Number of projects and density of restrictions - why classic planning inevitably fails with increasing complexity

In the practice of modern companies, organizations and public institutions, it is not only the number of projects that is increasing, but above all the complexity of their interactions. Decisions become more difficult not because there is too little data, but because too many projects have to be considered simultaneously under too many conditions.

Two factors are decisive here:

• the number of projects
• the density of restrictions

Only the interplay of these two factors determines whether planning can still be mastered using traditional methods - or whether algorithmic optimization is absolutely necessary.

1. What does the number of projects really mean?

The number of projects is often underestimated. In traditional planning, it is often understood as a simple list: Project A, Project B, Project C. In reality, however, each project is a bundle of:

• Sub-projects
• Dependencies
• Resource commitments
• Time frames
• Risks

Even a seemingly small number of projects can lead to a very large number of decisions.

Example

10 projects, each with only two decision options (yes/no), already generate

²¹⁰ = 1,024 possible combinations

If sub-projects, sequences or variants are taken into account, this number increases exponentially.

2. What is restriction density?

Restriction density describes the extent to which the decision space is restricted by constraints.

Restrictions include

• Budget limits
• Capacities (personnel, machines, management)
• time dependencies
• regulatory requirements
• Minimum or maximum quotas
• Risk and compliance rules

Formally, the restriction density can be described as a simplified ratio:

Restriction density ≈ number of restrictions / number of decision variables

It is not only the quantity that is important here, but also the coupling of the restrictions with each other.

3. Low vs. high restriction density

Feature	Low restriction density	High restriction density
Project dependencies	Hardly present	Highly networked
Budget restrictions	Simple, global	Multi-level, cross-project
Resources	Flexible	Tightly limited
Plannability	High	Limited
Suitable tools	Excel, simple models	Algorithmic optimization

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4. Why the number of projects and restriction density work together

A large number of projects alone is manageable as long as the restriction density is low. Conversely, even a small number of projects can become unmanageable if the restriction density is high.

Typical reality

• Many projects
• Limited budgets
• Shared resources
• Regulatory requirements

This combination leads to an exponentially growing decision space.

5. Why classic tools fail here

Classic planning tools work predominantly

• linear
• isolated
• with simplifications

They often evaluate projects individually or prioritize them using simple key figures. Interactions are either not taken into account at all or only roughly.

With a high density of restrictions, this leads to

• suboptimal sequences
• hidden bottlenecks
• unnecessary capital commitment
• missed opportunities

6. NP-Hard: The mathematical reality

Many real project optimization problems belong to the class of NP-hard problems. This means that

• An exact solution is theoretically possible
• The computing time grows exponentially
• Above a certain size, complete enumeration is not practicable

Therefore, the demand for "100 % exact calculation" is not reasonable in practice.

7. Why heuristic and hybrid algorithms are necessary

Algorithmic optimization systems such as StratePlan rely on

• mathematical optimization
• heuristic methods
• experimental algorithms
• Parallelization

The aim is not theoretical perfection, but a very high solution quality in a practicable time.

8. Number of projects, restriction density and ROI

The higher the restriction density, the greater the influence of the sequence and combination of projects on the real ROI.

Scenario	Low restriction density	High restriction density
Single project	ROI stable	ROI strongly dependent on environment
Project portfolio	Sequence secondary	Sequence decisive
Wrong decision	Limited damage	Systemic effect

9. StratePlan as a response to high restriction density

StratePlan is designed to work with:

• many projects
• high density of restrictions
• dynamic changes

dynamic changes.

Important here:

• The strategy comes from people (CEO, CFO, project manager)
• StratePlan validates and optimizes this strategy
• New assumptions can be recalculated at any time

This creates a continuous optimization process instead of one-off planning.

FAQ - Number of projects and restriction density

What is more important: number of projects or restriction density?

The restriction density is usually the more decisive factor. A high restriction density can create extreme complexity even with a small number of projects.

Why does experience alone no longer help?

Experience does not scale exponentially. The human mind can only evaluate a limited number of variables at the same time.

Can you reduce restriction density?

Partly. Through decoupling, clear priorities or additional resources. However, it cannot be completely eliminated in complex systems.

Why is Excel unsuitable?

Excel is an excellent tool for linear, straightforward problems - not for highly networked, combinatorial optimization tasks.

What happens when restrictions change?

Then the optimal solution space changes. This is precisely why iterative, algorithmic recalculations are necessary.

Is high restriction density bad?

Not per se. It is a sign of maturity, regulation and resource efficiency - but it requires better decision-making tools.

Conclusion

As the number of projects and the density of restrictions increase, traditional planning inevitably reaches its limits. Not because people make the wrong decisions, but because complexity grows faster than human intuition.

Algorithmic optimization is therefore not a luxury, but a necessary response to the reality of modern project landscapes.

The higher the density of restrictions, the more important it becomes to make decisions predictable.

Visualization: Why the number of projects and the density of restrictions together overturn planning

If you want to make complexity understandable, you need images. Project portfolios in particular show that it is not the number of projects alone that is critical, but the coupling of projects through restrictions. The following visualization ideas can be used as graphics in the blog, as slides or as AI-generated infographics.

1) Zone model: number of projects × restriction density

Graphic idea: A 2D coordinate system with three clear zones (green/yellow/red):

• X-axis: number of projects (few → many)
• Y-axis: Restriction density (low → high)

Zone	Typical situation	What still works	What happens frequently	Recommendation
Green (bottom left)	Few projects, few dependencies	Excel, simple prioritization, manual planning	Low error rate, stable plan	Classic planning is sufficient
Yellow (center)	More projects, increasing restrictions	Extended models, scenarios, structured reviews	Reprioritization, bottlenecks, re-work	Algorithmic validation becomes useful
Red (top right)	Many projects, high density of restrictions	Individual assessments are no longer sufficient	Systemic errors, portfolio tilts, decisions take too long	Algorithmic optimization becomes necessary

Note: It is not the number of projects that is the problem - but the connections between projects.

2) Combinatorics graphic: Why the decision space is exploding

Graphic idea: An exponential curve or a bar chart (ideally with a logarithmic Y-axis) that shows how much the number of possible combinations grows as the number of projects increases.

Number of projects (yes/no)	Combinations (2^n)	Why this is important
10	1.024	Manageable, but no longer "from the gut"
20	1.048.576	Full audit becomes impractical
30	1.073.741.824	"Check everything" is practically impossible

In reality, projects are rarely just yes/no. Variants, sequences, sub-projects and dependencies increase the complexity significantly.

3) Restriction network: projects as nodes, restrictions as connections

Graphic idea: Network representation:

• Nodes: Projects
• Edges: Restrictions/dependencies (budget, resources, sequence, compliance)
• Thickness/color: Strength of the coupling

Statement: Planning rarely fails because of projects - but because of the edges in between.

4) Business GPS visual: Strategy as route, restrictions as course change

Graphic idea: Navigation metaphor:

• Route = strategy
• Disruption = market/budget change
• Recalculation = StratePlan optimization

Statement: Every new restriction changes the optimal route - therefore iterative recalculation is crucial.

Other topics that fit perfectly with number of projects & restriction density

5) Restriction density as an early warning signal

High restriction density is often first recognized organizationally:

• increasing number of coordination rounds
• frequent reprioritizations
• conflicting budget and resource targets
• Plan changes shortly before implementation

Interpretation: The system is not "poorly managed" - it is mathematically tight. Traditional planning can no longer map this in a stable manner.

6) Human decision limits with exponential complexity

Experience helps enormously, but it does not scale exponentially. With high restriction density, humans have to

• evaluate too many variables at the same time
• keep an eye on too many dependencies
• think through too many scenarios in parallel

Note: Not because people make bad decisions - but because complexity grows faster than intuition.

7) Time is the hidden restriction

The higher the density of restrictions, the longer decisions take - not just calculations:

• more stakeholders
• more coordination
• more checks
• more feedback

Result: time itself becomes a restriction - and worsens the real ROI because windows of opportunity are missed.

8) Organizational maturity creates restriction density (and this is normal)

A high density of restrictions is often a sign of maturity:

• Compliance and governance requirements
• scaled processes
• efficient use of resources
• regulatory framework conditions

Conclusion: Mature organizations do not need fewer rules - they need better optimization tools.

9) Why "simplification" is often harmful

A typical reflex is: "Then let's just leave out a few restrictions." Although this reduces the model effort, it increases the risk:

• Dependencies become invisible
• Bottlenecks only become visible during implementation
• Re-work increases
• Budget and deadline risks increase

Note: Simplification reduces computational effort - but increases decision risk.

10) Robustness instead of best-case: Why stable portfolios win

With a high density of restrictions, the "best" portfolio in the best-case scenario is not automatically the best in reality. The decisive factor is robustness:

• How sensitive is the plan to cost increases?
• How stable is the ROI in the event of delays?
• How well does the portfolio compensate for the loss of individual projects?

Practical benefits: Robust solutions reduce re-work and keep the ROI more stable in turbulent phases.

11) Dynamic restriction density: Why the optimal plan is constantly shifting

Restrictions are not static. Typical changes:

• Budget releases shift
• Supply chains and capacities change
• Interest rates, prices and demand fluctuate
• Regulations are adapted

Consequence: Every relevant change creates a new optimization task. Therefore, iterative recalculation is not an "extra", but a must.

Mini-FAQ: Quick answers for readers

When is restriction density "high"?

When a few decisions can no longer be made independently, but budget, resources, timing and dependencies form a tight network.

Is high restriction density good or bad?

Neither. It is often a sign of scaling and governance - but makes planning mathematically more challenging.

What is the biggest mistake with high restriction density?

Evaluating projects in isolation or simplifying restrictions until the model "fits". Then reality no longer fits.

What is the biggest lever?

Portfolio thinking instead of individual project thinking - plus algorithmic validation/optimization as soon as the number of projects and restriction density get into the red zone.

Local optimization vs. global optimization

Why perfect individual decisions can worsen entire portfolios

A central, often overlooked phenomenon in complex project landscapes is the difference between local and global optimization.

In practice, projects are usually evaluated and optimized individually: Each department, each project team and each person responsible tries to to implement their own project as efficiently, successfully and with as little risk as possible.

What is often overlooked:

A locally optimized project is not automatically part of a globally optimized overall strategy.

Typical practical example

• Project A has the highest individual ROI
• Project B uses the same critical resources
• Project C generates cash flow early on, but is treated as a lower priority

If project A is prioritized, the decision appears correct when viewed in isolation. In the overall portfolio, however, it leads to

• Resource blockages
• delayed cash flow
• higher overall risk

Result: Each project was decided "correctly" - but the portfolio as a whole was wrong.

Why this happens systematically

Local optimization ignores interactions:

• Sequences
• Dependencies
• common restrictions
• Opportunity costs

The higher the number of projects and the tighter the restrictions, the stronger these effects are. Traditional planning therefore favors local excellence - at the expense of global efficiency.

Key point:
Local excellence often generates global inefficiency when the density of restrictions is high.

Restriction density and power structures

Why planning in large organizations is rarely neutral

Restrictions do not arise exclusively from technical or economic necessities. In many organizations, they are also the result of power structures, responsibilities and political negotiation processes.

Typical examples:

• Budgets are distributed historically, not optimally
• Resources are tied to organizational units
• Projects are prioritized in order to secure influence
• Restrictions arise from compromises, not from logic

This form of restriction density is particularly problematic, because it is rarely modeled transparently.

The consequence for planning

• Planning becomes negotiation
• Optimization becomes politically sensitive
• Decisions are defended instead of questioned

As a result, formal planning models do exist, but are in fact overlaid by informal rules.

Why this further increases complexity

Power-based restrictions are

• not clearly measurable
• dynamic
• situation-dependent

They increase the effective restriction density, without this becoming visible in classic models.

Result: The real complexity is significantly higher than the modeled complexity.

Classification

This observation is not a criticism of organizations, but a description of their reality. The larger and more mature an organization is, the greater the impact of such effects.

Note:
The higher the density of restrictions, the more political planning becomes - and the more difficult objective optimization becomes.

Synthesis: What this all means for decisions in practice

The number of projects and the density of restrictions do not work in isolation. It is their interaction that determines whether planning is still controllable or whether it tips over unnoticed into a complex, barely controllable system.

The perspectives described above - local vs. global optimization and the role of power structures - lead lead to a central insight:

Many planning problems are not caused by bad decisions, but by structural framework conditions that overtax classic decision-making logic.

1) Why good individual decisions are not enough

In complex organizations, projects are often decided correctly, cleanly and with a high level of expertise. Nevertheless, systemic undesirable developments arise:

• Resources are blocked
• Cash flows are shifted
• Risks become concentrated
• Flexibility is lost

The reason does not lie in the project itself, but in the interaction of all projects under common restrictions. Local optimization ignores precisely these interactions.

From a global perspective, the decisive factor is not which project is "best", but which combination, sequence and weighting achieves the greatest overall effect under real conditions.

2) Why planning becomes more political as the density of restrictions increases

The higher the density of restrictions, the more planning becomes a negotiation process. Budgets, resources and priorities are then no longer purely mathematical values, but an expression of historical decisions, responsibilities and power relations.

This has two consequences:

• Formal models only incompletely reflect reality
• Decisions are defended instead of optimized

The actual complexity often exceeds the modeled complexity. Restrictions have an effect without being explicitly named or quantified.

3) Why simplification is not a way out

An obvious reflex when complexity increases is simplification: fewer projects, fewer restrictions, coarser models. In the short term, this creates an overview - but in the long term, it creates new risks.

Simplification:

• hides dependencies
• delays the recognition of bottlenecks
• shifts problems to the implementation phase

What is simpler mathematically often becomes more expensive operationally.

4) What is necessary instead

As the number of projects and the density of restrictions increase, the role of planning changes fundamentally:

• from static plans to dynamic decision spaces
• from individual projects to portfolios
• from one-off decisions to iterative recalculation

Decisions must not only be "correct" but also robust - i.e i.e. remain viable even under changing framework conditions.

5) The central conclusion

The number of projects and the density of restrictions are not exceptions, but the normal state of modern organizations.

The decisive difference is not whether complexity exists - but in how it is dealt with.

Those who continue to plan locally, in isolation and statically, will generate systemic wrong decisions with a high density of restrictions.

On the other hand, those who think globally, networked and iteratively create the basis for stable, resilient decisions - even under uncertainty.

The more complex the system, the more important it becomes, Not to simplify decisions, but to make them predictable.

Systemic effects: What also happens with a high density of restrictions

When the number of projects and the density of restrictions increase, it is not only the computational complexity that changes. Systemic effects arise that conventional planning often fails to map because they are not linear and not immediately visible. The following four concepts help to understand this reality precisely.

1) Path dependency

In complex portfolios, decisions are rarely "isolated points". They create paths: Early decisions determine which options are even possible later.

Typical triggers for path dependency:

• budgets committed early (Capex/OpEx) with long durations
• Commitment of resources by key personnel
• advance technological or regulatory decisions
• Sequences of projects (A must be completed before B)

Why this is important: Early prioritization can limit the solution space for later decisions to such an extent, that even better alternatives are no longer achievable - not because they are wrong, but because they come too late.

Remember: Decisions create paths, not points.

2) Decision irreversibility

Not every decision is equally "expensive". In practice, there are decisions with high irreversibility (high lock-in effects) and decisions that are easy to correct.

Decision type	Characteristic	Example	Typical consequence
Reversible	easily adaptable	small budget shift, priority swap in a sprint	Corrections possible, low follow-up costs
Irreversible	high lock-in	large capex commitment, long-term contract, technology lock-in	late corrections expensive, detours necessary

Why this is important: In portfolios with a high density of restrictions, a few irreversible decisions often dominate the overall result often dominate the overall result. Classic planning, however, treats many decisions as if they were of equal value.

Note: The higher the irreversibility, the greater the necessary depth of calculation before the decision is made.

3) Learning ability of organizations under high restriction density

Organizations "learn" through feedback: A decision is made, the effect is observed and corrected. However, as the density of restrictions increases, this learning process becomes slower and more expensive.

Typical reasons:

• Errors only become apparent late in implementation (not in planning)
• Corrections require several release levels
• Re-work affects several projects at the same time
• Dependencies force additional adjustments

Why this is important: Learning is not impossible in highly restrictive systems - but it takes more time, more coordination and more money. Those who continue to plan "as before" learn too slowly for dynamic markets.

Remember: Complex systems learn more slowly - unless they are iteratively recalculated and updated.

4) Temporal decoupling of decision and effect

A particularly critical effect is the delay between decision and actual effect. Many consequences do not become apparent immediately, but only weeks, months or even years later.

Examples:

• Budget decisions only take effect once procurement and implementation have started
• Resource bottlenecks only become apparent when several projects enter the same phase at the same time
• Cash flow effects are often delayed (e.g. after commissioning, acceptance, scaling)

Why this is important: The more decoupled decisions are in terms of time, the greater the risk, that a portfolio moves in a direction that is only recognized as problematic at a very late stage.

Note: The higher the restriction density, the later the error becomes apparent - and the more expensive the correction.

Compact conclusion

A high number of projects and a high density of restrictions not only generate "more effort", but also systemic dynamics: Path dependency, irreversibility, slowed learning and time-delayed effects. Those who ignore these effects seemingly stable planning - and only notice the instability during implementation.

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