Project Portfolio Management Optimization: Optimally Selecting Projects Given Budget, Resource, and Dependency Constraints
Project Portfolio Management Optimization combines traditional project portfolio management with mathematical portfolio optimization. Rather than simply recording, evaluating, and prioritizing projects, it calculates which combination of projects generates the highest achievable total value given a limited budget, project dependencies, mandatory projects, and other portfolio constraints.
This is precisely where the central challenge of large project portfolios lies:
The company has more viable projects than it has budget and resources.
At the same time, projects cannot be selected independently of one another.
Project B may depend on Project A. Project C may be mandatory. Project D and Project E may require the same resources. Two projects may be mutually exclusive. Minimum or maximum budgets may apply to individual business units.
This turns project prioritization into a constraint optimization problem.
The crucial question is no longer:
“Which projects have the highest priority?”
But rather:
“Which permissible combination of all projects generates the highest total value under our real-world conditions?”
Table of Contents
- What Is Project Portfolio Management Optimization?
- What Is Portfolio Optimization?
- What Are Project Dependencies?
- What Are Mandatory Projects?
- What Are Portfolio Constraints?
- How to Prioritize Projects When the Budget Is Limited
- How to Select the Best Combination of Projects
- How to Optimize a Project Portfolio Under Constraints
- How to Model Project Dependencies
- How to Include Mandatory Projects in Portfolio Optimization
- What Types of Portfolio Constraints Are There?
- Why Project Ranking Is Not Sufficient When Dealing with Constraints
- The Mathematical Portfolio Model
- Typical Dependency Rules
- How Mandatory Projects Change the Decision Space
- Example: Selecting Projects with a Limited Budget
- Example: Project dependencies alter the optimal portfolio
- Example: Mandatory Projects in the Portfolio
- Optimizing Multiple Constraints Simultaneously
- Testing Portfolio Constraints with What-If Analysis
- Constraint Optimization Live in the Boardroom
- Project Portfolio Management Optimization with StratePlan
- Frequently Asked Questions About Portfolio Optimization and Constraints
What is Project Portfolio Management Optimization?
Project Portfolio Management Optimization extends traditional project portfolio management by adding a mathematical decision-making layer.
Traditional PPM typically provides transparency regarding:
- Projects
- Budgets
- Status
- Resources
- Milestones
- Risks
- Priorities
- Project Progress
This information is important for portfolio management.
However, it does not automatically answer the question of which projects from the entire project universe should actually be selected.
Project Portfolio Management Optimization therefore complements a mathematical selection process.
In this process, projects, target values, and constraints are considered within a common decision-making model.
PPM shows what is currently in the portfolio. Portfolio Optimization calculates which combination should be selected under the defined conditions.
What is Portfolio Optimization?
Portfolio Optimization refers to the mathematical optimization of a combination of projects or investments under defined objectives and constraints.
A simplified objective function might be:
Maximize the total value of all selected projects.
Subject to the condition:
Total expenditures ≤ available budget.
In real-world companies, additional conditions apply.
For example:
- Project A is mandatory
- Project B may only be implemented in conjunction with Project C
- Project D requires Project E
- Project F and Project G are mutually exclusive
- Business Unit A requires a minimum budget
- Business Unit B has a maximum budget
- Engineering capacity is limited
- A maximum of 25 projects may be implemented simultaneously
Portfolio optimization takes these conditions into account when selecting projects.
The goal is not to find the portfolio with the highest theoretical value without restrictions.
Instead, the goal is to identify the portfolio with the highest achievable value within the actual decision-making constraints.
What are project dependencies?
Project dependencies are relationships between projects whereby the selection or implementation of one project is influenced by one or more other projects.
A simple example:
New production software can only be implemented once the technical infrastructure has been modernized.
Thus, Project B depends on Project A.
Other forms of project dependencies may include:
- Project A is a prerequisite for Project B
- Project A and Project B must be selected together
- Project A and Project B must not be selected at the same time
- Project B may not begin until Project A is completed
- Project C is only economically viable if Project D is also implemented
- Multiple projects compete for the same resource
Dependencies alter the permissible decision space.
A combination of projects may appear financially attractive but still be inadmissible if it violates a necessary dependency.
What are Mandatory Projects?
Mandatory Projects are projects that must be part of the portfolio regardless of their relative economic attractiveness.
Reasons for this may include, for example:
- Legal requirements
- Compliance
- Occupational safety
- Cybersecurity
- Contractual obligations
- Regulatory Requirements
- Critical Maintenance
- Commitments Already Made
- Strategic Management Decisions
A mandatory project is not treated like an optional project during portfolio optimization.
It is included in the decision-making framework as a fixed condition.
The available budget for all other projects is reduced accordingly.
The optimization process does not determine whether the Mandatory Project is implemented. Instead, it calculates the best remaining portfolio decision given this constraint.
What are portfolio constraints?
Portfolio constraints are conditions that a valid project combination must satisfy.
They represent real-world financial, operational, strategic, and organizational limits within the mathematical portfolio model.
For example, a portfolio constraint might be:
Total budget ≤ 500 million €
or:
Engineering effort ≤ 20,000 hours
or:
Project A must be selected.
or:
If Project B is selected, Project C must also be selected.
Constraints therefore do not interfere with the optimization.
They define the actual decision space within which optimization is to take place.
How to Prioritize Projects When the Budget Is Limited
When the budget is limited, the traditional approach is often to prioritize projects and then work through the list from top to bottom until the budget is exhausted.
This method may seem reasonable, but it has a significant drawback:
It considers projects primarily on an individual basis.
Suppose the available budget is 100 million euros.
| Project | Cost | Expected Value |
|---|---|---|
| Project A | €100 million | €150 million |
| Project B | €60 million | €100 million |
| Project C | €40 million | €80 million |
Project A has the highest individual value.
If it is selected, the portfolio value will be 150 million euros.
However, Project B and Project C can be implemented together.
They also require exactly 100 million euros.
Their combined expected value is 180 million euros.
When the budget is limited, therefore, one should not focus solely on the priority of individual projects. What matters most is the combination that makes the most effective use of the available budget.
How to Select the Best Combination of Projects
The best combination of projects can only be determined once it is first defined what “best” means.
Possible objectives include:
- Maximize NPV
- Maximize expected revenue
- Maximize portfolio ROI
- Maximize strategic utility
- Maximize risk reduction
- Optimize Multiple Objectives in Combination
Next, the actual constraints are defined.
For example:
- Budget
- Resources
- Project Dependencies
- Mandatory Projects
- Business Unit Boundaries
- Location Rules
- Time Constraints
The optimization model then searches within the permissible decision space for the project combination that best fulfills the defined objective function.
The best combination is therefore not the sum of the best individual projects. It is the best portfolio under the defined conditions.
How to Optimize a Project Portfolio Under Constraints
A project portfolio under constraints is optimized by modeling objective functions and constraints together in a mathematical decision-making model.
The process can be carried out in six steps:
- Define the project universe: Identify all possible projects.
- Set the objective: For example, NPV, revenue, or strategic utility.
- Define the budget: Specify the available financial resources.
- Model constraints: Add resources, dependencies, mandatory projects, and other conditions.
- Optimize the portfolio: Mathematically calculate permissible project combinations.
- Compare scenarios: Test alternative assumptions and restrictions.
This ensures that the optimization is not merely theoretical and detached from the reality of the business.
The real-world conditions themselves become part of the mathematical model.
How to Model Project Dependencies
Project dependencies can be formulated as logical conditions within the optimization model.
For example, a binary decision variable can be used for each project:
1 = Project is selected
0 = Project is not selected
If Project B may only be implemented if Project A is also implemented, the logical relationship can be simplified as follows:
B ≤ A
If B is selected, A must also have the value 1.
Additional dependencies can be modeled in a similar way.
If A and B may only be implemented together:
A = B
If A and B are mutually exclusive:
A + B ≤ 1
If at least one of the two projects must be selected:
A + B ≥ 1
This transforms organizational project rules into mathematical constraints.
How to Include Mandatory Projects in Portfolio Optimization
Mandatory projects can be directly incorporated into the portfolio model as fixed decision conditions.
If project M is mandatory, the following is defined:
M = 1
This makes the project a component of every permissible portfolio configuration.
Assume:
Total budget = 500 million €
Mandatory Project = 80 million €
This leaves 420 million euros for optimizing the remaining projects.
The calculations continue to take into account all dependencies and other constraints.
Mandatory projects are not treated separately from the optimization. They are integrated into the optimization as fixed constraints.
What types of portfolio constraints are there?
Portfolio constraints can reflect various business realities.
Budget Constraints
The entire portfolio must not exceed a defined capital limit.
Resource Constraints
Projects collectively may not require more resources than are available.
Mandatory Constraints
Certain projects must be included in the portfolio.
Dependency Constraints
Some projects depend on other projects or must be implemented together.
Mutual Exclusion Constraints
Certain projects cannot be selected at the same time.
Business Unit Constraints
Minimum or maximum budgets may apply to business units.
Plant Constraints
Locations may have their own capital or resource requirements.
Strategic Constraints
A portfolio must meet defined strategic minimum requirements.
Time Constraints
Projects must be started or completed within specific time frames.
In real-world portfolios, many of these constraint types can occur simultaneously.
Why Project Ranking Is Insufficient When Dealing with Constraints
A ranking puts projects in a specific order.
However, complex constraints can render this order useless.
Suppose:
Project A has the highest score.
Project B has the second-highest score.
Project C has the third-highest score.
However, if Project B depends on Project D and B + D together exceed the available budget, Project B cannot simply be selected based on its position in the ranking.
Or Project A and Project C are mutually exclusive.
In that case, a simple top-down selection is also not possible.
The more constraints a portfolio has, the less meaningful a simple ranking is for the final portfolio decision.
The Mathematical Portfolio Model
A simplified portfolio model can consist of an objective function and several constraints.
For each project i, a decision variable xᵢ is defined:
xᵢ = 1 if project i is selected
xᵢ = 0 if project i is not selected
A simplified objective function might be:
Maximize Σ valueᵢ × xᵢ
subject to the budget constraint:
Σ Costᵢ × xᵢ ≤ Budget
Additionally, dependency, resource, mandatory, and other constraints can be added.
This results in a formal model of the real-world portfolio decision.
Typical Dependency Rules
| Business Rule | Simplified Model Logic |
|---|---|
| B requires A | B ≤ A |
| A and B only together | A = B |
| A or B, but not both | A + B ≤ 1 |
| At least A or B | A + B ≥ 1 |
| A is required | A = 1 |
| At most two of A, B, and C | A + B + C ≤ 2 |
This allows even more complex project rules to be represented in a structured way.
How Mandatory Projects Change the Decision Space
Mandatory Projects consume budget and resources before decisions are made among the freely selectable projects.
This can significantly alter the optimal composition of the remaining portfolio.
For example, a high-value project may be dropped from the portfolio because a new regulatory Mandatory Project ties up part of the budget.
It is therefore important not to simply eliminate any existing project following the introduction of a new mandatory requirement.
The entire remaining portfolio should be re-optimized under the new conditions.
New mandatory projects do not just alter the available budget; they can also change the optimal combination of all other projects.
Example: Selecting Projects with a Limited Budget
A company has 80 potential projects.
The total capital requirement is 750 million euros.
The available budget is 500 million euros.
All projects have already been evaluated and have positive business cases.
The problem, therefore, is not identifying poor projects.
The problem is selecting the best combination within the 500 million euro budget.
In portfolio optimization, therefore, all projects are considered together.
The calculation takes into account:
- Project costs
- Expected values
- Budget
- Resources
- Dependencies
- Mandatory Projects
The result is a valid project combination that best meets the defined target under these conditions.
Example: Project dependencies change the optimal portfolio
Suppose Project B has a high expected value.
However, Project B can only be implemented if Project A is funded at the same time.
| Project | Cost | Expected Value | Dependency |
|---|---|---|---|
| A | 30 million € | €20 million | Prerequisite for B |
| B | €70 million | €140 million | Required for A |
| C | €90 million | €145 million | None |
Project B costs 70 million euros on its own.
However, due to the dependency, the actual capital requirement for Decision B is 100 million euros, because A is also required.
This changes the comparison between B and C.
Project dependencies alter the economic logic of project selection and must therefore be taken into account before a portfolio decision is made.
Example: Mandatory Project in the Portfolio
A company has a portfolio budget of 400 million euros.
A new regulatory project with a cost of 75 million euros becomes mandatory.
This leaves 325 million euros for all other projects.
A simple approach would be to remove projects worth 75 million euros from the existing portfolio.
However, this may not result in the best new portfolio configuration.
Due to the changed budget limit, other project combinations may become more attractive.
Therefore, the Mandatory Project is included as a fixed constraint, and the entire portfolio is re-optimized.
Optimizing Multiple Constraints Simultaneously
The true complexity of real-world portfolios arises from the combination of various constraints.
For example, a portfolio may have the following conditions at the same time:
- Total budget of no more than 800 million €
- Business Unit A: at least 100 million €
- Business Unit B: maximum of 250 million €
- Project 17 is mandatory
- Project 22 requires Project 9
- Project 31 and Project 32 are mutually exclusive
- Maximum of 30 parallel projects
- Engineering capacity: maximum 25,000 hours
- Strategic Growth Score of at least 70
Each additional condition alters the permissible decision space.
This is precisely where the strength of mathematical portfolio optimization lies.
Budget, resources, dependencies, mandatory projects, and strategic guidelines are not evaluated one after another. Instead, they are integrated into the same decision-making model.
Test portfolio constraints with what-if analysis
Constraints are not always fixed.
Management can therefore examine how alternative conditions affect the portfolio.
For example:
“What happens if the budget decreases by 15 percent?”
“What happens if this project becomes mandatory?”
“What happens if we have 5,000 more engineering hours available?”
“What are the implications of a higher minimum investment in Business Unit A?”
“What happens if Project B is no longer dependent on Project A?”
The portfolio can be recalculated for every change.
This reveals the economic cost of individual constraints and the additional opportunities created by changing them.
Constraint Optimization Live in the Boardroom
Portfolio constraints are often adjusted right where the final decision is made: in the management meeting.
The CFO cuts the budget.
The COO reports a resource constraint.
Compliance declares an additional project mandatory.
The CEO changes a strategic priority.
As a result, the previous portfolio analysis may become outdated within minutes.
With StratePlan’s CAPEX Live Boardroom Simulation, prepared portfolio models can be recalculated under changed conditions.
Management can, for example, ask directly:
“Make this project mandatory.”
“Reduce the budget by 100 million euros.”
“Increase the minimum budget for Business Unit A.”
“Which projects will now be dropped?”
“How much portfolio value are we losing?”
“Is there a better combination?”
The decision model is recalculated, and alternative portfolio configurations can be compared with one another.
Ask a question. Change a constraint. Recalculate. Compare. Decide.
Project Portfolio Management Optimization with StratePlan
StratePlan combines Project Portfolio Management Optimization, Project Selection, and mathematical constraint optimization within a single decision-making model.
Companies can view projects, expenditures, expected outcomes, strategic criteria, and real-world portfolio constraints together.
These include, among others:
- Budget Constraints
- Resource Constraints
- Project dependencies
- Mandatory projects
- Mutual Exclusions
- Business Unit Constraints
- Plant Constraints
- Strategic Criteria
- Multi-Year Constraints
This allows for the calculation of the following management questions, among others:
- Which projects should be selected given a limited budget?
- Which combination yields the highest achievable total value?
- How do project dependencies affect the optimal project selection?
- How can mandatory projects be taken into account?
- Which projects are eliminated when a new mandatory project is added?
- How do resource constraints affect the outcome?
- What is the cost of a specific restriction in terms of portfolio value?
- What impact do business unit budget limits have?
- How does the portfolio change in response to new strategic guidelines?
- Which portfolio configuration is permissible and maximizes value under all defined constraints?
This transforms a prioritized list of projects into a mathematically defined decision space.
Don’t just prioritize projects. Optimize the portfolio under real-world constraints.
Frequently Asked Questions About Portfolio Optimization and Constraints
What is Project Portfolio Management Optimization?
Project Portfolio Management Optimization extends traditional project portfolio management to include mathematical optimization. It calculates which combination of projects best meets the defined objective within budget, resource, and other constraints.
What is Portfolio Optimization?
Portfolio optimization is the mathematical selection and combination of projects or investments based on defined objectives and constraints. The goal may be, for example, to maximize NPV, revenue, or strategic value.
What Are Project Dependencies?
Project dependencies are relationships between projects. For example, one project may require another project to be completed first, must be implemented together with another project, or may be mutually exclusive with another project.
What are Mandatory Projects?
Mandatory projects are projects that must be included in every permissible portfolio configuration. Reasons for this may include regulation, compliance, security, or strategic requirements.
What are Portfolio Constraints?
Portfolio constraints are conditions that a valid portfolio must meet. These include, for example, budget limits, resource limits, project dependencies, mandatory projects, business unit rules, and strategic minimum requirements.
How to Prioritize Projects When the Budget Is Limited?
When the budget is limited, projects should not be prioritized solely on an individual basis. Instead, you should also examine which combination of available projects makes the most efficient use of the budget and generates the highest overall value while adhering to all relevant constraints.
How to Select the Best Combination of Projects?
First, the target metric and portfolio constraints are defined. Then, mathematical optimization can be used to determine, within the permissible decision space, the combination of projects that best meets the defined target metric.
How to Optimize a Project Portfolio Under Constraints?
Projects, objective measures, and constraints are modeled within a single mathematical model. The optimization process then searches for a feasible combination of projects that maximizes, for example, total NPV, expected revenue, or strategic value.
How to Model Project Dependencies?
Project dependencies can be modeled as logical mathematical conditions. For example, if Project B depends on Project A, the relationship can be simplified to B ≤ A when using binary decision variables.
How to Include Mandatory Projects in Portfolio Optimization?
A mandatory project is modeled as a fixed selection condition. For a binary decision variable, the project is set to 1 and is thus part of every feasible portfolio configuration.
Why Is Project Prioritization Insufficient for Complex Portfolios?
Prioritization generates a ranking of individual projects. However, it does not automatically take into account which combination of projects generates the highest overall value given budget, resource, dependency, and other constraints.
How are mutually exclusive projects modeled?
If only one of two projects may be selected, the condition A + B ≤ 1 can be used for binary variables, for example.
Can multiple portfolio constraints be considered simultaneously?
Yes. Budget limits, resource limits, mandatory projects, dependencies, business unit rules, and other conditions can all be included in the optimization model simultaneously.
What happens when a new mandatory project is added?
The new mandatory project is incorporated into the portfolio as a fixed constraint. The remaining portfolio should then be re-optimized under the reduced budget and the remaining constraints, as the best combination of the other projects may change.
Can Portfolio Optimization show the cost of a constraint?
Alternative scenarios with and without a specific constraint can be compared. The difference between the respective optimal portfolio values can show the impact the constraint has on the target metric within the model being used.
How many possible portfolios result from 100 projects?
With 100 independent binary project decisions, there are theoretically 2^100 possible combinations. This corresponds to approximately 1.27 × 10^30 portfolios before additional constraints limit the permissible decision space.
What is the difference between a portfolio constraint and a project dependency?
A portfolio constraint is the umbrella term for conditions that a portfolio must satisfy. A project dependency is a specific type of constraint that describes a logical or temporal relationship between two or more projects.
