Operations Research

This paper presents ORPilot, an open-source agentic AI system that translates real-world business problems into solver-ready optimization models. Unlike academic LLM-for-OR tools that assume clean problem specifications with preformatted inline data, ORPilot is designed for production conditions: ambiguous descriptions, large-scale raw operational data, and the need for portability across solver backends. The system introduces four novel components: (1) a conversational interview agent to elicit complete problem specifications, (2) a data collection agent that retrieves data independently of prompts, (3) a parameter computation agent to bridge raw tabular data and model-ready parameters, and (4) a solver-agnostic Intermediate Representation (IR) for deterministic, zero-LLM-call recompilation to Gurobi, CPLEX, PuLP, Pyomo, or OR-Tools solvers. Additionally, self-correcting retry loops utilize solver tracebacks for targeted repairs. ORPilot represents the first attempt to target production-level business problems rather than textbook operations research (OR) cases. Evaluation on real-world problems demonstrates promising results. When tested against traditional academic benchmarks: IndustryOR, NL4OPT and NLP4LP, ORPilot outperformed state-of-the-art tools in accuracy on the IndustryOR benchmark and delivered comparable performance on NL4OPT and NLP4LP.

Optimization problems are central to decision-making in manufacturing, logistics, scheduling, and other industrial settings. Translating complicated descriptions of these problems into solver-ready formulations requires specialized operations research (OR) expertise, making it hard to scale. We present AutoOR, a scalable synthetic data generation and reinforcement learning pipeline that trains LLMs to autoformalize optimization problems specified in natural language across linear, mixed-integer, and non-linear categories. AutoOR generates verified training data from standard optimization forms and uses solver execution feedback as the reward signal for RL post-training. AutoOR applied to an 8B model achieves state-of-the-art or competitive results across six established OR benchmarks, matching significantly larger frontier models. For a non-linear problem class involving physical dynamics, where frontier models score near 0%, we introduce a curriculum RL strategy that bootstraps from limited initial training data to make this class tractable for post-training. We believe that methods such as AutoOR can significantly accelerate industrial decision-making with AI.

We study routing games in which travelers optimize over routes that are remembered or surfaced, rather than over a fixed exogenous action set. The paper develops a tractable design theory for endogenous recall and then connects it back to an explicit finite-memory micro model. At the micro level, each traveler carries a finite memory state, receives surfaced alternatives, chooses via a logit rule, and updates memory under a policy such as LRU. This yields a stationary Forgetful Wardrop Equilibrium (FWE); existence is proved under mild regularity, and uniqueness follows in a contraction regime for the reduced fixed-point map. The paper's main design layer is a stationary salience model that summarizes persistent memory and interface effects as route-specific weights. Salience-weighted stochastic user equilibrium is the unique minimizer of a strictly convex potential, which yields a clean optimization and implementability theory. In this layer we characterize governed implementability under ratio budgets and affine tying constraints, and derive constructive algorithms on parallel and series-parallel networks. The bridge between layers is exact for last-choice memory (B=1): the micro model is then equivalent to the salience model, so any interior salience vector can be realized by an appropriate surfacing policy. For larger memories, we develop an explicit LRU-to-TTL-to-salience approximation pipeline and add contraction-based bounds that translate surrogate-map error into fixed-point and welfare error. Finally, we define a Recall Braess Paradox, in which improving recall increases equilibrium delay without changing physical capacity, and show that it can arise on every two-terminal network with at least two distinct s-t paths. Targeted experiments support the approximation regime, governed-design predictions, and the computational advantages of the reduced layer.

Large language models are increasingly applied to operational decision-making where the underlying structure is constrained optimization. Existing benchmarks evaluate whether LLMs can formulate optimization problems as solver code, but leave open a complementary question. Can LLMs directly produce correct solutions to fully specified constrained optimization problems without access to a solver? We introduce ConstraintBench, a benchmark for evaluating LLMs on direct constrained optimization across 10 operations research domains, with all ground-truth solutions verified by the Gurobi solver. Each task presents a natural-language scenario with entities, constraints, and an optimization objective; the model must return a structured solution that a deterministic verifier checks against every constraint and the solver-proven optimum. We evaluate six frontier models on 200 tasks and find that feasibility, not optimality, is the primary bottleneck. The best model achieves only 65.0% feasibility, yet feasible solutions average 89 to 96% of the Gurobi-optimal objective. No model exceeds 30.5% on joint feasibility and optimality within 0.1% of the solver reference. Per-domain analysis shows large variation in difficulty, with average feasibility spanning from 85.0% in the facility location domain to 0.8% in the crew assignment domain. Further, systematic failure modes include duration constraint misunderstanding, entity hallucination, and a feasibility-optimality decoupling in facility location and vehicle routing where models achieve high feasibility but 0% optimality. ConstraintBench and all evaluation infrastructure will be publicly released.

Most existing safe reinforcement learning (RL) benchmarks focus on robotics and control tasks, offering limited relevance to high-stakes domains that involve structured constraints, mixed-integer decisions, and industrial complexity. This gap hinders the advancement and deployment of safe RL in critical areas such as energy systems, manufacturing, and supply chains. To address this limitation, we present SafeOR-Gym, a benchmark suite of nine operations research (OR) environments tailored for safe RL under complex constraints. Each environment captures a realistic planning, scheduling, or control problems characterized by cost-based constraint violations, planning horizons, and hybrid discrete-continuous action spaces. The suite integrates seamlessly with the Constrained Markov Decision Process (CMDP) interface provided by OmniSafe. We evaluate several state-of-the-art safe RL algorithms across these environments, revealing a wide range of performance: while some tasks are tractable, others expose fundamental limitations in current approaches. SafeORGym provides a challenging and practical testbed that aims to catalyze future research in safe RL for real-world decision-making problems.

We study Online Linear Programming (OLP) with batching. The planning horizon is cut into $K$ batches, and decisions on orders can be delayed to the end of their associated batch. The ability to delay decisions improves operational performance, as measured by regret. We study two questions: (1) What is a lower bound on the regret as a function of $K$ and the length of the planning horizon? (2) Which algorithms can achieve this regret lower bound? This paper analyzes these questions when the distribution of the reward has a continuous support. We provide an $Ω(\log K)$ regret lower bound in the single-resource case, and we provide pricing algorithms having an $O(\log K)$ regret in the setting with Poisson arrivals and multiple types of resources. All the algorithms update the prices at most $K$ times and only delay orders of the first and the last batches. All the regret bounds are independent of the length of the planning horizon. Finally, we study a more realistic large support setting where the number of distinct order types is finite but scales with the total number of orders. We prove that our $Θ(\log K)$ bounds still hold for the batching operation of a multisecretary problem with discretized uniform rewards in this large support setting, provided the support grows fast enough. This suggests that the continuous support setting that is the paper's focus serves as a useful theoretical surrogate for the more realistic large finite support setting.