arXiv subjects

Zi Ling

Publications and source records attributed to Zi Ling.

4 recordsLinked to original sources

arXiv2026

From Soliloquy to Agora: Memory-Enhanced LLM Agents with Decentralized Debate for Optimization Modeling

Optimization modeling underpins real-world decision-making in logistics, manufacturing, energy, and public services, but reliably solving such problems from natural-language requirements remains challenging for current large language models (LLMs). In this paper, we propose \emph{Agora-Opt}, a modular agentic framework for optimization modeling that combines decentralized debate with a read-write memory bank. Agora-Opt allows multiple agent teams to independently produce end-to-end solutions and reconcile them through an outcome-grounded debate protocol, while memory stores solver-verified artifacts and past disagreement resolutions to support training-free improvement over time. This design is flexible across both backbones and methods: it reduces base-model lock-in, transfers across different LLM families, and can be layered onto existing pipelines with minimal coupling. Across public benchmarks, Agora-Opt achieves the strongest overall performance among all compared methods, outperforming strong zero-shot LLMs, training-centric approaches, and prior agentic baselines. Further analyses show robust gains across backbone choices and component variants, and demonstrate that decentralized debate offers a structural advantage over centralized selection by enabling agents to refine candidate solutions through interaction and even recover correct formulations when all initial candidates are flawed. These results suggest that reliable optimization modeling benefits from combining collaborative cross-checking with reusable experience, and position Agora-Opt as a practical and extensible foundation for trustworthy optimization modeling assistance. Our code and data are available at https://github.com/CHIANGEL/Agora-Opt.

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arXiv2026

Online Order Fulfillment with Replenishment

In modern e-commerce and service operations, firms must jointly manage inventory replenishment and real-time order fulfillment to maximize profit under demand uncertainty. While each component has been studied extensively in isolation, their interaction remains underexplored. This paper investigates a fundamental operational question: which lever plays a more decisive role in overall system performance, replenishment or fulfillment? We model the system as a one-location online order fulfillment problem with lost sales and stochastic customer arrivals, each offering heterogeneous rewards. Replenishment follows either a base-stock or constant-order policy, while real-time fulfillment decisions are made using online algorithms. Our core performance metric is the expected average profit per replenishment cycle, evaluated across all combinations of these policies and algorithms. Our main theoretical result shows that when the replenishment cycle is long, the cumulative regret of online fulfillment remains of the same order as in a corresponding single-cycle problem, even under repeated replenishment, revealing a form of regret stability. This phenomenon also extends to a multi-location setting. We further develop a regret-based framework that quantitatively compares the value of improving replenishment versus improving fulfillment, and we characterize regimes in which optimizing replenishment yields a larger revenue impact than refining the online fulfillment algorithm (and vice versa). Motivated by examples where myopic algorithms underperform, we introduce a novel look-ahead online algorithm that anticipates future replenishment and demand. Numerical experiments verify that this algorithm outperforms myopic baselines. Overall, our results provide both theoretical and managerial insights into situations where inventory replenishment policies are more influential and vice versa.

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arXiv2026

OPT-Engine: Benchmarking the Limits of LLMs in Optimization Modeling via Complexity Scaling

We investigate the capabilities and scalability of Large Language Models (LLMs) in optimization modeling, a domain requiring structured reasoning and precise formulation. To this end, we introduce OPT-ENGINE, an extensible benchmark framework with quantifiable and controllable complexity. OPT-ENGINE spans ten canonical Operations Research problems, systematically scaling from Linear Programming to Mixed-Integer Programming, providing a structured environment to probe the limits of automated problem formulation and solving. Utilizing OPT-Engine, we address three pivotal research questions. First, we examine whether Pure-Text Reasoning (PTR) via classical Chain-of-Thought can efficiently tackle optimization tasks, finding that PTR suffers from a critical robustness gap as task complexity increases. Second, we examine whether integrating external computational tools can mitigate PTR's arithmetic weaknesses and improve performance. Our results indicate that while such tools help with local calculations, they still fail to adhere to global optimization constraints. Finally, we pinpoint that for the current SOTA paradigm, Solver-integrated Reasoning (SIR), the automated formulation of constraints represents the primary bottleneck. These findings clarify the limitations of current paradigms and provide a structured roadmap for developing next-generation LLMs for optimization modeling. We release our code and data to facilitate future research (https://github.com/Cardinal-Operations/OPTEngine).

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arXiv2020

Bounding probability of small deviation on sum of independent random variables: Combination of moment approach and Berry-Esseen theorem

In the context of bounding probability of small deviation, there are limited general tools. However, such bounds have been widely applied in graph theory and inventory management. We introduce a common approach to substantially sharpen such inequality bounds by combining the semidefinite optimization approach of moments problem and the Berry-Esseen theorem. As an application, we improve the lower bound of Feige's conjecture from 0.14 to 0.1798.

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