General Form Of Assignment Problem In Mecklenburg
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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).”
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.
Bottleneck generalized assignment problems☆ The basic problem involves the assignment of a number of jobs to a number of agents such that each job is performed by a unique agent, and capacity limitations on the agents are not exceeded. Two versions of the bottleneck generalized assignment problem (BGAP) are defined.
The Generalized Assignment Problem has shown to be NP-hard and therefore efficient algorithms are needed, especially for large problems.
The Hungarian method is a simple way to solve assignment problems.
Maximization case in Assignment Problem There may be situation when the assignment problem calls for maximization of profit. Such problem can be solved by converting the given maximization problem into minimization problem by substracting all the elements of the given matrix from the highest element.
Balanced Assignment Problem is an assignment problem where the number of facilities is equal to the number of jobs. Unbalanced Assignment Problem: Unbalanced Assignment problem is an assignment problem where the number of facilities is not equal to the number of jobs.
A branch and bound algorithm is developed that solves the generalized assignment problem by solving a series of binary knapsack problems to determine the bounds. Computational results are cited for problems with up to 4 000 0–1 variables, and comparisons are made with other algorithms.
Assignment problems are an integral part of optimization problems in operations research. In real life the application assignment problems can be used to allocate machines to jobs, vehicles to roads, products to factories, network computers, and airplanes for specific trips, etc.
