LLMs are emerging tools for simulating human behavior in business, economics, and social science, offering a lower-cost complement to laboratory experiments, field studies, and surveys. This paper evaluates how well LLMs replicate human behavior in operations management. Using nine published experiments in behavioral operations, we assess two criteria: replication of hypothesis-test outcomes and distributional alignment via Wasserstein distance. LLMs reproduce most hypothesis-level effects, capturing key decision biases, but their response distributions diverge from human data, including for strong commercial models. We also test two lightweight interventions -- chain-of-thought prompting and hyperparameter tuning -- which reduce misalignment and can sometimes let smaller or open-source models match or surpass larger systems.

Recent advances in mathematical reasoning and the long-term planning capabilities of large language models (LLMs) have precipitated the development of agents, which are being increasingly leveraged in business operations processes. Decision models to optimize inventory levels are one of the core elements of operations management. However, the capabilities of the LLM agent in making inventory decisions in uncertain contexts, as well as the decision-making biases (e.g. framing effect, etc.) of the agent, remain largely unexplored. This prompts concerns regarding the capacity of LLM agents to effectively address real-world problems, as well as the potential implications of biases that may be present. To address this gap, we introduce AIM-Bench, a novel benchmark designed to assess the decision-making behaviour of LLM agents in uncertain supply chain management scenarios through a diverse series of inventory replenishment experiments. Our results reveal that different LLMs typically exhibit varying degrees of decision bias that are similar to those observed in human beings. In addition, we explored strategies to mitigate the pull-to-centre effect and the bullwhip effect, namely cognitive reflection and implementation of information sharing. These findings underscore the need for careful consideration of the potential biases in deploying LLMs in Inventory decision-making scenarios. We hope that these insights will pave the way for mitigating human decision bias and developing human-centred decision support systems for supply chains.

This paper shows a comprehensive analysis of three algorithms (Time Series, Random Forest (RF) and Deep Reinforcement Learning) into three inventory models (the Lost Sales, Dual-Sourcing and Multi-Echelon Inventory Model). These methodologies are applied in the supermarket context. The main purpose is to analyse efficient methods for the data-driven. Their possibility, potential and current challenges are taken into consideration in this report. By comparing the results in each model, the effectiveness of each algorithm is evaluated based on several key performance indicators, including forecast accuracy, adaptability to market changes, and overall impact on inventory costs and customer satisfaction levels. The data visualization tools and statistical metrics are the indicators for the comparisons and show some obvious trends and patterns that can guide decision-making in inventory management. These tools enable managers to not only track the performance of different algorithms in real-time but also to drill down into specific data points to understand the underlying causes of inventory fluctuations. This level of detail is crucial for pinpointing inefficiencies and areas for improvement within the supply chain.

Distributionally Robust Optimization (DRO) is a popular framework for decision-making under uncertainty, but its adversarial nature can lead to overly conservative solutions. To address this, we study ex-ante Distributionally Robust Regret Optimization (DRRO), focusing on Wasserstein-based ambiguity sets which are popular due to their links to regularization and machine learning. We provide a systematic analysis of Wasserstein DRRO, paralleling known results for Wasserstein DRO. Under smoothness and regularity conditions, we show that Wasserstein DRRO coincides with Empirical Risk Minimization (ERM) up to first-order terms, and exactly so in convex quadratic settings. We revisit the Wasserstein DRRO newsvendor problem, where the loss is the maximum of two linear functions of demand and decision. Extending [25], we show that the regret can be computed by maximizing two one-dimensional concave functions. For more general loss functions involving the maximum of multiple linear terms in multivariate random variables and decision vectors, we prove that computing the regret and thus also the DRRO policy is NP-hard. We then propose a convex relaxation for these more general Wasserstein DRRO problems and demonstrate its strong empirical performance. Finally, we provide an upper bound on the optimality gap of our relaxation and show it improves over recent alternatives.

In this paper, we investigate the performance of Thompson Sampling (TS) for online learning with censored feedback, focusing primarily on the classic repeated newsvendor model--a foundational framework in inventory management--and demonstrating how our techniques can be naturally extended to a broader class of problems. We model demand using a Weibull distribution and initialize TS with a Gamma prior to dynamically adjust order quantities. Our analysis establishes optimal (up to logarithmic factors) frequentist regret bounds for TS without imposing restrictive prior assumptions. More importantly, it yields novel and highly interpretable insights on how TS addresses the exploration-exploitation trade-off in the repeated newsvendor setting. Specifically, our results show that when past order quantities are sufficiently large to overcome censoring, TS accurately estimates the unknown demand parameters, leading to near-optimal ordering decisions. Conversely, when past orders are relatively small, TS automatically increases future order quantities to gather additional demand information. Extensive numerical simulations further demonstrate that TS outperforms more conservative and widely-used approaches such as online convex optimization, upper confidence bounds, and myopic Bayesian dynamic programming. This study also lays the foundation for exploring general online learning problems with censored feedback.

Many important managerial decisions are made based on censored observations. Making decisions without adequately handling the censoring leads to inferior outcomes. We investigate the data-driven decision-making problem with an offline dataset containing the feature data and the censored historical data of the variable of interest without the censoring indicators. Without assuming the underlying distribution, we design and leverage {\epsilon}-insensitive operational costs to deal with the unobserved censoring in an offline data-driven fashion. We demonstrate the customization of the {\epsilon}-insensitive operational costs for a newsvendor problem and use such costs to train two representative ML models, including linear regression (LR) models and neural networks (NNs). We derive tight generalization bounds for the custom LR model without regularization (LR-{\epsilon}NVC) and with regularization (LR-{\epsilon}NVC-R), and a high-probability generalization bound for the custom NN (NN-{\epsilon}NVC) trained by stochastic gradient descent. The theoretical results reveal the stability and learnability of LR-{\epsilon}NVC, LR-{\epsilon}NVC-R and NN-{\epsilon}NVC. We conduct extensive numerical experiments to compare LR-{\epsilon}NVC-R and NN-{\epsilon}NVC with two existing approaches, estimate-as-solution (EAS) and integrated estimation and optimization (IEO). The results show that LR-{\epsilon}NVC-R and NN-{\epsilon}NVC outperform both EAS and IEO, with maximum cost savings up to 14.40% and 12.21% compared to the lowest cost generated by the two existing approaches. In addition, LR-{\epsilon}NVC-R's and NN-{\epsilon}NVC's order quantities are statistically significantly closer to the optimal solutions should the underlying distribution be known.

We consider a stochastic lost-sales inventory control system with a lead time $L$ over a planning horizon $T$. Supply is uncertain, and is a function of the order quantity (due to random yield/capacity, etc). We aim to minimize the $T$-period cost, a problem that is known to be computationally intractable even under known distributions of demand and supply. In this paper, we assume that both the demand and supply distributions are unknown and develop a computationally efficient online learning algorithm. We show that our algorithm achieves a regret (i.e. the performance gap between the cost of our algorithm and that of an optimal policy over $T$ periods) of $O(L+\sqrt{T})$ when $L\geq\log(T)$. We do so by 1) showing our algorithm cost is higher by at most $O(L+\sqrt{T})$ for any $L\geq 0$ compared to an optimal constant-order policy under complete information (a well-known and widely-used algorithm) and 2) leveraging its known performance guarantee from the existing literature. To the best of our knowledge, a finite-sample $O(\sqrt{T})$ (and polynomial in $L$) regret bound when benchmarked against an optimal policy is not known before in the online inventory control literature. A key challenge in this learning problem is that both demand and supply data can be censored; hence only truncated values are observable. We circumvent this challenge by showing that the data generated under an order quantity $q^2$ allows us to simulate the performance of not only $q^2$ but also $q^1$ for all $q^1

In this paper we address the problem of learning and backtesting inventory control policies in the presence of general arrival dynamics -- which we term as a quantity-over-time arrivals model (QOT). We also allow for order quantities to be modified as a post-processing step to meet vendor constraints such as order minimum and batch size constraints -- a common practice in real supply chains. To the best of our knowledge this is the first work to handle either arbitrary arrival dynamics or an arbitrary downstream post-processing of order quantities. Building upon recent work (Madeka et al., 2022) we similarly formulate the periodic review inventory control problem as an exogenous decision process, where most of the state is outside the control of the agent. Madeka et al. (2022) show how to construct a simulator that replays historic data to solve this class of problem. In our case, we incorporate a deep generative model for the arrivals process as part of the history replay. By formulating the problem as an exogenous decision process, we can apply results from Madeka et al. (2022) to obtain a reduction to supervised learning. Finally, we show via simulation studies that this approach yields statistically significant improvements in profitability over production baselines. Using data from an ongoing real-world A/B test, we show that Gen-QOT generalizes well to off-policy data.

Value iteration can find the optimal replenishment policy for a perishable inventory problem, but is computationally demanding due to the large state spaces that are required to represent the age profile of stock. The parallel processing capabilities of modern GPUs can reduce the wall time required to run value iteration by updating many states simultaneously. The adoption of GPU-accelerated approaches has been limited in operational research relative to other fields like machine learning, in which new software frameworks have made GPU programming widely accessible. We used the Python library JAX to implement value iteration and simulators of the underlying Markov decision processes in a high-level API, and relied on this library's function transformations and compiler to efficiently utilize GPU hardware. Our method can extend use of value iteration to settings that were previously considered infeasible or impractical. We demonstrate this on example scenarios from three recent studies which include problems with over 16 million states and additional problem features, such as substitution between products, that increase computational complexity. We compare the performance of the optimal replenishment policies to heuristic policies, fitted using simulation optimization in JAX which allowed the parallel evaluation of multiple candidate policy parameters on thousands of simulated years. The heuristic policies gave a maximum optimality gap of 2.49%. Our general approach may be applicable to a wide range of problems in operational research that would benefit from large-scale parallel computation on consumer-grade GPU hardware.

The rise of big data analytics has automated the decision-making of companies and increased supply chain agility. In this paper, we study the supply chain contract design problem faced by a data-driven supplier who needs to respond to the inventory decisions of the downstream retailer. Both the supplier and the retailer are uncertain about the market demand and need to learn about it sequentially. The goal for the supplier is to develop data-driven pricing policies with sublinear regret bounds under a wide range of possible retailer inventory policies for a fixed time horizon. To capture the dynamics induced by the retailer's learning policy, we first make a connection to non-stationary online learning by following the notion of variation budget. The variation budget quantifies the impact of the retailer's learning strategy on the supplier's decision-making. We then propose dynamic pricing policies for the supplier for both discrete and continuous demand. We also note that our proposed pricing policy only requires access to the support of the demand distribution, but critically, does not require the supplier to have any prior knowledge about the retailer's learning policy or the demand realizations. We examine several well-known data-driven policies for the retailer, including sample average approximation, distributionally robust optimization, and parametric approaches, and show that our pricing policies lead to sublinear regret bounds in all these cases. At the managerial level, we answer affirmatively that there is a pricing policy with a sublinear regret bound under a wide range of retailer's learning policies, even though she faces a learning retailer and an unknown demand distribution. Our work also provides a novel perspective in data-driven operations management where the principal has to learn to react to the learning policies employed by other agents in the system.