Online Allocation of Throughput-Constrained Resources Using Proxy Assignments

Abstract

We study a variation of the canonical online resource allocation problem in which resources are throughput, rather than budget, constrained. As in the classical setting, the decision-maker must assign sequentially arriving jobs to one of multiple available resources. However, in addition to the assignment costs incurred from these decisions, the decision-maker is also penalized for deviating from exogenous, time-varying target assignment rates for each resource, which represent the resources' respective throughput capacities throughout the horizon. The goal is to minimize the total expected assignment and deviation penalty costs incurred throughout the horizon when the distribution of assignment costs is unknown. We first show that naive extensions of state-of-the-art algorithms for classical budget-constrained resource allocation problems can fail dramatically when applied to throughput-constrained resource allocation. We then propose a novel ``proxy assignment" primal-dual algorithm that uses current arrivals to simulate the effect of future arrivals. We prove that our algorithm achieves the optimal $O(\sqrt{T})$ regret bound when the assignment costs of the arriving jobs are drawn i.i.d. from a fixed distribution. We demonstrate the practical performance of our approach by conducting numerical experiments on synthetic datasets, as well as real-world datasets from retail fulfillment operations.