# Assignment Problem Solver (Minimum-Cost Worker-Task Matching)

> 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.

## Facts

- Endpoint: POST https://decision-solver.use.x402atlas.com/assignment
- Price: $0.005/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/assignment-problem-solver-minimum-cost-worker-task-matching-f62cf9c2
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_GmR4s7Ns0mK4ql4Bw3Q_y

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability assignment-problem-solver-minimum-cost-worker-task-matching-f62cf9c2 -d '<json body>'
```

Example prompt: I have 4 workers and 4 tasks with a cost matrix — worker A costs 9/2/7/8 for tasks 1-4, worker B costs 6/4/3/7, worker C costs 5/8/1/8, and worker D costs 7/6/9/4. Find the minimum-cost one-to-one assignment and give me the optimality proof.

## When to prefer this

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.

## Known failure modes

- 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

## 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.

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/assignment-problem-solver-minimum-cost-worker-task-matching-f62cf9c2/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from decision-solver.use.x402atlas.com](https://www.zero.xyz/host/decision-solver.use.x402atlas.com/llms.txt)