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 theâ€¦Â CONTINUE READING