{"uid":"cap_GmR4s7Ns0mK4ql4Bw3Q_y","slug":"assignment-problem-solver-minimum-cost-worker-task-matching-f62cf9c2","name":"Assignment Problem Solver (Minimum-Cost Worker-Task Matching)","description":"Assignment solver — exact minimum-cost worker-to-task matching for resource allocation, with deterministic choices and a primal/dual optimality certificate.","url":"https://decision-solver.use.x402atlas.com/assignment","method":"POST","headers":{},"bodySchema":null,"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.005","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"registry","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.005/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.005","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.005","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_IjB7mpLqiXaxsBnkv1YIl","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.005","costPer":"request","priority":0,"asset":null,"unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"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.","exampleAgentPrompt":"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.","exampleUseCases":[{"title":"Shift-to-employee staffing optimization","prompt":"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."},{"title":"Freelancer-to-project allocation","prompt":"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?"},{"title":"Machine-to-job factory scheduling","prompt":"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."}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T06:36:31.999Z","isFirstParty":false}