Overview
Matching & Assignment focuses on pair resources, people, tasks, and markets optimally. In the map of OR, it connects Bipartite matching, Hungarian algorithm, Stable matching to decisions that must be modeled, solved, explained, and revised as evidence changes.
Assignment and matching models allocate workers to jobs, students to schools, organs to patients, ads to slots, and riders to drivers. The practical use case is clearest in Labor, Education, Healthcare, Ride-hail, Advertising, where the method helps turn constraints and tradeoffs into a decision artifact someone can inspect.
Core ideas
Bipartite matching
Bipartite matching is a core checkpoint for Matching & Assignment: define it concretely, attach units or rules where possible, and test whether stakeholders interpret it the same way.
Hungarian algorithm
Hungarian algorithm is a core checkpoint for Matching & Assignment: define it concretely, attach units or rules where possible, and test whether stakeholders interpret it the same way.
Stable matching
Stable matching is a core checkpoint for Matching & Assignment: define it concretely, attach units or rules where possible, and test whether stakeholders interpret it the same way.
Market design
Market design is a core checkpoint for Matching & Assignment: define it concretely, attach units or rules where possible, and test whether stakeholders interpret it the same way.
How to use it
- 1Start with Labor: write the decision, time horizon, actors, and objective in operational language.
- 2Translate the problem into Bipartite matching, Hungarian algorithm, and Stable matching; define units and data sources for each one.
- 3Build a small instance of Matching & Assignment that can be solved or simulated by hand inspection before using full production data.
- 4Compare the recommendation against a baseline policy, not just against mathematical optimality.
- 5Document assumptions, sensitivity results, and the conditions under which the recommendation should be revisited.
Applications
- Labor: compare feasible policies, quantify the operating tradeoffs, and make the assumptions behind the recommendation visible.
- Education: compare feasible policies, quantify the operating tradeoffs, and make the assumptions behind the recommendation visible.
- Healthcare: compare feasible policies, quantify the operating tradeoffs, and make the assumptions behind the recommendation visible.
- Ride-hail: compare feasible policies, quantify the operating tradeoffs, and make the assumptions behind the recommendation visible.
- Advertising: compare feasible policies, quantify the operating tradeoffs, and make the assumptions behind the recommendation visible.
Common pitfalls
- Applying Matching & Assignment because the label sounds appropriate while leaving the actual decision boundary vague.
- Treating Bipartite matching as a technical detail instead of a modeling choice that affects the recommendation.
- Reporting one answer without showing sensitivity to demand, capacity, costs, or behavioral assumptions.
- Ignoring implementation details such as data quality, explainability, ownership, and how users will override bad recommendations.
Resources
- Network Flows — Ahuja, Magnanti, Orlin
Topic-specific source curated for Matching & Assignment.
- Google OR-Tools
Practical toolkit for routing, assignment, CP-SAT, scheduling, flows, LP, and MIP.
- MIT OCW 15.053 — Optimization Methods in Management Science
Course materials for LP, IP, networks, nonlinear programming, and management science applications.
- INFORMS — FAQs About O.R. & Analytics
Use this for the professional definition of OR, analytics, decision support, and applied practice.