Convex Resource Allocation Problems on Directed Acyclic Graphs: Duality, Complexity, Special Cases, and Extensions

@article{Monma1990ConvexRA,
  title={Convex Resource Allocation Problems on Directed Acyclic Graphs: Duality, Complexity, Special Cases, and Extensions},
  author={Clyde L. Monma and Alexander Schrijver and Michael J. Todd and Victor K.-W. Wei},
  journal={Math. Oper. Res.},
  year={1990},
  volume={15},
  pages={736-748}
}
Consider the following resource allocation problem on a directed acyclic graph (the precedence graph). Each vertex has a known work load, and a fixed amount of total resource is available. The time required to process a vertex is inversely proportional to the amount of the resource allocated to it. The time to complete all of the work is the length of (time to complete) a longest chain in the graph. The problem of finding an allocation which minimizes the time required to complete all of the… CONTINUE READING

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