Linear Programming

2. A specific type of optimization problem where the goal is to assign a set of agents to a set of tasks, usually one agent per task, to minimize total cost or maximize total benefit.
6. The process of finding the best possible solution to a problem, typically by minimizing cost, time, or resources, or by maximizing profit or efficiency.
8. Algorithm A mathematical expression that defines the quantity to be minimized (e.g., total cost) or maximized (e.g., total profit) in an optimization problem.
9. A solution to an assignment problem that satisfies all the given constraints, but is not necessarily the best possible solution.
10. A mathematical technique used for optimizing an objective function (like maximizing profit or minimizing cost) subject to a set of linear equality and inequality constraints, often used to formulate and solve assignment problems.

1. A table or two-dimensional array that lists the costs (or benefits) associated with each possible assignment of an agent to a task.
3. Symbols or expressions in a mathematical model that represent the choices that need to be made, such as whether an agent is assigned to a specific task (often binary, 0 or 1).
4. Conditions or restrictions that must be satisfied by the decision variables in an assignment model, such as 'each agent must be assigned exactly one task' or 'each task must be assigned exactly one agent'.
5. A combinatorial optimization algorithm that solves the assignment problem in polynomial time and is often used to find the minimum cost assignment.
7. A feasible solution to an assignment problem that yields the best possible value for the objective function (e.g., the lowest total cost or the highest total benefit).