Motivated by large-scale applications, there is a recent trend of research on using first-order methods for solving LP. Among them, PDLP, which is based on a primal-dual hybrid gradient (PDHG) algorithm, may be the most promising one. In this paper, we present a geometric viewpoint on the behavior of PDHG for LP. We demonstrate that PDHG iterates exhibit a spiral pattern with a closed-form solution when the variable basis remains unchanged. This spiral pattern consists of two orthogonal components: rotation and forward movement, where rotation improves primal and dual feasibility, while forward movement advances the duality gap. We also characterize the different situations in which basis change events occur. Inspired by the spiral behavior of PDHG, we design a new crossover algorithm to obtain a vertex solution from any optimal LP solution. This approach differs from traditional simplex-based crossover methods. Our numerical experiments demonstrate the effectiveness of the proposed algorithm, showcasing its potential as an alternative option for crossover. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Funding: T. Liu is partially supported by National Natural Science Foundation of China [Grants NSFC-72225009, 72394360, 72394365]. H. Lu is partially supported by Air Force Office of Scientific Research [Grant FA9550-24-1-0051] and Office of Naval Research [Grant N000142412735]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc . 2024.0996 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0996 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

We study the construction of a confidence interval (CI) for a simulation output performance measure that accounts for input uncertainty when the input models are estimated from finite data. In particular, we focus on performance measures that can be expressed as a ratio of two dependent simulation outputs’ means. We adopt the parametric bootstrap method to mimic input data sampling and construct the percentile bootstrap CI after estimating the ratio at each bootstrap sample. The standard estimator, which takes the ratio of two sample means, tends to exhibit large finite-sample bias and variance, leading to overcoverage of the percentile bootstrap CI. To address this, we propose two new ratio estimators that replace the sample means with pooled mean estimators via the k-nearest neighbor (kNN) regression: the kNN estimator and the kLR estimator. The kNN estimator performs well in low dimensions, but its estimation error converges more slowly as the dimension increases. The kLR estimator combines the likelihood ratio (LR) method with the kNN regression, leveraging the strengths of both while mitigating their weaknesses; the LR method removes dependence of the error convergence rate on the dimension, whereas the kNN method controls the variance of the kLR estimator to be asymptotically bounded. From the asymptotic analyses and finite-sample heuristics, we propose an experiment design for the ratio estimators and demonstrate their superior empirical performances over the standard ratio estimator using three examples, including one in the enterprise risk management application. History: Accepted by Bruno Tuffin, Area Editor for Simulation. Funding: This work was supported by the National Science Foundation [Grants CAREER CMMI-2246281 and CMMI-2417616] and the Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2018-03755]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0914 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0914 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

This paper considers a bilevel program. To solve this bilevel program, it is generally necessary to transform it into some single-level optimization problem. One approach is to replace the lower-level program by its KKT conditions to transform the bilevel program as a mathematical program with complementarity constraints (MPCC). Another approach is to apply the lower-level Wolfe/Mond-Weir/extended Mond-Weir duality to transform the bilevel program into some duality-based single-level reformulations, called WDP, MDP, and eMDP, respectively, in the literature. In this paper, inspired by a conjecture from a recent publication that the tighter feasible region of a reformulation, the better its numerical performance, we present five new duality-based single-level reformulations, called TWDP/TMDP/eTMDP/ETMDP/eETMDP, with tighter feasible regions. Our main goal is to compare all above-mentioned reformulations by designing some direct and relaxation algorithms with projection and implementing these algorithms on 450 test examples generated randomly. Our numerical experiments show that, whether overall comparison or pairwise comparison, at least in our tests, in terms of dominant cases and objective values, WDP/MDP/TWDP/TMDP/ETMDP were always better than MPCC, whereas eMDP/eTMDP/eETMDP were always the worst ones among eight duality-based reformulations, which indicates that the above conjecture is incorrect. In particular, for the relaxation algorithms, WDP/MDP/TWDP/TMDP performed four to five times better than MPCC, whereas eMDP/eTMDP/ETMDP/eETMDP performed at least 1.8 times better than MPCC in terms of dominant cases. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This research was supported by the National Natural Science Foundation of China [Grants 12571324, 72501169, and 72394365], the China Postdoctoral Science Foundation [Grant 2024M761920], and the Postdoctoral Fellowship Program of the China Postdoctoral Science Foundation [Grant GZC20250524]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2025.1159 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2025.1159 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

It contains the source code, instances, results and scripts for the numerical study in A Polynomial-Time Inner Approximation Algorithm for Multi-Objective and Parametric Optimization by L. Nemesch, S. Ruzika, C. Thielen, A. Wittmann.

The emergence of in-store microfulfillment centers (ISMFCs) is transforming omnichannel retailing by facilitating the rapid fulfillment of orders placed online. Effective management, particularly of the complex decisions related to the dynamic selection of products to place in the ISMFC and the determination of inventory levels of each product selected therein, can go a long way in maximizing the benefits of ISMFCs. In this paper, we first formulate the ISMFC inventory decision problem as a Markov Decision Process. We then leverage intuition from this representation and introduce a threshold policy based on the optimal multiperiod marginal profit-to-volume ratio to efficiently manage stochastic demand and make forward-looking decisions. We establish the quality of the proposed approach using two sets of computational experiments. Because key benchmark approaches do not scale well, we restrict the first set of experiments to simulated data involving three products. In the second set of experiments—based on a retail data set with 3,498 products—we benchmark the threshold policy against scalable methods, employing model parameters obtained partly from data estimation and partly from observed data values. The results from these experiments demonstrate that our approach outperforms state-of-the-art benchmarks, identifying near-optimal solutions in a few seconds. The scalability and effectiveness of the threshold policy underscores its practical viability and highlights the substantial economic gains achievable in managing ISMFC operations. History: Accepted by Ram Ramesh, Area Editor for Data Science and Machine Learning. Funding: Q. Jia was supported by the National Natural Science Foundation of China [Grants 72394373 and 72231004]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0710 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0710 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

The software and data in this repository are a snapshot of the software and data that were used in the research reported on in the paper Multistage Mobile Anchor Redeployment in Indoor Positioning System Using Hierarchical State Lagrangian Cut-Augmented Stochastic Dual Dynamic Integer Programming by Lyu Zhongyuan, Tom Chan, and Daniel P.K. Lun.

The software and data in this repository are a snapshot of the software and data that were used in the research reported on in the paper Cone product reformulation for global optimization by D. Bertsimas, D. de Moor, D. den Hertog, T. Koukouvinos, and J. Zhen.

The software and data in this repository are a snapshot of the software and data that were used in the research reported on in the paper When Multimodal Interactions Impair Prediction: A Novel Regularized Deep Learning Strategy by Gang Chen, Shuaiyong Xiao, Chenghong Zhang, and Huimin Zhao.

The software and data in this repository are a snapshot of the software and data that were used in the research reported on in the paper Enabling Ultra-Fast Online Order Fulfillment: Efficient Inventory Management for In-Store Micro-Fulfillment Centers by Qian Jia, Zhengrui Jiang, and Syam Menon.

The software and data in this repository are a snapshot of the software and data that were used in the research reported on in the paper Efficient input uncertainty quantification for ratio estimator by L. He, M.B. Feng and E. Song. The snapshot is based on this SHA in the development repository.