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Combinatorial project optimization - free online service
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Use our free online service for combinatorial project optimization and analyze the entire decision space of your project portfolio within a few minutes Of your project portfolio.
Determine the mathematically optimal combination of your projects under real budget, capacity and restriction conditions.
Start free online serviceMost project decisions are made without calculating the full decision space
In many organizations, project portfolio management is seen as an analytical process. Projects are evaluated, business cases are created, risks are analyzed and budgets are prioritized. On this basis, board members, management and investment committees make decisions on investments worth billions.
However, despite extensive analysis, one crucial factor is usually overlooked:
The complete decision space of a project portfolio is almost never calculated in practice.
Even with a relatively small number of projects, a mathematical complexity arises that is no longer manageable using traditional methods.
With:
- 10 projects there are already 1,024 possible portfolio combinations
- 20 projects generate over 1 million combinations
- 30 projects already generate more than 1 billion possible portfolios
- 50 projects lead to over 1 quadrillion possible combinations
This exponential explosion is at the heart of the problem.
Companies often prioritize projects individually or compare them in pairs. However, this almost always only results in a local optimization, while the global optimum of the entire portfolio remains invisible.
This is precisely where combinatorial project optimization comes in.
A new approach makes it possible for the first time to calculate the complete decision space of a project portfolio and determine the mathematically optimal combination.
A free online service for combinatorial project optimization now also makes this technology accessible to companies.
Scientific sources on combinatorial optimization
The mathematical foundations of combinatorial optimization have been studied for decades at leading at leading universities and research institutes worldwide. The following sources offer sound scientific insights into Algorithms, decision spaces and optimization methods.
For decision-makers, analysts and strategy managers, these publications offer a valuable in-depth look at the theoretical foundations of project portfolio Project portfolio optimization and algorithmic decision analysis.
Max Planck Society - Basic research on complex systems
The Max Planck Society is one of the world's leading research organizations Leading research organizations in the field of basic research. The work published there provides important impulses for mathematical modelling, complexity research and algorithmic optimization.
Discover the Max Planck Society's research areas on mathematical optimization now
RWTH Aachen - Research on combinatorial optimization
RWTH Aachen University conducts intensive research in the field of discrete mathematics and combinatorial optimization. Among other things, the research group deals with Algorithms for solving complex decision problems in large decision spaces.
Visit the Research Group for Combinatorics and Optimization at RWTH Aachen University now
Springer - Scientific literature on combinatorial optimization
The scientific publisher Springer publishes numerous Standard works on combinatorial optimization, discrete mathematics and algorithmic and algorithmic decision problems. These books are used worldwide in research and teaching.
View the Springer textbook on combinatorial optimization now
Wikipedia - Overview of combinatorial optimization
The Wikipedia article on combinatorial optimization offers a generally understandable introduction to central concepts such as NP-hard problems, decision spaces and algorithmic solution methods.
Read the Wikipedia article on combinatorial optimization now
University of Osnabrück - Teaching material on combinatorial optimization
The University of Osnabrück provides teaching material on combinatorial optimization, which explain basic models Models, problem classes and solution algorithms.
View the lecture notes of the University of Osnabrück on combinatorial optimization now
University of Cologne - ZAIK Research Reports
The Center for Applied Computer Science Cologne (ZAIK) publishes Research reports on algorithmic optimization, combinatorial problems and their application in real decision models.
Read the research report of the ZAIK of the University of Cologne now
What is combinatorial project optimization?
Combinatorial project optimization is a mathematical method for determining the optimal combination of projects within a given budget or capacity framework.
In contrast to classical prioritization methods, this approach does not consider individual projects, but all possible project combinations simultaneously.
The aim is to find the combination that generates the maximum total value.
This total value can be defined, for example, as
- maximum return on investment
- maximum strategic benefit
- maximum EBIT improvement
- maximum increase in the value of a portfolio
- optimal utilization of an investment budget
The key difference is that the system does not ask:
"Which project is the best?"
But rather:
"Which combination of projects generates the highest overall benefit?"
This question changes the entire decision-making process.
Why traditional project prioritization often leads to suboptimal results
Most organizations use a mixture of the following methods:
- Scorecard models
- strategic prioritization
- Budget caps
- Expert panels
- Portfolio meetings
These methods have one thing in common:
They analyze projects in isolation or sequentially.
As a result, interactions between projects are often overlooked.
An example:
A company has a budget of 20 million euros and evaluates several projects:
| Project | ROI |
|---|---|
| Project A | 14 % |
| Project B | 13 % |
| Project C | 12 % |
| Project D | 11 % |
The intuitive decision would be to simply select the projects with the highest ROI.
But this logic only works if projects are completely independent of each other.
In reality, however, there are numerous interactions:
- Projects share resources
- Projects influence capacities
- Projects have time dependencies
- Projects influence strategic goals
As a result, a seemingly optimal decision can actually produce a suboptimal portfolio.
Combinatorial optimization solves precisely this problem.
The mathematics behind combinatorial portfolio optimization
The basic principle is based on the calculation of all possible combinations of a project set.
If a portfolio consists of N projects, there are mathematically
2^N possible portfolios.
An example:
With 15 projects, there are already over 32,000 possible combinations.
With 30 projects, there are
over 1,073,000,000 possible portfolios.
With 50 projects, this number increases to:
more than 1,125,899,906,842,624 possible combinations.
These figures show why traditional analysis approaches quickly reach their limits.
No management team can evaluate billions of portfolio options manually.
This is where algorithmic optimization comes into play.
From heuristic decisions to the global optimum
Many organizations try to solve this problem with heuristic methods.
These include:
- Greedy algorithms
- simple portfolio scoring models
- Excel-based simulations
- Monte Carlo analyses
These methods can provide helpful approximations.
However, they do not guarantee the global optimum.
The global optimum is the mathematically best solution in the entire decision space.
It represents the combination that generates the highest benefit under all constraints.
To determine this optimum, all possible combinations must be analyzed or intelligent optimization algorithms must be used to systematically search the decision space.
Exactly this technology is now also available via a free online service for combinatorial project optimization.
A free online service for combinatorial project optimization
With the increasing availability of modern optimization algorithms, it is now possible for the first time to automatically calculate complex project portfolios.
A new approach is to make this technology available via an online service.
Companies can enter their project list and the most important parameters, for example
- Investment volume
- expected ROI
- Budget restrictions
- Capacity limits
- strategic priorities
On this basis, the system automatically calculates the optimum combination.
The advantage of such a service lies in several factors.
Firstly, the analysis effort is considerably reduced.
Secondly, the entire decision space is taken into account.
Thirdly, companies can recognize within a few minutes whether their current portfolio is actually optimally structured.
Of particular interest is the possibility to test this process free of charge.
Why a free service makes sense for companies
Many organizations underestimate the opportunity costs of suboptimal investment decisions.
Even small improvements in portfolio quality can have a significant financial impact.
An example:
A company invests 100 million euros annually in projects.
If a better portfolio composition increases the ROI by just 3 percentage points, this already corresponds to an additional annual value contribution of 3 million euros.
Over several years, such effects quickly add up to tens of millions of euros.
A free online service enables companies to test this potential risk-free.
Organizations can check
- whether their current portfolio is already optimally structured
- which alternative project combinations exist
- which projects have the greatest impact on overall success
This significantly improves the quality of strategic decisions.
Typical areas of application of combinatorial project optimization
Combinatorial portfolio optimization can be used in numerous areas.
It is particularly relevant wherever organizations need to evaluate several investment options simultaneously.
Typical areas of application are
Investment portfolios in industrial companies
Companies often have to decide which production facilities to modernize, which plants to expand or which technologies to develop.
Combinatorial optimization helps to find the combination that generates the highest long-term value.
Research and development portfolios
R&D budgets are limited. At the same time, there are numerous potential innovation projects.
An optimized portfolio can significantly increase the probability of technological breakthroughs.
Real estate investments
With real estate portfolios, investors must decide which properties to buy, develop or sell.
Combinatorial optimization makes it possible to deploy capital more efficiently.
Infrastructure projects
Cities and regions also face similar challenges.
Budgets are limited, while numerous infrastructure projects compete for funding.
An optimized portfolio can significantly improve the impact of public investments here.
Why Excel and traditional PPM tools are reaching their limits
Many organizations try to analyze their project portfolios using Excel or traditional PPM systems.
These tools are helpful for basic planning, but quickly reach their mathematical limits.
The reason lies in the structure of the problem.
Project portfolio optimization belongs to the class of NP-hard optimization problems.
This means that the number of possible solutions grows exponentially.
Excel is designed for linear calculations.
However, it is not designed to systematically analyze billions of possible portfolio options.
Specialized optimization algorithms are much more powerful here.
They can efficiently search through large decision spaces and identify optimal solutions.
How companies can use the free online service
Getting started with combinatorial project optimization is much easier today than it was a few years ago.
A typical process could look like this.
First, the company creates a list of all potential projects.
Basic parameters are defined for each project, for example
- Investment costs
- expected benefit
- strategic relevance
- Time schedule
- Capacity requirements
This data is then transferred to the online service.
The system then automatically calculates the mathematically optimal project combination.
In many cases, this shows that a slightly different portfolio composition can generate a significantly higher overall benefit.
Why combinatorial optimization is the future of project portfolio management
The economic reality of modern organizations is characterized by increasing complexity.
At the same time, companies are faced with numerous strategic decisions:
- Digitalization
- Sustainability
- Infrastructure investments
- Innovation programs
- Cost efficiency
These decisions often compete for the same resources.
The central challenge is to use the limited budget in such a way that the maximum overall benefit is achieved.
Combinatorial optimization offers a mathematically sound approach to this.
Instead of basing decisions solely on experience or heuristic methods, organizations can calculate the entire decision space for the first time.
This makes it possible to see which portfolio composition is actually optimal.
Conclusion: Why a free online service for combinatorial project optimization can be a strategic advantage
Strategic investment decisions are among the most important tasks of managers.
However, the mathematical complexity of modern project portfolios means that many decisions are based on incomplete information.
Combinatorial project optimization fundamentally changes this process.
By calculating the complete decision space, it becomes visible for the first time which combination of projects generates the maximum value.
A free online service enables companies to test this technology without risk and significantly improve the quality of their portfolio decisions.
Especially in times of limited budgets, the difference between a good portfolio and the global optimum can have an enormous economic impact.
Organizations that use combinatorial optimization at an early stage therefore gain a strategic advantage in an increasingly complex decision-making world.