General Form Of Assignment Problem In Wake
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The Generalized Assignment Problem has shown to be NP-hard and therefore efficient algorithms are needed, especially for large problems.
Since integer linear programming is NP-hard, many problem instances are intractable and so heuristic methods must be used instead.
The Generalized Assignment Problem has shown to be NP-hard and therefore efficient algorithms are needed, especially for large problems.
However, the opposite direction is not true: some problems are undecidable, and therefore even more difficult to solve than all problems in NP, but they are probably not NP-hard (unless P=NP).
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 problem is NP-hard, so there is no known algorithm for solving this problem in polynomial time, and even small instances may require long computation time. It was also proven that the problem does not have an approximation algorithm running in polynomial time for any (constant) factor, unless P = NP.
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).”
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.
