Calculate shadow price of capacity

What it's for

Shows which scarce engineering capability is economically worth expanding and what one decision-sized increment could unlock.

What you give it

Inputs split into evidence read from your connected systems, calibration your team owns, and numerical controls that affect precision but never the result's meaning.

{
  "initiatives": [
    {
      "id": "platform",
      "net_value_scenarios": [
        90,
        100
      ],
      "resource_requirements": {
        "backend": 2,
        "design": 1
      }
    },
    {
      "id": "growth-a",
      "net_value_scenarios": [
        50,
        60
      ],
      "resource_requirements": {
        "backend": 1,
        "design": 1
      }
    },
    {
      "id": "growth-b",
      "net_value_scenarios": [
        45,
        55
      ],
      "resource_requirements": {
        "backend": 1,
        "design": 1
      }
    }
  ],
  "resources": [
    {
      "capacity": 2,
      "capacity_increment": 1,
      "id": "backend"
    },
    {
      "capacity": 10,

What you get back

This is the actual output of running the example above — computed by the same function the platform calls, not an illustration.

{
  "assumptions": [
    "Initiatives are indivisible, requirements and capacities share one planning horizon, scenario columns are aligned, and net values include every incremental cost and opportunity cost represented by the decision.",
    "A discrete shadow price is the re-optimized objective gain from the declared capacity increment divided by that increment; it may be zero or discontinuous and is not a continuous linear-program dual.",
    "Exact mode certifies the represented subset search only; heuristic-mode prices are policy-dependent lower-quality estimates without an optimality certificate and must not justify hiring, procurement, or person-level action alone."
  ],
  "configuration": {
    "initiative_count": 3,
    "maximum_exact_states": 262144,
    "resource_count": 2,
    "risk_aversion": 0.5,
    "scenario_count": 2,
    "solver_mode": "exact_enumeration",
    "tail_probability": 0.1
  },
  "decision": "capacity_shadow_prices_exact",
  "method": "discrete_portfolio_reoptimization_shadow_price_v1",
  "resource_diagnostics": [
    {
      "augmented_selected_initiative_ids": [
        "platform",
        "growth-a"
      ],
      "baseline_slack": 0,
      "baseline_usage": 2,
      "capacity": 2,
      "capacity_increment": 1,
      "discrete_shadow_price_per_capacity_unit": 67.5,
      "marginal_risk_adjusted_portfolio_value": 67.5,
      "portfolio_changes_after_increment": true,
      "resource_id": "backend"
    },
    {
      "augmented_selected_initiative_ids": [
        "growth-a",
        "growth-b"
      ],
      "baseline_slack": 8,
      "baseline_usage": 2,
      "capacity": 10,
      "capacity_increment": 1,
      "discrete_shadow_price_per_capacity_unit": 0,
      "marginal_risk_adjusted_portfolio_value": 0,
      "portfolio_changes_after_increment": false,

How it works

Constrained optimization — Pick the best feasible option under real limits — budget, headcount, dependencies, capacity — rather than ranking a list and hoping it fits.

1. 1 Freeze indivisible initiatives, complete aligned net-value scenarios, resource requirements, capacities, and a decision-relevant increment for every capacity pool.
2. 2 Optimize the baseline portfolio under expected value minus the governed CVaR loss penalty, add one capacity increment at a time, re-optimize, and divide objective gain by the increment.
3. 3 Treat zero and discontinuous prices as legitimate lumpy-portfolio results and use heuristic-mode prices only as uncertified screening estimates requiring exact or operational follow-up.

Before you trust it

Every tool in the catalog ships with the conditions under which its answer is meaningful — and the conditions under which it should abstain instead of guessing.

Calibrating it to your org

Calibration workflow

1. 1 Define the management decision, target outcome, aggregate unit, privacy boundary, cadence, and prediction/intervention horizon for this organization.
2. 2 Build a tenant-scoped historical cohort using only information available before each prediction or decision; preserve zero periods, censoring, assignment probabilities, and unresolved outcomes when the method requires them.
3. 3 Estimate statistical parameters on training history, but obtain costs, utilities, risk tolerance, practical-effect thresholds, capacity, and policy constraints from accountable decision owners.
4. 4 Validate on later time windows or held-out aggregate units at the deployment grain, against a simple baseline and the function-specific validation strategy.
5. 5 Deploy only if the returned decision clears evidence, overlap, calibration, robustness, and guardrail checks; warning, unsupported, schema-gap, and fallback decisions are abstentions.
6. 6 Monitor realized outcomes, data drift, coverage, and decision regret; recalibrate at a governed cadence or after a detected regime/definition change, never merely because a stakeholder dislikes the result.

Call it from your AI

You don't wire up 388 tools in your MCP client. The GitRevio MCP server exposes 18 tools, three of which let an agent search the catalog, read a tool's schema, and run it — so the assistant finds this one on its own.

gitrevio_capabilities_search
  { "q": "calculate lumpy discrete capacity shadow prices" }
  → finds "calculate_shadow_price_of_capacity"

gitrevio_capability_describe
  { "capability_id": "calculate_shadow_price_of_capacity" }
  → returns the input schema and agent guidance shown on this page

gitrevio_capability_run
  { "capability_id": "calculate_shadow_price_of_capacity", "arguments": { ... } }
  → returns the result shown above

Works in Claude Desktop, Claude Code, Cursor, Cline, Continue.dev, Goose and Aider. See the MCP server.

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