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Assignment Problem Solver (Minimum-Cost Worker-Task Matching)
x402
Assignment Problem Solver (Minimum-Cost Worker-Task Matching) is a paid API for AI agents from decision-solver.use.x402atlas.com, paid per call via x402, $0.005/call, status unknown (last checked 2026-09-14).
Solves the linear assignment problem to find the exact minimum-cost one-to-one matching between workers and tasks, returning a primal/dual optimality certificate.
Price / call$0.005
Success—
StatusUnknown
How this service works
Assignment solver — exact minimum-cost worker-to-task matching for resource allocation, with deterministic choices and a primal/dual optimality certificate.
Output
Returns the exact minimum-cost one-to-one assignment mapping each worker to a task, the total minimum cost, and a primal/dual optimality certificate proving the solution cannot be improved further.
Example use cases
Shift-to-employee staffing optimization
“I have 5 nurses and 5 shifts this weekend — here's the cost matrix of preference scores for each nurse-shift combo. Find the exact minimum-cost assignment so every shift is covered and every nurse gets exactly one shift.”
Freelancer-to-project allocation
“I need to assign 3 freelancers to 3 client projects. I have a cost table — Alice costs $200/$350/$150, Bob costs $300/$250/$400, and Carol costs $180/$320/$280 for projects X, Y, and Z respectively. Which assignment minimizes total spend?”
Machine-to-job factory scheduling
“We have 6 machines and 6 jobs on the factory floor, with a processing-time matrix. Give me the exact minimum-total-time assignment of jobs to machines along with a certificate proving it's optimal.”
Technical details
Endpoint
POSThttps://decision-solver.use.x402atlas.com/assignmentWhen to prefer
Choose this endpoint when you need an exact, provably optimal minimum-cost one-to-one assignment between two equally-sized sets (workers and tasks), and require a dual certificate of optimality. Prefer this over heuristics or bin-packing siblings when correctness guarantees matter, the assignment is strictly one-to-one, and you need deterministic results you can audit. Use the knapsack or bin-packing siblings instead when items can be split or multiple items can go to one bin.
Side effects
- Non-square cost matrix (unequal numbers of workers and tasks) — may require padding or return an error
- Infeasible or degenerate cost matrix (e.g. all-zero rows) — may produce trivially correct but unhelpful results
- Very large matrices may exceed compute or time limits
- Malformed or missing cost matrix input returns a 400-level error
- Network or payment processing failures return 402 or 5xx errors
Tags
x402
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