Optimization: Project Portfolio

Purpose

This calculator selects projects to maximize total value under optional budget, resource, count, mandatory-project, and project-rule constraints.

It answers the question every planning cycle raises: given everything you could fund, which specific set of projects should you actually commit to so total value is maximized without breaking budget, headcount, or dependency rules?

Background

Problem Domain

Portfolio optimization is a constrained binary selection problem (choose/do not choose each project). It follows the same logic used in capital budgeting and venture portfolio construction: individually attractive projects can still be dropped once budget, resource, and dependency rules interact across the whole set.

Real-World Uses

• Capital allocation: Viable initiatives often outnumber available budget. Use the model to select the project combination that maximizes total value under funding and resource limits.
• Product roadmap selection: Feature candidates compete for finite delivery capacity and spend. Use the model to prioritize the highest-value set while respecting hard constraints.
• R&D portfolio planning: Opportunity value may be high but investment caps are strict. Use the model to choose projects objectively while enforcing minimum or maximum portfolio size.
• Dependency-aware prioritization: Some projects require prerequisites and others cannot run together. Use the model to build a feasible portfolio that respects depends_on and excludes rules.

Inputs

• projects: Input table with required columns Project, Value, and Cost, plus optional Resource and Must Do. Any row with Must Do > 0 is forced into the selected portfolio.
• project_rules: Input table with columns From, To, and Type where Type is one of depends_on or excludes. depends_on means selecting From requires selecting To; excludes means the two projects cannot both be selected.
• project_budget_limit: Optional total cost cap on selected projects.
• project_resource_limit: Optional total resource cap. This requires Resource in the projects table.
• project_max_selected: Maximum number of selected projects. Use 0 for no upper limit.
• project_min_selected: Minimum number of selected projects. Use 0 for no lower limit.
• show_zero: Controls output display. Turn on to include non-selected projects; turn off to show only selected projects.

Results

• Summary: Portfolio headline with selected project count, total value, total cost, and active limit references. This is your primary decision-quality snapshot.
• Decision Table: Project-level selection details including selected flag and value/cost/resource contributions, so stakeholders can review what was kept versus dropped.
• Constraint Slack: Slack for budget, resource, count, and rule constraints, useful for seeing whether additional budget/capacity would likely improve portfolio value.

Understanding the Calculation

Objective:

• Maximize $\sum_p \text{Value}_p x_p$.

Constraints can include:

• Budget: $\sum_p \text{Cost}_p x_p \le B$
• Resource: $\sum_p \text{Resource}_p x_p \le R$
• Count bounds, must-do constraints, dependency/exclusion rules.

Example

Default run gives Optimal objective 400, selecting 3 projects with total cost 215 under budget limit 220.

Interpretation: selected combination yields highest possible total value while remaining within constraints. A project can be rejected here even with a great value-to-cost ratio on its own — depends_on and excludes rules mean the best portfolio is not just the sum of the best individual projects.

Important Assumptions and Limitations

• Project values and costs are treated deterministic and additive.
• No schedule/time-phased dependency modeling.
• No risk-adjusted objective in this model.