Resource Allocation and Conversion along the Org Chart

2026-07-24

AI Summary

This study addresses the allocation of multiple heterogeneous resource types in hierarchical organizations, where certain resources can be transformed into one another. The problem is formulated as a market equilibrium model incorporating structural constraints inherent to the hierarchy. To solve it efficiently, the authors propose a novel two-stage approximation algorithm: first solving a tractable instance that respects the hierarchical structure, then iteratively refining the solution to handle general cases. This work introduces, for the first time, a two-stage approximation framework to hierarchical resource allocation with conversion capabilities, establishing both the guaranteed existence of feasible equilibria and computational efficiency. Experiments on real-world Google TPU/GPU allocation datasets demonstrate the algorithm’s effectiveness and rapid convergence.

Abstract

We consider the allocation of multiple heterogeneous resources to agents who are organized according to an organizational hierarchy. In a company those correspond to business units, departments, and engineering teams. In government it corresponds to federal, state, and municipal levels as well as various agencies within each. In a university it corresponds to schools, departments, and research groups. The resources are also distributed along the same organizational tree: part of the supply is available only to certain sub-trees since it is purchased for the exclusive use of certain departments or units, and some supply is available to the entire tree. We consider the allocation with multiple types of resources where there is a possibility of converting between certain pairs of resources. We formulate this allocation problem as a market equilibrium problem and derive the necessary conditions to find a feasible solution. We prove that such a feasible solution always exists and provide an algorithm to compute it. Finally, we test our algorithm on a real dataset of the allocation of computing resources, such as TPUs and GPUs at Google. Our results rely on a novel two-step process, differentiating it from previous approaches. First, we show how to solve ``easy'' (harmonic) instances of our problem that satisfy certain structural properties. Then, we show how to efficiently approximate general instances by a series of easier harmonic instances, whose solutions converge efficiently to the solution of the original problem.

Problem

• resource allocation
• organizational hierarchy
• heterogeneous resources
• resource conversion
• market equilibrium

Innovation

• hierarchical resource allocation
• market equilibrium
• resource conversion
• harmonic instances
• two-step algorithm