主题：Index Policies for Dynamic Job Assignment

动态作业分配的指数策略

时间: 2025年12月26日 上午10:00

地点:东校区 第五教学楼5101

主讲人: Xu Sun，University of Miami Herbert Business School

Bio:

Xu Sun is an Assistant Professor of Management Science at the Miami Herbert Business School, University of Miami. His research focuses on the modeling, analysis, and control of dynamic systems, with applications in call centers, smart manufacturing, dynamic pricing, and energy systems. He develops algorithms for online decision-making that are simple, practical, and theoretically grounded. His work has appeared in Management Science, Operations Research, Manufacturing and Service Operations Management, Production and Operations Management, and Mathematics of Operations Research. He has been recognized as a finalist in the INFORMS Finance Section Best Student Paper Competition, a recipient of the Institute for Mathematics and its Applications Travel Award, and the PhD Student Mentoring Award. He serves the profession as a frequent reviewer for leading journals in operations research and management science.

照片：

Abstract:

We study dynamic assignment in systems with multiple job classes and heterogeneous reusable resource pools, aiming to maximize rewards net of congestion costs. We introduce a fluid–dual framework that yields two lightweight index policies. The Lagrangian Index (LI) arises from the dual of a Lagrangian-relaxed fluid linear program, while the Deterministic–Dual Index (DDI) uses the dual vector of a deterministic relaxation. DDI routes each arrival to the pool that maximizes “reward – shadow price,” with small state-dependent perturbations that adapt to congestion levels. Both policies are simple to implement: the dual vector is computed once offline, and online operation incurs negligible overhead. Our analysis shows that when the relaxation is nondegenerate, DDI achieves an O(1) long-run average profit loss to the fluid bound with O(1) congestion. Under degeneracy, the profit gap grows to O(√n), while congestion remains bounded, where n measures system size. Because LI and DDI share an index structure, the analysis of DDI also provides a transparent near-lower-bound benchmark for LI. We further quantify the value of queues, showing that modest buffering suffices to retain near-optimal performance. Numerical experiments support the theoretical results.