Assignment Problem Calculators & Solvers
Choose the Right Assignment Problem Calculator
Looking for an assignment problem calculator or assignment problem solver? Choose the tool that matches your matrix: a balanced minimization problem, a maximization problem, an unbalanced or rectangular assignment problem, or a restricted problem with prohibited assignments. Each calculator is free to use and is designed to show the optimization logic clearly.
For standard cost-minimization matrices, start with the Hungarian method calculator. If your objective, matrix shape, or restrictions are different, use one of the specialized solvers below.
Assignment Problem Solvers by Type
Select the calculator that matches your assignment model. These four tools cover the most common assignment problem variants used in operations research, management science, scheduling, workforce allocation, machine-job assignment, and cost or profit optimization.
Hungarian Method Calculator for Balanced Assignment Problems
Solve a standard balanced minimization assignment problem where the number of agents equals the number of tasks. View Hungarian algorithm steps and the optimal assignment with total minimum cost, time, or distance.
Maximization Assignment Problem Calculator
Solve profit, output, benefit, or effectiveness matrices when the goal is to maximize the total value. The calculator converts the maximization model appropriately and applies the Hungarian method.
Unbalanced Assignment Problem Calculator for Rectangular Matrices
Use this solver when the number of workers and jobs is different. It balances the rectangular matrix with dummy rows or columns and then solves the resulting assignment problem.
Restricted / Prohibited Assignment Problem Calculator
Solve assignment problems containing forbidden worker-task pairs or other prohibited assignments. The solver checks feasibility and finds an optimal feasible assignment when one exists.
Which Assignment Problem Calculator Should You Use?
The quickest way to choose a solver is to identify your objective, matrix shape, and whether any assignments are forbidden.
| Your assignment problem | What you want to optimize | Recommended calculator |
|---|---|---|
| Balanced square matrix | Minimize cost, time, or distance | Hungarian Method Assignment Problem Solver |
| Profit or benefit matrix | Maximize profit, output, score, or effectiveness | Maximization Assignment Problem Calculator |
| Rectangular matrix: rows β columns | Minimize or optimize after balancing | Unbalanced Assignment Problem Calculator |
| Some worker-task pairs are not allowed | Find the best feasible assignment | Restricted / Prohibited Assignment Problem Calculator |
Assignment Problem Solver for Operations Research
The assignment problem is a one-to-one optimization model used to allocate agents such as workers, machines, vehicles, or salespeople to tasks such as jobs, routes, projects, or locations. Depending on the problem, the objective may be to minimize total cost or time, maximize profit or effectiveness, handle unequal numbers of agents and tasks, or obey restrictions that make some assignments impossible.
Balanced Assignment Problem and Hungarian Algorithm
A balanced assignment problem has the same number of agents and tasks. For a minimization objective, the Hungarian algorithm calculator is the natural starting point. It reduces the matrix systematically and identifies an optimal one-to-one assignment.
Maximization Assignment Problem
If each matrix entry represents profit, output, benefit, or another value to maximize, use the maximization assignment problem solver. It transforms the objective into an equivalent form that can be solved with the Hungarian method.
Unbalanced Assignment Problem with Dummy Rows or Columns
When rows and columns are unequal, the problem is unbalanced. The unbalanced assignment calculator adds dummy rows or columns so the matrix can be solved as a balanced assignment problem while preserving the interpretation of real assignments.
Restricted or Prohibited Assignment Problem
If certain assignments are forbidden because of skills, licensing, policy, location, or other constraints, use the restricted assignment problem calculator. It checks whether a complete feasible matching exists before optimizing the allowed assignments.
Questions People Ask About Assignment Problem Calculators
Open any question below for a detailed explanation. These answers cover the Hungarian method, maximization, unbalanced matrices, prohibited assignments, and choosing the correct online assignment problem solver.
What is an assignment problem calculator?
An assignment problem calculator is an operations research tool that matches agents to tasks on a one-to-one basis while optimizing an objective such as minimum cost, minimum time, maximum profit, or maximum effectiveness. CalcTypes provides separate solvers for balanced Hungarian method problems, maximization problems, unbalanced matrices, and restricted or prohibited assignments so you can use the method that matches your model.
Which Hungarian method calculator should I use for a balanced assignment problem?
Use the Assignment Problem Solver β Hungarian Method when your matrix is balanced, meaning the number of agents equals the number of tasks, and your objective is to minimize a quantity such as cost, time, or distance. The solver shows key Hungarian method stages so you can follow the logic and verify manual work.
Can the Hungarian method solve a maximization assignment problem?
Yes. A maximization assignment problem can be converted into an equivalent minimization form and then solved with the Hungarian method. If your entries represent profit, production, benefit, or effectiveness, use the Maximization Assignment Problem Calculator, which performs the conversion and reports the result using the original values.
How do I solve an unbalanced assignment problem online?
An unbalanced assignment problem has a different number of agents and tasks, so its matrix is rectangular. Use the Unbalanced Assignment Problem Calculator. The tool adds the required dummy row or dummy column to create a square matrix, solves the balanced problem, and distinguishes real assignments from dummy assignments in the result.
How do I solve an assignment problem with prohibited or forbidden assignments?
Use the Restricted / Prohibited Assignment Problem Calculator when some worker-task combinations are not allowed. Mark those combinations as forbidden. The solver checks whether a complete feasible assignment exists and, if it does, finds the best solution without using prohibited pairs.
What is the difference between a balanced and unbalanced assignment problem?
A balanced assignment problem has an equal number of agents and tasks, producing a square cost or profit matrix. An unbalanced assignment problem has unequal numbers of agents and tasks, producing a rectangular matrix. Unbalanced problems are commonly converted to balanced form by adding dummy rows or columns before optimization.
Do these assignment problem solvers show step-by-step solutions?
The CalcTypes assignment tools are designed to be useful for both calculation and learning. Where applicable, they show the main stages used to reach the solution, including matrix preparation, Hungarian method reductions, assignment selection, balancing with dummy rows or columns, and feasibility handling for restricted cases. This makes them useful for students, teachers, and practitioners who want to check the method as well as the final result.
Are the CalcTypes assignment problem calculators free to use?
Yes. The assignment problem calculators linked from this page are free to use online without registration. They can be used for learning, practice, checking homework, exploring examples, or verifying operations research calculations. For graded coursework or exams, follow your instructor’s rules about calculator use and required working steps.