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Critical Path Method (CPM) DAG & Resource Constraint Scheduler

schedule_critical_path_tasks
Read-onlyIdempotent

Schedules dependent tasks with CPM to compute earliest/latest start and finish times, float, minimum makespan, and the critical path for identifying zero-slack bottlenecks.

Instructions

Solves a task dependency DAG via the Critical Path Method (CPM) to compute ES/EF/LS/LF, Total Float/Slack, optimal makespan, and the Critical Path. Use when scheduling dependent engineering milestones or workflow steps to find the minimum project duration and zero-slack bottleneck path; for detecting circular code imports and file blast radius without task durations, use audit_module_dependency_cycles instead. Read-only edge call (32 KB, 60 RPM): accepts 'tasks_json' ('time_unit' defaults to 'minutes'), supports '?demo=true' or L402 (20 sats), and returns HTTP 400 if invalid.

Input Schema

NameRequiredDescriptionDefault
time_unitNoDuration unit label attached to the schedule; defaults to 'hours' when omitted.
tasks_jsonYesJSON string or array of tasks '[{"id":"t1","duration":3,"dependencies":[]}]' to schedule.

Output Schema

NameRequiredDescriptionDefault
total_tasksYesNumber of DAG tasks scheduled.
critical_pathYesOrdered task IDs with zero slack that determine the overall project duration.
task_scheduleYesPer-task earliest_start, earliest_finish, latest_start, latest_finish, and total_float_slack.
optimal_makespan_durationYesMinimum total duration required to complete all tasks.

Schema Changelog

Changes observed during successful MCP inspections.

  1. Addedv1.3.3

TDQS

A4.4/5.0
Behavior5/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Goes well beyond the annotations (which only cover read-only/idempotent/non-destructive) by disclosing a 32 KB payload cap, 60 RPM rate limit, demo-mode access, L402 payment cost (20 sats), and HTTP 400 on invalid input. That is exactly the operational context an agent needs before calling.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Purpose and scope are front-loaded, then the alternative routing, then operational constraints. The final sentence is a dense run-on packing size, rate limit, auth, and error code together, but every clause carries information; nothing is filler.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

An output schema exists, so return structure need not be explained, and the description covers auth, limits, and error behavior for a 2-parameter tool. The only shortfall is the incorrect default-unit claim, which leaves the caller with conflicting information about the one enum parameter.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters2/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The description asserts "'time_unit' defaults to 'minutes'", but the input schema states the default is 'hours'. With 100% schema coverage the baseline would be 3, but a stated default that contradicts the schema is actively misleading and could produce wrong-unit schedules. The tasks_json shape is only echoed from the schema, adding no new guidance.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb+resource combination ('Solves a task dependency DAG via the Critical Path Method') and enumerates concrete outputs (ES/EF/LS/LF, float, makespan, critical path). An agent can distinguish this scheduling tool from the many audit/analyze siblings without opening the schema.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines5/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Explicitly names the use case ('scheduling dependent engineering milestones or workflow steps') and the goal (minimum project duration, zero-slack bottleneck). It also names the alternative sibling, audit_module_dependency_cycles, and the condition that selects it ('detecting circular code imports and file blast radius without task durations').

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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