Assignment Problem Solver

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Assignment Problem Calculators

Solve assignment problems of different types—balanced, unbalanced, minimization, maximization, and restricted— using interactive tools that apply the Hungarian method and related techniques step by step.

All calculators on this page are live and free to use. You can also explore more tools in our Operations Research (Optimization) section or return to the homepage.

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Assignment Problem Solver – Hungarian Method

Solve standard balanced minimization assignment problems. Shows each Hungarian method step and the final optimal assignment with total cost.

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Assignment Problem – Maximization

Convert and solve maximization assignment problems using the Hungarian method. Automatically handles profit/benefit matrices and returns the maximum total value.

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Unbalanced Assignment Problem Calculator

Handle cases where the number of jobs and agents are not equal. The tool adds dummy rows or columns as needed and then applies the Hungarian method.

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Restricted Assignment Problem Calculator

Solve assignment problems with prohibited assignments or restrictions. Mark forbidden cells and get a feasible optimal assignment if one exists.

Which Assignment Problem Calculators Are Available?

This section focuses on the classical assignment problem and its common variants that appear in operations research, engineering, and management science courses. You can currently use:

  • Hungarian Method (Balanced Minimization) For standard assignment problems where the number of agents equals the number of tasks and the objective is to minimize overall cost, time, or distance. The calculator shows each Hungarian method step so you can follow or check your manual solution.
  • Maximization Assignment Problem For profit or effectiveness matrices where you want to maximize the total value. The tool internally converts the maximization model into an equivalent minimization form and then applies the Hungarian method.
  • Unbalanced Assignment Problem For situations where the number of agents and tasks are not equal. The calculator automatically introduces dummy rows or columns to balance the problem and then solves it optimally.
  • Restricted Assignment Problem For models where some assignments are forbidden (for example, an agent cannot perform a certain job). You can mark such cells as restricted, and the solver will search for an optimal feasible solution if it exists.

These tools are designed for students, teachers, and practitioners who want quick, reliable solutions without getting lost in manual tables, while still seeing the underlying method.

Frequently Asked Questions

What is an assignment problem?
An assignment problem is a special type of optimization model where a set of agents (such as workers, machines, or salespeople) must be assigned to a set of tasks (such as jobs, locations, or projects), usually one-to-one, in order to minimize total cost or maximize total profit. It is typically solved efficiently by the Hungarian method.
Which calculator should I use for my problem?
Use the standard Hungarian Method calculator when the problem is balanced and you are minimizing cost. Choose the Maximization calculator if you are maximizing profit or benefit. Select the Unbalanced calculator when the numbers of agents and tasks differ, and the Restricted calculator when some assignments are not allowed.
Do these calculators show the Hungarian method steps?
Yes. The tools are designed to be educational as well as practical. They show the key Hungarian method stages such as row and column reductions, covering zeros, adjusting the matrix, and reading the final assignment, so you can learn or verify your own calculations.
How are unbalanced and restricted assignment problems handled?
For unbalanced problems, the calculator introduces dummy rows or columns with appropriate values to transform the model into an equivalent balanced assignment problem. For restricted problems, forbidden assignments are modeled so that they are never selected in the optimal solution, while still applying the core Hungarian method logic.
Are these tools free, and can I use them for exams or homework?
All assignment problem calculators on CalcTypes are free to use with no registration. They are ideal for practice, learning, and checking your work. For graded exams and assignments, always follow your instructor’s rules about calculator use and show your solution steps when required.
Want more optimization tools? Visit the CalcTypes homepage or explore the full Operations Research (Optimization) section.