Abstract
We consider a variation of the maximum bipartite matching problem where each completed task must have at least two agents assigned to it. We give an integer programming formulation for the problem, and prove that the basic solutions of LP-relaxation are half-integral. It is shown that a fractional basic solution can be further processed to obtain an optimal solution to the problem.
Highlights
Problem DefinitionWe consider the following variation of the maximum bipartite matching problem
The problem can be given by the following integer program (IP): max ∑y j s.t.∑xpj ≤ 1, for each p ∈ P, (2)
The maximum bipartite matching problem can be solved by network flow techniques
Summary
We consider the following variation of the maximum bipartite matching problem. Each agent still can be assigned to at most one task. In our problem a task can be completed only if at least two agents are assigned to it. The goal is to maximize the number of completed tasks. How to cite this paper: Melkonian, V. Open Journal of Discrete Mathematics, 4, 44-54.
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