The silent fallacy in the management board: Why experience and traditional spreadsheets fail in portfolio decisions

When decision spaces explode exponentially

In many companies, strategic decisions are still based on two pillars: personal experience and models in classic spreadsheets. Both are justified - but both come up against hard mathematical limits very early on. These limits are not of a psychological, organizational or methodological nature. They are structural.

As soon as decisions no longer have to be made in isolation, but as a portfolio under constraints, classic tools systematically fail.

1. The error in thinking: "There aren't that many options"

At first glance, many decision-making situations seem straightforward:

• a few projects
• several alternative courses of action per project
• a limited budget
• a clear time frame

What is often underestimated: Decisions multiply, they do not add up.

Simple examples - dramatic effect

Even very small scenarios lead to an explosive increase in possible combinations:

• 8 decision groups with 4 options each ( 8 projects with 4 restrictions)
  →⁴⁸ = 65,536 possible portfolios
• 10 decision groups with 5 options each
  →⁵¹⁰ ≈ 9.8 million possible portfolios

And this is still the idealized case - without any restrictions.

Additional point to point 1: The path of the mathematical explosion (visual thought, not intuitive)

What at first glance appears to be a straightforward decision structure very quickly develops into a branching decision tree in which each additional group opens up new paths. Each decision does not generate each decision does not generate a single subsequent path, but a whole bundle of new combinations.

The decisive effect is not the individual decision, but the depth of branching:

• Each decision group multiplies the existing space
• Each option creates new branches
• Each combination influences other combinations

The decision space thus grows like a tree, not linearly:

• a few nodes become a dense network
• overview becomes unmanageable
• comparison becomes computational overload

Exemplary development along this path:

• 6 decision groups with 3 options each
  →³⁶ = 729 portfolios
  Still conceivable for rough comparisons and heuristics.
• 9 decision groups with 3 options each
  →³⁹ = 19,683 portfolios
  The higher number of subject areas alone causes the space to explode - without any qualitative change in the decisions themselves.
• 9 decision groups with 4 options each
  →⁴⁹ = 262,144 portfolios
  An additional realistic course of action per group increases the decision space tenfold.

At this point, the transition is reached at which:

• visual or tabular representations collapse
• Completeness is no longer achievable
• every selection is inevitably based on partial considerations

As soon as restrictions (budget, dependencies, exclusions, sequences) are added, a simple power calculation becomes a highly simple power calculation becomes a highly non-linear optimization problem.

Additional example: Large corporation with 50 projects - why the decision space immediately gets out of control

In a large corporation, portfolio decisions are rarely "8 groups with 4 options". More realistic is a Program or transformation portfolio with 50 projects (IT, production, sales, compliance, ESG, M&A integration, Efficiency programs, location decisions, etc.). Each project typically has several realistic characteristics - not as a not as a "nice to have", but as a mandatory management reality.

Let's take a conservative scenario: 50 projects, each with 3 implementation options (e.g. "Stop", "Basic", "Ambitious"). The combinatorial space is then:

• 50 projects × 3 options
  →³⁵⁰ = ~ 7.18 × ¹⁰²³ possible portfolios

To categorize: That's hundreds of thousands of trillions of portfolio combinations. Even if you could only million portfolios per second, a complete check would take an astronomical amount of time. In practical terms, this means that a traditional approach can only look at a tiny number of variants.

And this example is deliberately conservative. In practice, many projects have more than three options. If you take 4 options per project (e.g. "Stop", "Minimal", "Standard", "Full expansion"), the result is:

• 50 projects × 4 options
  →⁴⁵⁰ = ~ 1.27 × ¹⁰³⁰ possible portfolios

The decisive factor, however, is that the actual leap in complexity is not even due to the options, but by the restrictions that a large corporation inevitably has.

Typical corporate restrictions that make the problem "hard"

• Multi-year budget (CAPEX/OPEX separate, subject to approval, with roll-over rules)
• Resource caps (FTE, key competencies, external service providers, supply chain capacity)
• Dependencies (project B only after A; project C only if D is not selected)
• Gating & milestones (stage gate, regulatory approvals, audit window)
• Risk budgets (group-wide risk tolerance, cyber/compliance limits)
• Regional/operational constraints (location, plants, works council, maintenance window)

These restrictions do not simply reduce the number of portfolios - they create non-linear interactions. This turns "many combinations" into a combinatorial optimization problem: each portfolio must not only be evaluated, but also checked for admissibility also be checked for admissibility.

What this means operationally (CEO/CFO perspective)

• Inevitably, you only see a tiny fraction of the decision space.
• "Best-of-Meeting" is no substitute for global portfolio optimization.
• Excel/spreadsheet logic does not scale in terms of dimension, dependency and restriction density.
• The greatest danger is not the wrong choice - but the uncalculated alternative.

Conclusion:

With 50 projects, the decision space is so large that classic methods only provide provide "manual random samples". As soon as the budget, dependencies and resources are realistically modeled, the decision must be calculated - otherwise it remains a formally well-founded but mathematically incomplete selection.

The central error at this point:

The explosion does not occur suddenly - it is the logical consequence of correctly conceived but multiplied decisions.

This is precisely where the systematic fallacy of classic management logic begins.

Additional example: Federal Republic of Germany - why infrastructure decisions explode mathematically

At the level of the Federal Republic of Germany, decisions are not made about individual projects, but on hundreds to thousands of parallel infrastructure measures. These include, among others: Transport routes, energy infrastructure, digitalization, defence, education, housing construction, water and wastewater Wastewater systems as well as climate adaptation and resilience projects.

Let's take a deliberately realistic, non-exaggerated scenario:

• 300 infrastructure projects nationwide
• 4 decision options per project

Typical options per project are, for example

• do not implement / postpone
• Minimum variant (maintenance)
• Standard variant (expansion according to planning)
• Accelerated or extended variant

The purely combinatorial decision space thus results in

300 projects × 4 options
→⁴³⁰⁰ ≈ ~¹⁰¹⁸⁰ possible investment portfolios

This number is so large that it goes beyond any intuitive imagination. For comparison: Even if you could check billions of portfolios per second, a complete view would be would be practically impossible.

Why it gets even more complex at state level

In contrast to corporate portfolios, there are additional highly interconnected constraints:

• Multi-year budget cycles (federal, state, municipal, special funds)
• Debt brake and credit rules
• Co-financing (EU, federal states, municipalities, private partners)
• Regional equalization logic (equal living conditions)
• Dependencies between projects (e.g. networks before charging infrastructure)
• Planning, approval and construction times
• political and legal constraints
• Resource bottlenecks (planners, construction capacities, materials)

These restrictions do not act in isolation, but overlap. Mathematically, this does not create a "big budget problem", but a high-dimensional, non-linear optimization problem.

The central fallacy in the public debate

Public discussions and political decision-making processes often give the impression that that infrastructure issues can be solved by

• Priority lists
• Individual assessments
• political consideration
• annual budget negotiations

solve "sufficiently well".

Mathematically speaking, this is untenable. In reality, only a tiny fraction of the possible investment space is considered. Most alternatives - including potentially more effective combinations - are never never become visible.

What this means in concrete terms

• Investment funds are inevitably allocated suboptimally
• Effects are random, not systemic
• Dependencies are only recognized in retrospect
• Cost overruns are structurally pre-programmed
• The question "Why exactly this portfolio?" remains unanswerable

The decisive point here is not political evaluation but mathematical feasibility:

As soon as hundreds of infrastructure projects are combined with budgets, dependencies, timelines and legal constraints are combined, the decision is no longer an administrative is no longer an administrative problem - but a pure calculation problem.

This is precisely where the "math explosion" manifests itself in its most extreme form: Not because politics fails - but because classic decision-making logic is fundamentally not designed for this scale.

2. The reality: constraints massively exacerbate the problem

In real business decisions, there are always additional factors:

• Budget caps
• time dependencies
• human resources
• technical or regulatory restrictions
• mutual exclusions or dependencies between options

These constraints do not simply reduce the options, but rather complicate the calculation. Why? Because they are not linear, but transform the decision problem into a combinatorial optimization problem.

The result is an exponential explosion of calculation and evaluation logic.

3. Why experience no longer helps here

Experience is excellent for:

• Patterns
• Repetitions
• familiar market situations
• stable environments

However, it fails where:

• many variables act simultaneously
• Effects are not intuitively visible
• Interactions dominate
• the optimal solution goes against your gut feeling

No CEO, no CFO, no project manager - regardless of experience or intelligence - can Mentally compare, evaluate and weigh up millions of portfolio combinations.

This is not a personal shortcoming. It is a cognitive impossibility.

4. Why classic spreadsheets fail structurally

Models in classic spreadsheets are excellent tools for:

• linear calculations
• Scenarios with few variables
• Reporting, planning and controlling

However, they are not decision optimizers.

The structural limits of classic spreadsheets

• Each new decision group increases the dimension
• Each dependency requires additional logic
• Each portfolio variant must be explicitly calculated or simulated
• Brute force approaches are practically impossible
• Solvers very quickly reach time and accuracy limits

Even highly complex models end up considering only a tiny fraction of the actual decision space.

This feels precise - but is mathematically blind to alternatives.

5. The core problem: portfolio decisions are not individual decisions

The crucial change of perspective is:

Companies do not make individual decisions.
They make portfolio strategies.

The value of an option is often only created

• through its combination with other options
• through their sequence
• through the timing
• through interactions

Looking at individual projects in isolation almost inevitably leads to suboptimal overall results, even if each project appears "reasonable" on its own.

6. Exponential problems require exponential thinking - not more experience

As soon as the number of possible combinations grows exponentially, new rules apply:

• Intuition becomes unreliable
• Heuristics become dangerous
• Simplifications distort the result
• Transparency is lost

Neither more meetings nor larger tables help here. What is needed here is systematic decision-making intelligence that:

• takes the entire solution space into account
• Precisely maps constraints
• Mathematically resolves conflicting objectives
• Optimizes portfolio effects instead of individual effects

7. The consequence for management

Anyone who still believes that complex strategic decisions can be reliably managed with experience, gut feeling, spreadsheets Gut feeling, spreadsheets and simplified scenarios is taking a risk:

• massive opportunity costs
• Misallocation of capital
• wrong priorities
• decisions that cannot be explained to the Supervisory Board, investors and the public

The real danger does not lie in the wrong decision - but in the the uncalculated decision.

Conclusion

With just a few decision groups, the number of possible portfolios explodes to a level beyond human and classical analytical capabilities.

Experience remains valuable. Traditional spreadsheets remain useful. But neither is enough as soon as decisions are networked, budgeted, dependent and strategically relevant and strategically relevant.

From this point on, decisions must be calculated - not interpreted.

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