Advances in machine learning (ML) have created new opportunities to complement traditional operations research (OR) methods. In particular, transformer models can capture complex interactions in token sequences by mapping tokens into a high-dimensional embedding space and propagating contextual information via attention. This makes them a candidate to model non-permutation flow shop scheduling with secondary resources as a next-token prediction task, where tokens represent job-machine-secondary resource tuples. For training, mixed-integer linear programming (MILP)-generated schedules are tokenized and used as next-token prediction data. During inference, partial token sequences (prefixes) are randomly generated and completed by the trained transformer through constrained decoding. A computational study is conducted on a flow shop with 8 jobs, 4 machines, and 3 secondary resources, where jobs are selected from a fixed pool of 20 jobs that is sampled during training and provides the candidates during prefix completion. The transformer achieves better solution quality (smaller makespans) compared to a genetic algorithm (GA), the NEH heuristic, and random search. It is outperformed only by the MILP model and the iterated greedy (IG) heuristic. The study concludes that transformer models can, to some extent, learn patterns from MILP-optimized non-permutation flow shop schedules and that transformer-based scheduling represents an interesting direction for future research, particularly in settings with a fixed, recurring job set.
We ask whether large language models (LLMs) can design effective algorithms for well-specified operations research (OR) problems. We study inventory control, queueing network control, and assortment optimization. We evaluate two levels of LLM use: at level 1, the model receives one problem instance and returns a solution for that instance; at level 2, it receives only the problem class description and broad parameter ranges, and returns an algorithm that maps instance parameters to solutions. Human input is minimal: we give one untuned prompt that describes the problem, and the model has access to a Python sandbox tool with a fixed compute budget. The strongest model we test, gpt-5.6-sol, matches or outperforms the best existing method on almost all evaluated instances. This holds even at level 2, where the returned algorithm is fixed before seeing the evaluation instances. Performance also improves sharply across models released less than eight months apart, suggesting that this capability is moving quickly. Thus, for the well-specified operations problems we study, a single untuned LLM query can already produce algorithms competitive with specialized methods. These results suggest that frontier LLMs can be a serious empirical baseline for algorithm design in well-specified OR problems.
Large traveling salesman problem (TSP) instances require a solver to allocate limited computation while preserving the validity of its outputs. Existing neural--operations-research (OR) hybrids predict guidance without requiring learned transitions to satisfy constraints discovered during search. DualCert introduces \emph{constraint-coupled learning}, in which current degree equations and dynamically separated subtour-elimination constraints (SECs) define each learned transition. At each refinement, the degree equations and selected, strictly satisfied SEC equations, with positive slacks, define an iterate-dependent primal-slack Karush--Kuhn--Tucker (KKT) manifold. Repaired dual variables and violated SEC rows define a local cost field. An exact constrained mirror-descent step maps each finite state to a positive state on the same manifold. Where selected rows and deterministic ties remain fixed, implicit differentiation maps parameter perturbations into the manifold tangent space and reuses the forward constraint operator for the local-cost-field derivative. The terminal edge state allocates computation across Held--Karp ascent, candidate-graph edge tests, and tour construction under a fixed budget. Deterministic verification recomputes original costs and accepts only verified candidate-graph lower bounds and edge decisions. On 1,000 held-out TSP1000 instances, DualCert attains a mean tour-cost gap of \(0.0573\%\) from Lin--Kernighan--Helsgaun version 3 (LKH-3) reference tours in \(9.55\) batch-amortized seconds per instance. It returns a verified candidate-graph lower bound for every instance and achieves \(81.46\%\) edge-decision coverage. The mean gap is \(67.1\%\) smaller than the reported NeuroLKH mean gap. Thus, optimization constraints govern learning, while deterministic verification preserves output validity.
Can supply-chain AI move beyond isolated decision modules toward unified operational planning? A complete replenishment plan specifies which products each location carries, which upstream facility supplies it, how often it is replenished, and how deliveries are routed. These decisions are operationally coupled: the selected assortment changes the demand and load passed to later stages; source assignment and replenishment frequency reshape the delivery requests; and route feasibility and cost, in turn, determine the system value of the earlier choices. Yet in modern supply chains, these decisions are often handled by separate departments and optimized through separate systems, which can lead to stockouts, inventory exposure, and avoidable transportation. We propose SCOPE: Supply-Chain Operations through Coupled Policies for End-to-End Coordination, a composite policy model that represents supply-chain entities as tokens, contextualizes them through a shared operational representation, and maps each token type to the corresponding decision interface. Each decision builds on the partial plan formed by earlier decisions while the completed plan is evaluated using a shared system-level utility. We instantiate this framework in urban fresh-retail replenishment, where service frequency, assortment, capacity pressure, and road-network routing interact strongly, and evaluate it on real operational data from Dingdong and JD.com, two large-scale supply chains operating at different replenishment echelons. Across both settings, SCOPE consistently outperforms methods that optimize each decision stage separately, as well as practice-oriented baselines commonly used in supply-chain operations. These results show that learning and coordinating cross-department operational couplings lead to more effective end-to-end supply-chain decisions.
Multi-warehouse inventory allocation is typically formulated as a mixed-integer programming (MIP) problem, yet no single formulation consistently matches heterogeneous instance-level regimes induced by demand concentration, inventory imbalance, replenishment scale, service constraints, and forecast volatility. We study this issue as instance-wise operations research (OR) formulation selection, where each allocation instance is assigned to a solver-executable formulation from a candidate OR expert library. We propose a solver-guided large language model (LLM) framework for OR formulation selection, in which each OR expert corresponds to a MIP formulation encoding a distinct allocation priority. To train the selector, the framework first constructs balanced expert-conditioned supervised fine-tuning (SFT) records for schema learning, and then uses MIP solver evaluation on historical instances to convert solver-evaluated allocation-quality gaps into margin-weighted identity preference optimization (IPO) preferences and per-instance expert-score metadata for reward lookup during group relative policy optimization (GRPO) to assign rewards to sampled responses. Experiments on multi-warehouse inventory allocation instances from JD$\mathord{.}$com, one of China's largest e-retailers, demonstrate that GRPO substantially improves expert-selection accuracy relative to the SFT+IPO selector and, more importantly, produces higher realized allocation quality than both the preference-trained selector and the best fixed formulation. With GRPO, Hit Ratio@1 and Hit Ratio@2 increase from 21.45% to 50.42% and from 70.47% to 82.31%. The resulting selector achieves an allocation accuracy gain of 12.57 percentage points over the incumbent baseline, outperforming both the SFT+IPO selector and the best fixed OR expert, and reduces the gap to the ex-post oracle to 4.85 percentage points.
Dongfang Li, Xiaodong Luo, Ruoyu Sun +62cs.CL cs.AI
Full-parameter post-training of trillion-parameter-scale MoE models introduces substantial system-level challenges for large-scale distributed training, including severe memory pressure, non-overlapped communication overhead, and inefficient kernel execution. While most large-scale LLM training systems are built around GPU-based clusters, this report presents an end-to-end optimization practice on the Ascend NPU SuperPOD. Using the DeepSeek-V4 model family as the target workload, we develop a hierarchical optimization framework spanning model-level parallelism, computation-communication orchestration, and low-level kernel execution. The resulting system achieves 34.22% Model FLOPs Utilization (MFU) with a 2.93x improvement over the open-source baseline recipe while maintaining training stability. Building on this optimized infrastructure, we further establish a CPT and SFT workflow for complex Operations Research (OR) tasks. We refer to the integrated framework as SLAI T-Rex. Using DeepSeek-V4-Flash, we develop OR-oriented CPT and SFT data pipelines that combine collected domain resources with solver-verified synthetic optimization documents. The resulting dataset contains 10K high-quality SFT samples spanning four task categories and three problem representations. The specialized model achieves the highest average zero-shot Pass@1 score among the evaluated models, reaching 71.81% and outperforming GPT-5.4-Mini and the base DeepSeek-V4-Flash model by 3.98 and 11.27 percentage points, respectively. Overall, this work demonstrates a full-stack pathway from efficient trillion-parameter model post-training on Ascend infra to domain-specialized Flash models for solver-grounded mathematical modeling, advancing frontier-model systems for complex reasoning.
The rapid growth of the global aging population presents severe challenges to healthcare systems, necessitating efficient, equitable, and patient-centered care models. While Industrial Engineering and Operations Research (OR) provide robust optimization and decision-support tools to address these multidimensional complexities, current applications often remain fragmented. This paper presents a thematic review of 30 seminal studies at the intersection of OR and elderly care, categorizing the literature into home healthcare operations, polypharmacy management, and clinical chronotherapy. Our analysis highlights a significant methodological evolution from static, deterministic models toward dynamic and stochastic frameworks integrated with artificial intelligence (AI). Despite these advancements, a critical translational gap persists: the current OR literature is heavily dominated by process-level optimizations, such as staff routing, and struggles to translate these operational efficiencies into measurable clinical outcomes. Furthermore, holistic models bridging the transition between hospital and community care remain critically underexplored. To develop resilient and smart healthcare systems, this study proposes a conceptual framework that shifts the research focus from isolated operational tasks to integrated, multi-level decision-making. We emphasize the critical need for robust systems analysis, human-inclusive design, and the smartification of care through emerging digital technologies - including digital twins and large language models - to successfully bridge the gap between theoretical operational metrics and tangible patient-level health outcomes.
We present JOR-Bench, a collection of five Japanese-language benchmarks for evaluating the ability of large language models (LLMs) to formulate and solve operations research (OR) problems. Each benchmark is a Japanese translation of an existing English benchmark: IndustryOR, MAMO Complex LP, NL4OPT, OptiBench, and OptMATH, covering 1,319 problems spanning linear programming, mixed-integer programming, non-linear programming, and combinatorial optimization. JOR-Bench is a solver-independent benchmark that can be used with any solver or programming language, and consists of pairs of Japanese problem statements and expected numerical answers. We evaluate seven LLMs, including multilingual general-purpose models and Japanese-specialized models, on both the original English and the new Japanese versions, and compare performance across languages. For the main evaluation, we standardize execution with the Python interface to OR-Tools to make model outputs comparable and reproducible with open-source software. Our results show that OR formulation ability is largely language-neutral for strong multilingual models; the overall average accuracy difference between English and Japanese is only $-0.3$ pp. Yet error analysis reveals subtle cross-lingual differences, including a pragmatic disambiguation failure in some domains that causes models to output decision-variable values instead of the objective value when the prompt is in Japanese.
Adriana Laurindo Monteiro, Nayse Fagundes, Gabriel Mattos Langeloh +4cs.AI cs.MA
We propose OptiAgent, a multi-agent framework that, given a natural language description of an Operations Research problem, is able to output a solver-ready mathematical formulation as well as executable code. Our architecture prioritizes the mathematical modeling step, where dedicated agents extract structures, such as decision variables and constraints, enabling iterative self-correction. We introduce a novel multi-loop validation architecture with four specialized feedback mechanisms, each targeting a distinct failure mode such as misinterpretation, structural defects, mathematical inconsistencies, validation failures, and code errors. Alongside accuracy, our modular design improves the process of solving optimization problems by improving transparency, as each agent exposes its reasoning and feedback, making the full modeling process auditable. Our framework achieves state-of-the-art performance on 3 out of 4 benchmarks across LP, MILP, and Nonlinear Programming tasks, while remaining highly competitive on the remaining dataset.
While traditional hub capacity planning models optimize effectively for quantitative inputs, they often fail to digest qualitative business context. We propose a novel framework where a large language model (LLM) agent iteratively proposes hub capacity decisions guided by natural-language business context descriptions. The key mechanism is a chain-of-thought reasoning protocol: the LLM constructs a structured decision table that maps each contextual item to specific capacity adjustments based on the implied direction and magnitude of changes. The new capacity decision is then validated through a feedback loop with an optimization model, which provides routing-based performance metrics to guide the agent's selection. On a real-world 13-hub freight network in the southeastern US, our framework achieves a 2.8% optimality gap relative to the hidden ground-truth, a significant improvement over the 11.0% gap produced by the traditional optimization model without textual business inputs. This demonstrates that LLMs can serve as a contextual bridge, integrating qualitative business insights into Operations Research workflows.
Liang Guo, Lin Shaochong, Shen Zuo-Jun Max +1cs.LG cs.AI
Deploying large language models (LLMs) for operations research (OR) tasks remains challenging because correctness depends on a coherent modeling process, not merely a correct final answer. Standard autoregressive generation operates on a myopic policy, which sometimes fails to anticipate whether a partial formulation can be validly extended into a globally consistent optimization model. Consequently, locally plausible steps may propagate into catastrophic downstream formulation or solver code errors. To address this, we propose an uncertainty-aware, training-free inference framework for OR mathematical modeling. Without updating model parameters, our method evaluates intermediate candidate steps using short lookahead simulations to quantify downstream predictive uncertainty or probability concentration. Candidates that demonstrate a higher likelihood of yielding coherent mathematical formulations are then dynamically selected via importance resampling. Empirical evaluations across multiple OR benchmarks (including NL4OPT, MAMO, and IndustryOR) demonstrate that our framework consistently outperforms both standard and low-temperature baselines, establishing an efficient, training-free paradigm for reliable OR formulation generation.
Balance-oriented multi-warehouse inventory allocation is a recurring decision problem in large-scale e-commerce supply chains, in which a fixed replenishment quantity is distributed across warehouses to balance post-allocation inventory coverage while accounting for demand forecasts and heterogeneous allocation constraints. In practice, allocation requirements are often scenario-dependent and expressed in semi-structured or natural-language form rather than as ready-to-solve operations research (OR) formulations. We propose an OR-guided Large Language Model (LLM) for Allocation (ORLA) that uses solver feedback to generate, verify, and select OR formulations. ORLA integrates automatic "Problem-Model-Code (PMC)" generation, learning-based formulation selection, and feasibility restoration. We develop three complementary mixed-integer programming formulation families based on deviation minimization, soft band compliance, and knapsack-inspired allocation, together with solver-ready mixed-integer linear programming reformulations, modular constraint extensions, and a penalty-based relaxation mechanism for infeasible cases. The LLM component generates candidate formulations and executable solver code from textual or semi-structured specifications, while the solver provides verification signals for executability, feasibility, and solution quality. To address instance heterogeneity, ORLA estimates the expected quality of candidate formulations, selects promising candidates, and combines their outputs through score-aware aggregation. Experimental results on 29 production evaluation batches from JD.com show that the best single OR formulation improves allocation accuracy by 3.4 percentage points over the incumbent approach, while the full ORLA framework achieves a 4.5 percentage-point overall improvement and improves allocation accuracy in 26 of the 29 evaluation batches.
Operations Research (OR) provides a rigorous framework for high-stakes decision-making, but effective OR modeling requires substantial domain knowledge, mathematical abstraction, and solver expertise. Recent LLM-based systems automate parts of this pipeline, yet remain limited by low accuracy on complex problems, opaque outputs, and narrow solver support. We propose COOPA (COoperative OPerations Agent), a modular LLM-agent architecture for interpretable and scalable OR decision support. It combines three components: iterative confidence-based modeling, which generates multiple candidate formulations, self-evaluates them across modeling dimensions, and selects one using a max-min confidence criterion; element-level provenance and confidence explanations, which link variables, parameters, constraints, and objectives to quoted source text and provide an audit trail for human verification; and multi-solver routing to specialized optimizer agents for different OR problem classes. Across three OR benchmarks, eight LLM backbones, and four baselines under identical conditions, COOPA achieves the best macro-average accuracy on six of eight backbones and improves over the strongest baseline by up to 6.7 percentage points. A within-system ablation isolates the contribution of iterative confidence-based modeling, while additional analyses and case studies illustrate the value of source traceability and multi-solver dispatch.
Large language models are increasingly deployed as autonomous agents for multi-step tasks in executable environments, yet their ability to perform realistic operations research (OR) work remains unclear. Existing OR evaluations often decouple modeling from solving, rely on pre-formalized or text-only instances, and rarely test the full workflow from operational artifacts to validated decisions. In this work, we introduce ORAgentBench, an execution-grounded benchmark for evaluating autonomous agents on challenging end-to-end operations research tasks. It contains 107 human-reviewed tasks across diverse operational scenarios, each packaged in an isolated environment with a natural-language brief, multi-file data, configuration artifacts, and a required submission schema. Agents must write and run solution code, and their submissions are evaluated by hidden validators for schema validity, hard-constraint feasibility, and normalized objective quality. Experiments with fourteen frontier agent-model configurations show that current agents remain far from reliable OR practice. The best agent passes only 35.51% of all tasks and 20.59% of hard tasks, and many feasible submissions still fall below the required quality threshold. Failure analysis further shows that errors are dominated by strategic weaknesses, including missed operational rules, brittle formulations, weak feasible-solution construction, and insufficient solution improvement. OR-specific procedural skills increase hard-task feasibility, but do not reliably improve solution quality or pass rate. These results suggest that progress in OR agents requires moving beyond plausible optimization code toward dependable, high-quality operational decision-making.
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.