Allocation of Fungible Resources via a Fast, Scalable Price Discovery Method

We consider the problem of assigning or allocating resources to a set of jobs. We consider the case when the resources are fungible, that is, the job can be done with any mix of the resources, but with different efficiencies. In our formulation we maximize a total utility subject to a given limit on the resource usage, which is a convex optimization problem and so is tractable. In this paper we develop a custom, parallelizable algorithm for solving the resource allocation problem that scales to large problems, with millions of jobs. Our algorithm is based on the dual problem, in which the dual variables associated with the resource usage limit can be interpreted as resource prices. Our method updates the resource prices in each iteration, ultimately discovering the optimal resource prices, from which an optimal allocation is obtained. We provide an open-source implementation of our method, which can solve problems with millions of jobs in a few seconds on CPU, and under a second on a GPU; our software can solve smaller problems in milliseconds. On large problems, our implementation is up to three orders of magnitude faster than a commerical solver for convex optimization.