Calculate global maximum with AI

Why AI-based project portfolio management is structurally overtaking traditional decisions

Executive Summary

Companies invest billions in projects, programs and transformations every year. Nevertheless, a recurring pattern emerges in practice:

It is not individual projects that are the problem - but their combination.

Traditional project portfolio management (PPM) structures, prioritizes and creates transparency. What it does not usually do, however, is systematically calculate the globally optimal project portfolio.

As the number of projects increases, the decision space grows exponentially:

• 10 projects → 1,024 combinations
• 20 projects → over 1 million combinations
• 30 projects → over 1 billion combinations
• 50 projects → ~1.125 quadrillion combinations

This order of magnitude is unmanageable for conventional methods.

This is exactly where AI-supported combinatorial optimization comes in: It transforms project portfolio management from a structuring process to a decision-making system that calculates the global maximum ex ante.

1. The structural problem in project portfolio management

Project portfolio management fulfills three central functions:

• Collection and structuring of projects
• Creation of transparency
• Supporting decision-making processes

These functions are necessary - but not sufficient.

The crucial blind spot

The following applies implicitly in almost all organizations:

Decisions are made without analyzing the complete decision space.

Instead, they are used:

• Scoring models
• Business cases
• Prioritization rounds
• Management workshops
• Scenario analyses

These methods have a common structural feature:

They reduce complexity instead of fully calculating it.

2. The decision space: Why 2^N changes everything

The central mathematical principle behind project portfolios is simple - but has far-reaching consequences:

Each project can either be chosen or not chosen.

This results in:

Number of possible portfolios = 2^N

With each additional project option, the decision space doubles.

Consequence

With 30 projects:

• over 1,000,000,000 possible combinations

With 50 projects:

• more combinations than seconds since the creation of the universe

Practical implication

No management board, no PMO, no Excel model can

• think through all combinations
• consider all dependencies
• optimize all constraints simultaneously

The result is systematic suboptimality.

3. Why classic methods do not lead to the global maximum

3.1 Heuristic prioritization

Typical:

• Top-down selection
• Budget-based cuts
• "Top 10 projects"

Problem:

→ considers only a subset of the decision space

3.2 Scoring models

Typical:

• weighted criteria (ROI, risk, strategy fit)
• Ranking of projects

Problem:

→ optimizes projects in isolation, not their combination

3.3 Scenario and Monte Carlo approaches

Typical:

• Simulation of uncertainties
• Probability distributions

Problem:

→ simulate outcomes, but do not make optimal choices

3.4 decision rounds / governance

Typical:

• Committee decisions
• iterative adjustments

Problem:

→ limited cognitive capacity + biases

4. The actual goal: The global maximum

The goal of a project portfolio is not

• the best project
• the best ranking
• the most plausible scenario

But rather:

The combination of projects that generates the maximum overall benefit under all restrictions.

This is the global maximum.

Formally abstracted:

Maximize:

• Total value (e.g. NPV, EBIT, impact)

Under constraints:

• Budget
• Resources
• Dependencies
• Risks
• strategic requirements

Decisive point

The global maximum is:

• no opinion
• no simulation
• not an estimate

But:

a property of the underlying data space

5. AI as a decision engine: from PPM to optimization

AI in project portfolio management is often misunderstood as a

• Dashboard
• Forecasting model
• Assistance system

This falls short.

The real paradigm shift

AI enables

the complete or approximately complete analysis of the decision space

Core components of modern decision AI

1. Combinatorial optimization

• Searches the space of 2^N combinations
• Uses methods such as:
  • Mixed Integer Programming (MIP)
  • Branch-and-bound
  • Constraint Programming

2. Constraints as a mathematical model

Example:

• Budget ≤ 500 million
• Project A only with project B
• max. 20 % risk share
• regional distribution

3. Parallelization

• massive reduction in computing time
• Scaling to large decision spaces

4. Decision modeling

• Integration of strategic goals
• Weighting of risks
• Mapping of organizational logic

6. Fixed assets: Why mistakes here are particularly costly

The issue is particularly critical in the area of

Fixed assets

Examples:

• Infrastructure projects
• Real estate developments
• Production facilities
• Energy projects

Characteristics

• high capital commitment
• long terms
• low reversibility

Problem

Wrong decisions lead to

• years of capital misallocation
• limited liquidity
• structural competitive disadvantages

Typical pattern

Organizations:

• evaluate projects individually
• make decisions sequentially
• consider combination effects only to a limited extent

Reality

The value of a project depends on

• other projects in the portfolio
• Synergies
• Cannibalization
• Resource commitment

The optimal portfolio is not the sum of optimal individual decisions.

7. The complete investment list as a prerequisite

An often underestimated point:

Optimization requires completeness.

Required before making a decision:

• complete list of all relevant projects
• no pre-filtering through intuition
• no premature elimination

Why?

Every removed option:

→ changes the decision space
→ Prevents potentially better combinations

Typical error

• "We have already preselected"
• "These projects are set anyway"

Consequence

→ the global maximum can be systematically excluded

8. Quantitative effect: What does this mean in practice?

Experience from optimized portfolios shows

• +20% to +60% added value from the same projects
• significantly better return on investment
• more stable risk structure

Exemplary effect

Dimension	Classic	Optimized (AI)
Decision basis	Subset	Entire space
Consideration of dependencies	limited	complete
Return on investment	suboptimal	globally maximized
Risk allocation	inconsistent	systematic
Transparency	high	high + explainable
Decision quality	plausible	mathematically optimal

9. From "good decisions" to optimal decisions

A central misconception in organizations:

"If we have good processes, we make good decisions."

This is only partly true.

Reality

Good processes lead to:

• comprehensible decisions
• accepted decisions

But not necessarily to

• optimal decisions

Difference

Category	Classical	Optimization
Decision type	plausible	calculated
Basis	reduced complexity	complete space
Quality	good	globally optimal

10. Strategic implication for companies

The ability to calculate the global maximum becomes a structural competitive advantage.

Why?

Because it enables

• better capital allocation
• higher returns with the same budget
• faster strategic adaptation

Comparison

Two companies with identical projects:

• Company A uses classic methods
• Company B uses optimization

→ Company B achieves significantly higher results in the long term

11. Conclusion

Project portfolio management remains essential - but:

It is the basis of the decision, not the decision itself.

The real transformation lies in the ability to

analyze the entire decision space and calculate the global maximum

AI is not an assistance system, but rather

a decision engine

FAQ

1. What does "global maximum" mean in the project portfolio?

The global maximum is the combination of projects that generates the maximum overall benefit under all given restrictions (budget, resources, risk, etc.). It is a mathematically defined optimal solution.

2. Why is classic project portfolio management not enough?

Because it does not systematically analyze the complete decision space (2^N combinations). Decisions are therefore inevitably based on subsets and lead to suboptimal results.

3. Is the global maximum really calculable in practice?

Yes, with modern methods of combinatorial optimization and parallelization, the decision space can be searched efficiently or approximated with high precision.

4. Is this not just a theoretical concept?

No. In real applications, significant differences in return and effect can be seen, as combination effects are systematically taken into account.

5. What data is required?

• List of all projects
• Investment costs
• expected values (e.g. NPV)
• Restrictions (budget, resources, etc.)

Optional:

• Risks
• Dependencies
• strategic weightings

6. What is the difference between optimization and simulation?

Simulation shows possible developments. Optimization determines the best decision within these possibilities.

7. Is this only relevant for large companies?

No. Especially with limited budgets, optimal allocation is crucial, as wrong decisions carry more weight.

8. How does this change the role of management?

Management continues to make decisions - but on the basis of

• complete transparency
• quantified alternatives
• clearly identified opportunity costs

9. What specific role does AI play?

AI enables:

• Modeling of complex decision spaces
• efficient search for optimal solutions
• Integration of multiple targets and restrictions

10. What is the biggest lever?

The greatest leverage lies not in better projects, but in

the better combination of existing projects