7 152 106 134 1514 2515 2716 2412 2014 2720 4415 347 17

Y22 since X=10

10 ?


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.


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


MAD & MSE

MAD = Actual forecast

n

MSE = Actual forecast)

-1

2

n

(


Tracking Signal

Tracking signal = (Actual-forecast)

MAD

Tracking signal = (Actual-forecast)Actual-forecast

n


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



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.

Let’s use ES with =0.1 {Recall Ft = Ft-1 + (At-1- Ft-1) }

0

2

4

6

8

10

0 5 10 15 20 25 30 35



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 MSE=1.23

Week Actual ES Forecast Error MAD MSE1 72 7 7 0.003 5 7.0 -2.004 9 6.80 2.20

23 9 6.29 2.7124 4 6.56 -2.5625 6 6.30 -0.3026 3 6.27 -3.2727 6 5.95 0.0528 8 5.95 2.0529 7 6.16 0.84 0.84 0.7130 7 6.24 0.76 0.76 0.5831 5 6.32 -1.32 1.32 1.7332 7 6.18 0.82 0.82 0.66

Average= 0.93 1.23



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:



Aggregated Sales:

We can now predict the 8th month demand given the previous 7 months and weekly forecasts may be monthly averages!

0

2

4

6

8

10

0 2 4 6 8 10



ES forecasts 6.58 average sales for the 8th month. In this case error in terms of MAD and MSE would be as follows

Week Actual ES Forecast Error1 72 4.75 7 -2.253 6 6.8 -0.784 8.25 6.70 1.555 5.75 6.85 -1.106 6 6.74 -0.747 5.75 6.67 -0.928 6.5 6.58 -0.08



MAD = 0.75 and MSE=1.06

Note that it was MAD = 0.93 and MSE=1.23 without aggregation.

Week Actual ES Forecast Error MAD MSE1 7

27 6 5.99 0.0128 8 5.99 2.0129 7 6.58 0.42 0.42 0.1830 7 6.58 0.42 0.42 0.1831 5 6.58 -1.58 1.58 2.5032 6 6.58 -0.58 0.58 0.34

Average= 0.75 1.06


Exponential SmoothingT3-2


Linear Trend EquationT3-3


Trend Adjusted Exponential SmoothingT3-4


Simple Linear RegressionT3-5


Which Forecasting Approach to Take?

http://129.128.94.195/mgtsc352/web_notes/forecasting/2_02.asp#2.2.3


Resources

Textbooks!

http://129.128.94.195/mgtsc352/web_notes/forecasting/toc.asp (MGTSC 352)

http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm

Documents

Www.izmirekonomi.edu.tr Mahmut Ali Gökçe 1 Introduction to System Engineering ISE 102 Spring 2007 Notes & Course Materials Asst. Prof. Dr. Mahmut Ali GOKCE