General Form Of Assignment Problem In King
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In applied mathematics, the maximum generalized assignment problem is a problem in combinatorial optimization. This problem is a generalization of the assignment problem in which both tasks and agents have a size. Moreover, the size of each task might vary from one agent to the other.
The Generalized Assignment Problem has shown to be NP-hard and therefore efficient algorithms are needed, especially for large problems.
For example, suppose an accounts officer has 4 subordinates and 4 tasks. The subordinates differ in efficiency and take different time to perform each task. If one task is to be assigned to one person in such a way that the total person hours are minimised, the problem is called an assignment problem.
The assignment problem in the general form can be stated as follows: “Given n facilities, n jobs and the effectiveness of each facility for each job, the problem is to assign each facility to one and only one job in such a way that the measure of effectiveness is optimised (Maximised or Minimised).”
Explanation: The Hungarian method is a well-known algorithm for solving assignment problems, which involves finding the optimal assignment of n workers to n jobs. However, the Hungarian method can also be used to solve other optimization problems, such as transportation problems and linear programming problems.
The assignment problem in the general form can be stated as follows: “Given n facilities, n jobs and the effectiveness of each facility for each job, the problem is to assign each facility to one and only one job in such a way that the measure of effectiveness is optimised (Maximised or Minimised).”
The assignment problem consists of finding, in a weighted bipartite graph, a matching of a given size, in which the sum of weights of the edges is minimum. If the numbers of agents and tasks are equal, then the problem is called balanced assignment. Otherwise, it is called unbalanced assignment.
Using the assignment method, the teacher creates an assignment with clear instructions, milestones, and grading criteria based on an outcome that students need to achieve. The teacher monitors and advises students as they work on the assignment and provides feedback that challenges students to improve.
For example, suppose an accounts officer has 4 subordinates and 4 tasks. The subordinates differ in efficiency and take different time to perform each task. If one task is to be assigned to one person in such a way that the total person hours are minimised, the problem is called an assignment problem.
The assignment method is a way of allocating organizational resources in which each resource is assigned to a particular task. The resource could be monetary, personnel, or technological.
