Monte Carlo versus AI: Fixed asset decisions under uncertainty: simulation versus optimization

Why simulation is no longer enough for fixed assets - and mathematical optimization is becoming the new governance necessity

Executive Summary

For decades, Monte Carlo simulation was considered the methodological gold standard for evaluating uncertainties in investment decisions. Particularly in the area of fixed assets - i.e. long-term capital commitments such as real estate, infrastructure, production facilities or large-scale IT systems - it was the preferred instrument for risk modeling.

Monte Carlo was up to date.
Monte Carlo made sense from a mathematical point of view.
Monte Carlo was an advance over deterministic individual assumptions.

But Monte Carlo does not make a decision.
It simulates them.

And in the context of modern portfolio and CapEx management, this means that a potentially structurally incorrect decision is varied 10,000 times - but not optimized.

With increasing complexity, dependencies between projects, budget restrictions and multiple conflicting objectives, simulation reaches a systemic limit. It evaluates scenarios. It does not search the entire decision space.

This is precisely where algorithmic ex-ante optimization comes in. Instead of simulating probability distributions, the combinatorial space of all possible portfolio configurations is mathematically analyzed - and the global optimum is identified.

In the area of fixed assets in project portfolio management (PPM), this does not improve Monte Carlo, but makes it obsolete.

1. Historical classification: Why Monte Carlo was useful

The Monte Carlo method was developed in the 20th century to mathematically approximate complex probability problems. It was revolutionary in finance, risk management and investment calculation because it made uncertainty quantifiable.

Instead of a single assumption about cash flows or capacity utilization, thousands of random draws were generated. This resulted in

• Expected values
• Variance
• Value-at-risk
• Confidence intervals
• Scenario bands

For fixed assets this means

• Construction cost uncertainty
• Interest rate fluctuations
• Market price volatility
• Utilization risks
• Residual value assumptions

All these factors could be modeled statistically.

In a world with limited computing power and a manageable number of projects, this was rational.

But this world no longer exists.

2. The structural problem: simulation is not optimization

Monte Carlo answers the following question:

If we choose this project or this portfolio - how likely is which outcome?

What Monte Carlo does not answer:

Is this portfolio even the best possible among all admissible combinations?

This is a fundamental difference.

Simulation

• Evaluates a given decision
• Varies parameters
• Provides probabilities

Optimization

• Searches decision space
• Considers restrictions
• Maximizes objective function
• Identifies global optimum

Monte Carlo thus simulates uncertainty within a structural decision that has already been made.

If this structural decision is suboptimal, only its dispersion is analyzed.

This corresponds to a 10,000-fold simulated misallocation.

3. Fixed assets in PPM: why complexity becomes exponential

The classic fixed assets portfolio contains

• Several investment projects
• Different maturities
• Budget restrictions
• Synergy effects
• Exclusion relationships
• regulatory conditions
• ESG requirements
• strategic priorities

There are already over a million possible portfolio combinations for 20 projects.

With 50 projects:

²⁵⁰ ≈ 1,125,899,906,842,624 combinations

Monte Carlo simulates within a selected combination. It does not search through these 1.1 quadrillion possibilities.

This is not a gradual weakness. It is a structural one.

4. Typical application of Monte Carlo in fixed assets

In the fixed assets context, Monte Carlo is typically used for:

• NPV distribution of a project
• IRR ranges
• Sensitivity analyses
• Stress tests
• Risk assessment of individual assets

But in practice this means

1. Projects are evaluated individually.
2. A portfolio is formed on the basis of ranking or heuristic criteria.
3. Monte Carlo simulates uncertainties within this selection.

The ranking remains local. The portfolio structure remains heuristic. The budget allocation remains approximate.

5. Comparison: Monte Carlo vs. global optimization

Criterion	Monte Carlo simulation	Global optimization
Question	How does a selected scenario scatter?	Which portfolio combination maximizes the objective function?
Methodology	Random sampling	Deterministic / hybrid algorithms
Decision space	Fixed	Fully searched
Dealing with restrictions	Ex-post evaluation	Integrated constraints
Complexity	Linear in simulations	Exponential space - algorithmically mastered
The result	Probability distribution	Mathematical global optimum
Governance quality	Risk representation	Resource optimization

6. Why Monte Carlo is systemically inadequate for fixed assets

6.1 Capital commitment

Fixed assets tie up capital for years or decades. Misallocations have a long-term effect.

6.2 Irreversibility

Infrastructure, real estate or production facilities cannot be reallocated without significant losses.

6.3 Interdependencies

A logistics center influences transport costs.
An IT investment influences personnel costs.
An ESG measure influences financing costs.

Monte Carlo models uncertainty within a project - not the combinatorics of dependencies.

7. The mathematical change of perspective

The relevant question is not:

"How safe is project A?"

But rather:

"What combination of A, B, C ... under budget and constraints maximizes the total value?"

This is a combinatorial optimization problem.

Above a certain number of projects, this problem becomes NP-hard.

Simulation does not help here. Only algorithmic search methods can systematically structure the space.

8. Why 10,000 simulations do not provide structural certainty

10.000 simulations generate 10,000 possible outcomes.

But they are all based on the same portfolio structure.

If this structure is 15 % below the globally possible optimum, this gap is never recognized.

Monte Carlo answers:

"How likely is the outcome of this choice?"

Optimization answers:

"Was this choice the best choice in the first place?"

These are two different levels.

9. Ex-ante optimization as the new governance norm

Modern decision architecture in fixed assets PPM requires:

• Complete combination analysis
• Integration of budget restrictions
• Multi-objective optimization (ROI, ESG, risk)
• Constraints
• Dependency logics
• Scenario consistency

An ex-ante optimization not only analyses individual projects, but the system as a whole.

The objective function is defined, constraints are formalized and the combinatorial space is searched in an algorithmically structured manner.

The result is not an expected value band, but a mathematically determined portfolio.

10. Why the global optimum replaces Monte Carlo in fixed assets PPM

When the global optimum is calculated, the result is

• Maximum capital productivity
• Minimized opportunity costs
• Structured risk integration
• Transparent decision-making logic
• Audit-proof governance

Monte Carlo can still serve as a sensitivity tool - but not as a basis for decision-making.

In the context of fixed assets, it loses its primary role.

11. The role of StratePlan

StratePlan analyzes the complete decision space of a fixed assets portfolio, taking into account

• Budget constraints
• Project dependencies
• Multi-objective optimization
• regulatory constraints
• Risk parameters

Instead of carrying out 10,000 random draws, the optimum portfolio configuration is identified algorithmically.

This does not improve Monte Carlo. It becomes superfluous.

This is because uncertainty can be integrated into the target function without fixing the decision space.

12. Consequences for CFOs and the board

For CFOs this means

• Higher return on capital
• Better allocation logic
• Transparent decision templates
• Reduction of decision debt
• Minimization of structural misallocation

For boards this means

• Verifiable decision quality
• Auditable logic
• Governance robustness

Monte Carlo was an answer to uncertainty. Optimization is an answer to complexity.

13. Conclusion

Monte Carlo was a milestone in risk modeling. It was contemporary.

But in fixed assets in PPM, risk assessment is no longer enough.

What is needed is a complete penetration of the decision space.

Simulation answers the wrong question about the right decision. Optimization answers the right question.

The global optimum is not a simulation. It is a property of the decision structure.

And as soon as it is calculated, Monte Carlo loses its strategic relevance.

FAQ

Is Monte Carlo fundamentally wrong?

No. Monte Carlo is a valid instrument for analyzing uncertainty. However, it is not an optimization method and is therefore unsuitable for identifying the globally best portfolio.

Can Monte Carlo be useful in combination with optimization?

Yes, as a supplementary sensitivity analysis after identification of the optimal portfolio. Not as primary decision logic.

Why is ranking by NPV not sufficient?

Because projects are interdependent and budget restrictions generate combinatorial effects that ranking does not reflect.

Is global optimization mathematically realistic for large portfolios?

Yes, modern algorithmic methods enable the structured analysis of exponential decision spaces.

Does this mean the end of risk modeling?

No. Risk is integrated - but no longer simulated in isolation.

Why is this particularly relevant for fixed assets?

Because misallocations here are long-term and hardly reversible.

Does this change the role of the CFO?

Yes, from the risk assessment of individual projects to the systemic capital allocation architecture.

The strategic consequence is clear: it is not the simulation of uncertainty that determines the return on capital. It is the mathematical structuring of the decision space. And this is where the future of fixed asset governance begins.