c - Fakultät für Mathematik und Informatik

OR als Handwerkszeug des IT-Architekten 

Tag der Mathematik 

Jena, 28. Januar 2006 

Karlheinz Mohr 

Mgr of SSD/SSE Center of Competence IMT Germany 

Mgr of Architects IMT CEMAAS 

mohr@de.ibm.com 

Bertus G Eggen 

Executive IT Architect 

Information Technology Services – Service Delivery | © 2006 IBM Corporation

Information Technology Services – Service Delivery 

ertus Eggen 

xecutive IT Architect 

ember of IBM Academy of Technology 

Education 

1982-1989: Technische Universität Braunschweig; Diplom (Master) in Mathematics 

Career 

2000: Executive IT Architect 

1995: Senior IT Architect 

1994: Founding member of ESM Knowledge Network's Core Team, responsable for 

research and development 

1990-1993: Support of VOLKSWAGEN regarding Application Development, 

Networking and Systems Management on UNIX and AIX 

1990: Joined IBM as Systems Engineer in Braunschweig, Germany 

1987-1990: "Grafik und Datenverarbeitung GbR", Owner of application development 

company (see also next section) 

Publications 

"Numerische Methoden im CAD" (“Numerical Methods in Computer Aided Design"), 

Vieweg 

"System Management Design Samples - A Management Summary", IBM Redbook 

"System Management Design Guidelines", IBM Redbook 

Key Engagements 

1997-2001: DKV (Deutsche Krankenversicherung, ITERGO), Cologne, Germany; 

Lead Architect/Project; Leader/Consulting Architect 

1997: Germany Stock Exchange, Frankfurt, Germany; Lead Architect/Project Leader 

1996: Daimler Benz Aerospace, Hamburg, Germany; Lead Architect/Project Leader 

1996: Boeing, Seattle, Washington, USA; Leading Architect/Mentor 

1993-1996: LIT (Landesamt für Informationstechnik), Berlin Germany; Leading 

Architect 

Recognition 

2000: Elected as Member, IBM Academy of Technology 

1999: Engagement Excellence Award, DKV Engagement, Cologne, Germany 

1998: Team Excellence Award, DKV Engagement, Cologne, Germany 

1995: Team Excellence Award, Fiscus Engagement, Hannover, Germany 

1995: Engagement Excellence Award, LIT Engagement, Berlin, Germany 

1994: Software ExcellenceAward, Systems Management Assessment Workshop 

Karlheinz Mohr 

Mgr of SSD/SSE IMT Germany & CEMAAS 

Business Unit Technical Leader 

Education 

Career 

1981-1986 Uni Heidelberg, Dipl.-Math 

1977-1980 Uni Hamburg, Versicherungs Mathematik 

2001-2004 Competency&Professional Development Execeutive EMEA 

200-2001 Manager Foundation IBM Germany 

1998 Manager, Security Services and Systemsmanagement 

1994 Project Lead, Chemistry Applications 

1990 Speech Product Development Manager, ELBU 

1988, Research Staff meber at IBM TJ Watson Research Lab 

1986, Scientific Staff Member, IBM Heidelberg 

1981-1986 MOHR EDV -Arbeiten and IBM Science Center Heidelberg 

1979, 1980 Summerstudent at IBM with several customers 

Recognition 

1990 Patent Application Award 

1988 First Patent Application Award 

1987 Outstanding Technical Achievement Award 

Tag der Mathematik, Uni Jena | Slide 2 © 2006 IBM Corporation

Agenda 


� What is IT Consulting / IT Architecture 

� What is Operations Research ? 

� General Approach 

� Some Areas of Operations Research 

� Example 

� References 



IT Consultants and IT Architects work in the early 

phases of a project. 

Phase 1: 

Solution Strategy 

Selection 

Phase 4: 

Deliver Service 

Assessment 

Strategy 

Selection 

Operation 

Manage Delivery 

Architecture Data 

Processes 

D Design 

Develop 

Deploy 

HLDesign 

Tag der Mathematik, Uni Jena | Slide 4 © 2006 IBM Corporation 

Org 

Phase 2: 

Design Solution 

Phase 3: 

Implement Solution


The roles do overlap regarding the time in the 

solution life cycle. 

Priority of Role 

Consultants Architects Specialists 

Time in Life Cycle 


IT Consultant 


� Works „high and early“: 

Leads in phase 1 and 2 

Consults and develops strategies 

Skill Depth 

Skill range 


IT Architect 


� Leads in phase 2 and 3 

Develops the the complete solution 

„Thinks in the next larger context“ 

Skill depth 

Skill range 



What is Operations Research ? 

Some „Definitions“ 

� „Operations Research is part of applied 

Mathematics.“ 

� „Operations Research (OR) is the use of the 

scientific methodology in studying systems whose 

design or operation require human decision making. 

.... OR is interdisciplinary in nature, drawing on (and 

contributing to) the techniques from many fields, 

including the mathematical sciences, engineering, 

economics and the physical sciences.“ 1 

� „Application of quantitative methods to prepare 

optimal decisions“ 2 

u „OR is application of scientific thinking to real 

life problems.“ 

Sources: 

1 http://www.or.ncsu.edu/Overview.dir/overview. 

2 Translated from [1] 



What is Operations Research ? 

History 

Blaise Pascal 

(19.6.1623 - 19.8.1662) 

Carl Friedrich Gauß 

(30.4.1777 - 23.2.1855) 

His approaches to gambling 

games are the base for Game 

Theory which today is the 

framework for decision support in 

terms of tactic and strategy. 

Wanting to describe the tracks of 

asteroids, he invented calculus... 

The distribution function 

introduced byand later named after 

him is one of the most important 

formula in statistics. 

Leonhard Euler 

(15.4.1707 - 18.9.1783) 

Agner Krarup Erlang 

(1.1.1878 - 3.2.1929) 

His work on the problem of „The Seven Bridges of 

Königsberg“ was the foundationof the theory of 

graphs, 

which is the base for many structural or topological 

approaches. 

By studying a village telephone exchange he worked 

out a formula, nowknown as Erlang's formula, to 

calculate the fraction of callers attempting to call 

someone outside the village that must wait because all 

of the lines are busy. 

The mathematics underlying today's complex 

telephone networks is still based on Erlang‘s work. 

The term „Operations Research“ appeared in the 1950ies and covers a broad range 

of scientific topics related to decision support. 



When to use Operations Research ? 

� In general 

Decision Support 

Describe problems in a structured manner 

To find quantitative answers to problems 

� Especially 

Analysis of problems and results 

Design of solutions 

Determine stable estimations 

Preparation of interviews and test cases 



General Approach in OR 

„Real World“ 

„Model World“ 

Picture based on [1] 

Real Real Problem 

Mathematical 

Model Model 

Solution for forReal Real 

Problem 

Abstraction Interpretation 

Description: 

„Analysis“ 

Calculation 

If abstraction and interpretation do not match, a 

solution for one problem leads to solutions for other 

problems ! 

Model Model Solution 

Solution: 

„Design" 


! 

(This is a bless AND a curse.)


Analogy: Abstraction and Interpretation 

This is 

Blue This is 

Red 

This is 

Grey 



Areas of OR: Probabilities and Statistics 

Are the results of my 

evaluation or ranking 

significant ? 

? 

0,14 

0,12 

0,1 

0,08 

0,06 

0,04 

0,02 

0 

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 

n 

2 

2 ( ni 

− np) 

χ < α 

np 

= ∑ 

i= 

1 


Density 

Probability 

!


Areas of OR: Queueing Theory 

How many 

� Employees 

� Server 

� Replica 

� ... 

do I need ? 

C( 

c, 

t) 

c 

t 

c! 

c 

∑ − 

= c 

1 n 

t 

t 

+ ( 1−U 

) 

c! 

n= 

0 n! 

Client 

Call Center 

Help Desk 

⎛ C( 

c, 

t) 

⎞ 

ERT = ES⎜1 

+ ⎟ 

⎝ c( 

1−U 

) ⎠ 



Areas of OR: Graphs 

Köln 

4 MBit 

Stuttgart 

2 MBit 

7 MBit 

Frankfurt 

6 MBit 

Hamburg 

5 MBit 

2 MBit 

10 MBit 

5 MBit 

München 

Berlin 

v 1 

8 

2 

v 4 

5 

v 3 

2 

v 2 

7 

5 

3 

3 

v 6 


v 5 

Nr. Vorgangsname Dauer 

1 

2 

3 

4 

5 

6 

V1 

V2 

V3 

V4 

V5 

V6 

1 Tag 

1 Tag 

1 Tag 

1 Tag 

1 Tag 

1 Tag 

Die 01. Mai Mit 02. Mai Don 03. Mai Fre 04. Mai Sam 05. Mai Son 06. Mai Mon 07. Mai 

0 6 12 18 0 6 12 18 0 6 12 18 0 6 12 18 0 6 12 18 0 6 12 18 0 6 12


Areas of OR: Queueing Systems/Netplan Technique 

How long does it take to 

make a bar of gold ? 

The farm makes 

wheat 

he mill needs wheat 

nd makes flour 

The Store needs gold 

The coal mine needs food and makes coal 

The ore mine needs foo 

and makes gold ore 

The bakery needs flour 

and water and makes 

bread 

The melt needs coal and 

ore and makes gold bars 



Other areas of OR 

Linear Programming 

Integer Programming 

Transportation 

Dynamics Optimization 

Non-Linear Optimization 

Decision Theory 

Game Theory 

Simulation 

Optimal Storage 

... 

The trick is re-combination of the areas... 



Example: System Design/Analysis 

� Problem 

Usually system designs are incomplete or inconsistent (or: „not good 

enough“). 

The methods currently used do not have any metrics „built in“ u no 

optimization possible 

The available tools are always depending on a specific method. 

� Related business issue 

It is very cost intensive to create high quality 

GP is lower than possible 

� Summary 

Approach to describe/evaluate system designs, e.g.: 

Process Models 

Data Models 

E2E Architectures 

... 

Based on discrete math (the same stuff we are using for VLSI design) and 

some algebraic stuff 


Component I 


Every entity in a system design can be decomposed to entities of the 

same type („children“). 

Subcomponent I 

Subcomponent II 

Subsubcomponent 

Subcomponent III 

Level 2 = Activity ? 

Level 1 = Task ? 

Level 0 = Process ? 

Subcomponent I 

Component I 

Subcomponent III 

Subcomponent II 

Subsubcomponent 



An entities properties depend on the properties of its children. 

Subcomponent II: 

Property Value 

Scalability XXX 

Availability XXX 

Duration 9 

Cost XXX 

In general, „sum“ is a function: 

decomposes to 

ai, n = f ( a1, 

n,..., 

ai−1, 

n, 

ai+ 

1, 

n,..., 

am, 

n, 

ai, 

n−1, 

1,..., 

ai, 

n−1, 

k 

Properties of 

same entity 

* the last level components are building a linear sequence (see prev. foil) 

is sum * Aggregation: 

of 

Same 

property of 

all children 

) 




Duration 3 

Cost XXX 




Duration 5 

Cost XXX 




Duration 1 

Cost XXX 



To determine the aggregation completely and consistently the system‘s description has to 

cover three classes of information: Hierarchies, Relationships and Graphs 

Hierarchies: 

� Processes 

� Architectural 

components 

� Data Entities 

� Organizational units 

(„Org Charts“) 

� Roles 

� ... 

(Decomposition-) 

Trees describing 

„set-like“ 

properties 

Hier Namen eingeben 

Hier Titel eingeben 

Kommentar 1 

Kommentar 2 

Relationsships: 

� Who is responsable for 

what ? 

� Which process is 

applied to what 

component ? 

� Who has which role ? 

� ... 

Matrices describing 

relational properties 

1 1 1 1 1 1 1 

1 0 1 0 1 0 1 

1 0 0 0 1 0 0 

0 1 0 1 0 1 0 

0 1 1 1 0 1 1 

0 0 1 0 0 0 1 

Graphs: 

� Workflows 

� Dependencies 

� Interactions 

� ... 

general general 

general 



Kommentar 1 

Kommentar 2 



Kommentar 1 

Kommentar 2 



Kommentar 1 

Kommentar 2 

directed Graphs 

describing 

structural/topological 

properties 



Aggregation of metrics 

serial case 

parallel case 

Scalability 

f1, 1 f1, 2 

f1 

o ( g1( 

n)) 

o( 

g2 

( n)) 

o g ( n) 

+ g 

( 1 2 

Availability 1 a 2 a 1 2 a a 

Duration 1 d 2 d 1 2 d d + 

Cost 1 c 2 c 1 2 c c + 

Scalability 

* “o(g)“ means Landau Symbol 

o ( g1( 

n)) 

o( 

g2 

( n)) 

Availability 1 a 2 a 

Duration 1 d 2 

( n)) 

o ( g1( 

n) 

+ g2( 

n)) 

1− ( 1− 

a1) * ( 1− 

a2) 

d ) , d 

max( 1 2 d 

Cost 1 c 2 c 1 2 c c + 


References 


[1] Werner Zimmermann „Operations Research - 

Quantitative Methoden zur 

Entscheidungsvorbereitung“ 

Oldenbourg, 1999 

[2] Donald E. Knuth "The Art of Computer 

Programming", Vol. 1-3 

Addison Wesley, 1997 

[3] Simon Singh "Fermat's Last Theorem" Fourth Estate, 1997 

[4] Bronstein, I.N. and K.A. 

Semendyayev 

"Handbook of Mathematics" Verlag Harri Deutsch, 1985 

[5] Tom DeMarco "The Deadline" Dorset House Publishing, 1997 



Online References 

„Operations Research at NCSU“ 

http://www.or.ncsu.edu/Overview.dir/overview.html 

„Mathematics Archives - Lessons and Tutorials“ 

http://archives.math.utk.edu/tutorials.html 

„Dictionary of Algorithms, Data Structures, and Problems “ 

http://hissa.nist.gov/dads/ 

„IBM Research - Operations Research“ 

http://www.research.ibm.com/math/OpResearch/index.html 

„IBM Research - Ponder This/Monthly Challenge“ 

http://www.research.ibm.com/ponder/ 

„Management Science Techniques“ 

http://www.cs.adfa.edu.au/teaching/studinfo/mst2/ 



An old fashioned slogan... 

Think.

c - Fakultät für Mathematik und Informatik

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