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Scientific consulting and training

Turn Math into Profit!
Benefit from our unique blend of academic expertise, real-world modeling, and in-depth industry experience

Scientific Consulting Training and Seminars  Science and R&D

Math for Industry
24+ years designing, developing, and implementing math and advanced planning for various industries in several roles around the globe

Math in Industry
5 years advanced technology & math modeling at one of the leading chemical corporations
9 years shaping the portfolio of the leading business application provider

Leading-edge Research & Development
11+ years high performance computing
Member of a transnational team developing and deploying solid-body impact & collision codes

PhD in Astrophysics, thesis on numerical general relativity summa cum laude
Dozens of peer-reviewed publications
Continued learning and teaching with a focus on turning math into profit

Scientific Consulting & Technical Coaching

GAMS concepts, modeling and troubleshooting
Map business requirements to SAP© APO algorithms
Effective spot consulting

Training and Seminars

Mathematical programming with GAMS
Solving real-world optimization problems
Public and in-house courses

Science, Research & Development

Hypervelocity impacts, penetration
Computational physics
Artificial intelligence
High-performance computing

Scientific Consulting & Technical Coaching

Optimization and Mathematical Programming

We help in developing and implementing mathematical programming and optimization applications.

Our preferred tool is GAMS, the General Algebraic Modeling System.

Virtually any business profits from optimization, recent projects helped customers in manufacturing, logistics, and service providers (see about our customers).

Project sizes range from just a few hours to long-term engagements covering years of spot consulting.

Our engagement models vary, we are flexible. Some customers require spot consulting for specific issues or on an as-needed basis, others may require a complete implementation or solution architecture advice in certain phases of the project.

For more information, please contact us!

SAP® APO Process and Algorithm Coaching


SAP® APO offers a multitude of different planning methods in its modules SNP and PP/DS.

Mapping business requirements to the right planning algorithm makes projects run significantly smoother. Also, project delays can be avoided by mitigating the risk of unrealistic expectations such as sequence-dependent setup operations in connection with MILP-based optimization.

We help in laying out planning processes with the advanced planning modules of SAP® APO and selecting the right planning algorithm for the task.

Rather than “classic” SAP implementation consulting, we see our role in process and algorithm coaching. Hence, we engage in solution architecture and algorithmic spot consulting.

For more information, please contact us!



Officially named GAMS Solution Specialist:

Training and Seminars

We specialize in training courses for the General Algebraic Modeling System (GAMS), a leading high-level system for mathematical programming and optimization.

  • Highly interactive courses with many examples and exercises
  • Custom GAMS model library with many examples and exercise-solutions
  • Full-size course license covering GAMS and most solvers

On a regular basis we offer public introductory to mid-level courses on

Advanced Analytics: Modeling and Optimization with GAMS

Covers all important aspects needed for getting up and running with GAMS in only three days.

Energy and Power System Modeling in GAMS

Provides a two-day GAMS introduction and two days of Energy and Power System Modeling.

For specific GAMS training needs we gladly offer custom courses in Vienna or in-house at your location.

Please contact us with your question or request, we look forward to working with you!

Past seminar announcements and in-house courses

September 24-26, 2018 Vienna, Austria Advanced Analytics: Modeling and Optimization with GAMS
Juni 12-15, 2018 Vienna, Austria Energy and Power System Modeling in GAMS
April 9-11, 2018 Vienna, Austria Advanced Analytics: Modeling and Optimization with GAMS
October 2-5, 2017 Vienna, Austria Energy and Power System Modeling in GAMS
September 25-27, 2017 Vienna, Austria Introduction to Programming in Python
March 29-31, 2017 Vienna, Austria F171, Modeling and Optimization with GAMS Fundamentals
March 30 – April 1, 2016 Vienna, Austria F161, Modeling and Optimization with GAMS Fundamentals
November 02-04, 2015 Vienna, Austria F153, Modeling and Optimization with GAMS Fundamentals
September 10-11, 2015 Vienna, Austria F152, Modeling and Optimization with GAMS Compact
April 22-24, 2015 Vienna, Austria F151, Modeling and Optimization with GAMS Fundamentals
July 2-3, 2014 Berlin, Germany Introduction to GAMS (energy industry in-house course)
April 28-30, 2014 Vienna, Austria F142, Modeling and Optimization with GAMS Fundamentals
April 7-9, 2014 Laxenburg, Austria Modeling and Optimization with GAMS Fundamentals (International Institute for Sustainability in-house course)
March 31 – April 3, 2014 Vienna, Austria F141, Modeling and Optimization with GAMS Fundamentals incl. Workshop
December 03-04, 2013 Toronto, Canada F132, Modeling and Optimization with GAMS Compact
April 22-25, 2013 Vienna, Austria F131, Modeling and Optimization with GAMS Fundamentals
November 27-28, 2012 Vienna, Austria GAMS Fundamentals Course (energy industry in-house course)
May 19-20, 2012 Vienna, Austria F121, Modeling and Optimization with GAMS Fundamentals
May 16-19, 2011 Vienna, Austria F111, Modeling and Optimization with GAMS Fundamentals
November 11-12, 2010
Weisenheim a.B., Germany
Modeling and Optimization with GAMS (advanced)
November 08-10, 2010
Weisenheim a.B., Germany
Modeling and Optimization with GAMS (basic)


Officially named GAMS Solution Specialist:

Science, Research & Development


Scientific computing and computational physics

Co-developed a smooth particle hydrodynamics (SPH) hypervelocity impact code featuring full elasto-plastic continuum mechanics and a damage model.

High-performance parallel computing based on NVIDIA® CUDA™.

Applications include hypervelocity impacts and penetration studies. Example peer-reviewed publications:

Maindl, Schäfer, Speith, Süli, Forgács-Dajka, Dvorak, 2013, SPH-based simulation of multi-material asteroid collisions

Schäfer, Riecker, Maindl, Speith, Scherrer, Kley, 2016, A smooth particle hydrodynamics code to model collisions between solid, self-gravitating objects

Artificial intelligence

Use of machine learning (neural networks and genetic algorithms) for predicting (numerical) experiment outcome. First peer-reviewed publication:

Winter, Galiazzo, Maindl, 2018, Analysis of close encounters with Ganymede and Callisto using a genetic n-body algorithm

Sample SPH simulation

A rocky 1 cm asteroid at a speed of 10 km/s cuts through a 1 cm aluminum spacecraft shielding. For better visibility the actual 3D SPH simulation has been cut in half.

Disclaimer: the methods and codes mentioned in this section are leading-edge and hence of a scientific, experimental nature.

Please reach out to us if you are interested in a project-based engagement.

About Our Customers

  • Applied mathematics per se is not industry specific
  • Our business acumen and industry experience turn it into profit for a host of different businesses
  • Industries successfully served in the past include:
    Chemicals — Consulting & Professional Services — Energy — High Tech & Semiconductors — Machinery & Construction — Pharmaceuticals — Pulp & Paper — Rail Logistics — Space Agencies — NGOs — Universities

Optimal tower crane locations

Customer: Texas-based construction consultant

Business goal: select optimal crane location(s)

Savings potential: up to 30% crane operating costs

Decision factors (examples):

  • Observe supply and demand points (multiple materials)
  • Select crane configuration(s):
  • Observe crane operating speeds (horizontal/vertical/rotation)


Energy portfolio planning

Customer: RWE/Innogy, Germany

Business goal: support future corporate strategy

Decision problem:

  • Establish a network-flow model
  • Mulitude of constraints on network flows and knots: cost, capacity, thresholds, etc.

Stochastic electric network optimization

Customer: UK-based consultancy

Business goal: stable network operating modes minimizing cost of fulfilling demand

Decision problem:

  • Generator failure probability
  • Demand uncertainty
  • Scenario analysis

Train network optimization

Customer: European rail cargo logistics provider

Business goal: optimize cargo train operations

Savings potential: up to 30% cargo train operating costs

Decision problem:

  • Train cost EUR/km
  • Shunting cost per wagon
  • Observe maximum train length
  • Routing along multiple arcs
  • Implement column generation algorithm

I’d like to thank you for the training course, also on behalf of the project team. It made a lasting and good impression on all of us. I am convinced that the information we got leaves us well positioned for the further course of our project.

M. W.

Host of in-house GAMS optimization course, German energy company, 2014

Many thanks for this great course!

Dr. L. C.

Python course participant, Austrian high-tech company, 2017

Dr. Maindl provided a lot of cases to help me to understand the new language. The most useful thing is that this course provides not only practical modelling, but also the theoretical background of each model. Because of this, I can apply GAMS to my research well. I really appreciate his lecture.

Dr. J. Shin

Professor, South Korea, 2018

Very nice – looking for future workshops!

GAMS course participant, Austria, 2017

The course was really nice and I had opportunity to learn a lot from this. I learned GAMS for the first time in my life and it is a very powerful tool. I am really thankful for the course.

P. Verma

Researcher, IIT, Madras, 2016

Also, I attach photo files which are our commemorative photos.

Thanks to you, I learned a lot about GAMS.

Dr. I. K.

GAMS course participant, South Korea, 2016

Thank you so much for the great course, the exercises, … It was indeed very nice!

Dr. A. I.

GAMS course participant, Rio de Janeiro, 2014

I’d also like to thank you for this course. Both structure ans content were outstanding. It is a shame no such course is offered for biologists…

M. K.

Python university course participant, Vienna, 2016

Who I am

Thomas I. Maindl is fascinated with converting scientific methodology into real, tangible profit. He developed and sold his first business application at the age of 16 and held expert and management positions in the chemical and software industries in the US and Germany for more than 15 years before founding the freelance business Dr. Maindl Consulting in 2009. He successfully developed, implemented, and deployed optimization-based advanced planning applications with measurable ROI for customers in the chemical, energy, high-tech and other industries around the world and wrote the book “Real optimization with SAP© APO” (Springer). Presently, he focuses on delivering spot consulting and seminars & training on challenging topics.

Dr. Maindl earned his MSc and PhD degrees in astronomy from the University of Vienna, Austria and is still an active scientist. He has published numerous research papers in astrophysics, edited a book on extrasolar planetary systems, wrote a textbook on cubic spline interpolation, and delivers first-class lectures on astrophysics, applied numerical mathematics, scientific high-performance computing, advanced planning, logistics, and supply chain management at universities and business schools internationally.


Achievements and Competences

  • Developed and sold first business application at the age of 16 (accounting and customer management for small businesses)
  • In-depth background on mathematical programming, computational physics, and developing & implementing algorithms: PhD on numerical general relativity, numerous publications on real-world modeling, productive industry applications
  • Technology savvy and able to implement for the benefit of large organizations: various expert and management positions in industry e.g., BASF Corp. USA (Sr. Staff Specialist Advanced Technology), SAP SE Germany (Sr. Program Manager Competitive Intelligence)
  • Versatile global player: successful projects in a wide range of industries on a global scale (Europe, USA, India, Japan)

Cubic spline interpolation with examples in Python

Spline Course

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