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Instead of evaluating projects in isolation, we analyze all possible combinations - and identify the best solution.

The global optimum is not an assumption - it can be calculated.

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Solving complex portfolio problems with AI


Why 2¹⁵ is not even a point in the real decision space - and 2⁵⁰ defines a new dimension

Executive Summary

Modern investment and transformation portfolios no longer operate in linear planning logics. They exist in exponentially growing decision spaces that structurally overtax any human intuition.

The accompanying figure shows this situation in a mathematically correct way:

  • 215 = 32,768 possible portfolios
  • 250 ≈ 1.13 quadrillion possible portfolios

The difference in size is not gradual, but dimensional. On a real scale, the entire 215 space would not even be visible as a point in the 250 space.

Size ratio:
(215 /250) =2-35 ≈ 1 : 34 billion

What is considered "complex" today is statistically irrelevant in the real decision space.

From projects to decision-making universes

Every additional project doubles the decision space. However, real portfolios do not consist of isolated projects, but of:

  • Dependencies
  • Conflicting objectives
  • Resource restrictions
  • regulatory limits
  • multiple impact dimensions (ROI, resilience, ESG, acceptance)

This turns a project list into a high-dimensional optimization universe.

What the picture shows is precisely this leap: The large cube is not "very large" - it is a different reality.

Why classic methods fail structurally

At 215, there are already more than 30,000 possible portfolios. It is an NP-hard problem.

What is an NP-hard problem? Exponential growth and examples: Travelling Salesman, Knapsack problem, Job scheduling

That means:

  • No Excel
  • no scenario model
  • no expert panel

can still determine a global optimum here. From this point on, decisions become heuristic, not optimal.

And at 250, there is no longer even an imaginable basis for comparison.

The green route in the picture

The blue network structure shows all possible decision paths. The green route is the mathematically optimal solution.

It is:

  • non-linear
  • not intuitive
  • cannot be explained by experience

It is the result of a calculation, not an opinion.

What StratePlan makes possible here

StratePlan does not calculate the entire room - that would be physically impossible. But it analyzes systematically:

  • 97.00 % to 99.99 % of the relevant decision space

and identifies the optimal starting point for strategic decisions.

Not as a simulation.
Not as a gut feeling.
But as a calculated basis for decision-making.

Conclusion

The image makes visible what classic control cannot see:

The true costs do not arise in the project - but in the alternatives that are not chosen.

And these only become visible when the decision space is calculated.

This is the new reality of portfolio decisions.

Author: Dr. Igor Kadoshchuk CTO mAInthink

Dr. Igor Kadoshchuk is a computer scientist, algorithm architect, and one of the leading minds behind mAInthink's optimization and decision-making algorithms. As scientific director of the StratePlan™ and DeepAnT platforms, he combines in-depth mathematical research with practical applications in project portfolio optimization, business, finance, and public administration.

He holds a PhD in computer science from the renowned Moscow Institute of Physics and Technology (MIPT), where he also taught as a professor of computer engineering and mathematics. He has decades of experience developing highly complex mathematical models for project portfolio optimization and financial systems, investment planning, and strategic decision-making. His professional career includes leading positions such as Head of IT at Gazprombank and Director of Project Management at TransTeleCom.

Dr. Kadoshchuk writes on the mAInthink AI Blog. Kadoshchuk on:

  • Algorithmic strategy optimization
  • New methods for calculating ROI and impact
  • Project portfolio optimization beyond traditional tools
  • The limits of human decision-making – and how AI overcomes them

His aim: to calculate strategy, not estimate it.

His contributions combine scientific precision with clear, understandable language – always with the goal of making complex decision-making spaces transparent, manageable, and measurable.

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