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.
This problem in its most general form is as follows: There are a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost and profit that may vary depending on the agent-task assignment. Moreover, each agent has a budget and the sum of the costs of tasks assigned to it cannot exceed this budget. It is required to find an assignment in which all agents do not exceed their budget and total profit of the assignment is maximized.
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The assignmentproblem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: The problem instance has...
several scheduling and clustering problems including the k-center and k-median problems and the generalizedassignmentproblem. Polynomial-time approximation...
p_{ij}} . Notice that as opposed to the classic assignmentproblem or the generalizedassignmentproblem, more than one agent (i.e., weapon) can be assigned...
SAT problem, it is useful to define the notion of a generalized conjunctive normal form formula, viz. as a conjunction of arbitrarily many generalized clauses...
is called the assignmentproblem. If each vertex can be matched to several vertices at once, then this is a generalizedassignmentproblem. A priority matching...
system) (Groups, Algorithms and Programming), a software package Generalizedassignmentproblem Generic access profile, an interoperability protocol used in...
In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing...
satisfying assignments. This can be further generalized by using larger domain sizes and attaching a weight to each satisfying assignment and computing...
theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject...
Sudoku are noteworthy examples of exact cover problems. The n queens problem is a generalized exact cover problem. Given a collection S {\displaystyle {\mathcal...
problem, set cover problem, minimal graph coloring, max independent set problem, bin packing problem, and generalizedassignmentproblem. More recent applications...
Operations Research has a page on the topic of: Transportation and AssignmentProblem The problem of estimating how many users are on each route is long standing...
mathematical logic, a formula is satisfiable if it is true under some assignment of values to its variables. For example, the formula x + 3 = y {\displaystyle...
activities than A, contradicting the optimality. The generalized version of the activity selection problem involves selecting an optimal set of non-overlapping...
knapsack problem, we add the constraint that each subset is of size n and remove the restriction on total weight, we get the assignmentproblem, which is...
is an example of a generalized exact cover problem, of which sudoku is another example. n-queens completion The completion problem asks whether, given...
In computational complexity theory, generalized geography is a well-known PSPACE-complete problem. Geography is a children's game, where players take...
convex; otherwise the problem may be NP hard. Allowing inequality constraints, the KKT approach to nonlinear programming generalizes the method of Lagrange...
such it treats the same set of problems as does logistic regression using similar techniques. When viewed in the generalized linear model framework, the...
used with nominal data, which have purely qualitative category assignments. Generalized mean A generalization of the Pythagorean means, specified by an...
The routing and wavelength assignment (RWA) problem is an optical networking problem with the goal of maximizing the number of optical connections. The...
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