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This paper studies a distributionally robust multi-item newsvendor problem, where the demand distribution is unknown but specified with a general event-wise ambiguity set. Using the event-wise affine decision rules, we can obtain a conservative approximation formulation of the problem, which can typically be further reformulated as a linear program. In order to efficiently solve the resulting large-scale linear program, we develop a column generation-based decomposition scheme and speed up the computational efficiency by exploiting a special column selection strategy and stopping early based on a Karush-Kuhn-Tucker condition test. Focusing on the Wasserstein ambiguity set and the event-wise mean absolute deviation set, a computational study demonstrates both the computational efficiency of the proposed algorithm, which significantly outperforms a commercial solver and a Benders decomposition method, and the out-of-sample superiority of distributionally robust solutions relative to their sample average approximation counterparts. History: Accepted by Nicola Secomandi, Area Editor for Stochastic Models & Reinforcement Learning. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada [492997-2016, RGPIN-2016-05208], the National Natural Science Foundation of China [71972012], Alliance de recherche numérique du Canada, and Canada Research Chairs [CRC-2018-00105]. It was also supported by Groupe d'études et de recherche en analyse des décisions (GERAD). Finally, this research was enabled in part by support provided by Digital Research Alliance of Canada (https://alliancecan.ca/en). 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.2022.0010) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0010). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

In this paper, we study the classic submodular maximization problem subject to a group equality constraint under both nonadaptive and adaptive settings. It is shown that the utility function of many machine learning applications, including data summarization, influence maximization in social networks, and personalized recommendation, satisfies the property of submodularity. Hence, maximizing a submodular function subject to various constraints can be found at the heart of many of those applications. On a high level, submodular maximization aims to select a group of most representative items (e.g., data points). However, the design of most existing algorithms does not incorporate the fairness constraint, leading to underrepresentation or overrepresentation of some particular groups. This motivates us to study the submodular maximization problem with group equality, in which we aim to select a group of items to maximize a (possibly nonmonotone) submodular utility function subject to a group equality constraint. To this end, we develop the first constant-factor approximation algorithm for this problem. The design of our algorithm is robust enough to be extended to solving the submodular maximization problem under a more complicated adaptive setting. Moreover, we further extend our study to incorporating a global cardinality constraint and other fairness notations. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2022.0384. [ABSTRACT FROM AUTHOR]

In the biobjective branch-and-bound literature, a key ingredient is objective branching, that is, to create smaller and disjoint subproblems in the objective space, obtained from the partial dominance of the lower bound set by the upper bound set. When considering three or more objective functions, however, applying objective branching becomes more complex, and its benefit has so far been unclear. In this paper, we investigate several ingredients that allow us to better exploit objective branching in a multiobjective setting. We extend the idea of probing to multiple objectives for the 0-1 case, enhance it in several ways, and show that, when coupled with objective branching, it results in significant speedups in terms of CPU times. We also show how to adapt it to the general integer case. Furthermore, we investigate cut generation based on the objective branching constraints. Besides, we generalize the best bound idea for node selection to multiple objectives, and we show that the proposed rules outperform, in the multiobjective literature, the commonly employed depth-first and breadth-first strategies. We also analyze problem-specific branching rules. We test the proposed ideas on available benchmark instances for three problem classes with three and four objectives, namely, the capacitated facility location problem, the uncapacitated facility location problem, and the knapsack problem. Our enhanced multiobjective branch-and-bound algorithm outperforms the best existing branch-and-bound–based approach and is the first to obtain competitive and even slightly better results than a state-of-the-art objective space search method on a subset of the problem classes. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: This work was supported in whole, or in part, by the Austrian Science Fund [Grant P 31366]. Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2022.0299. [ABSTRACT FROM AUTHOR]

We propose a methodology at the nexus of operations research and machine learning (ML) leveraging generic approximators available from ML to accelerate the solution of mixed-integer linear two-stage stochastic programs. We aim at solving problems where the second stage is demanding. Our core idea is to gain large reductions in online solution time, while incurring small reductions in first-stage solution accuracy by substituting the exact second-stage solutions with fast, yet accurate, supervised ML predictions. This upfront investment in ML would be justified when similar problems are solved repeatedly over time—for example, in transport planning related to fleet management, routing, and container yard management. Our numerical results focus on the problem class seminally addressed with the integer and continuous L-shaped cuts. Our extensive empirical analysis is grounded in standardized families of problems derived from stochastic server location (SSLP) and stochastic multi-knapsack (SMKP) problems available in the literature. The proposed method can solve the hardest instances of SSLP in less than 9% of the time it takes the state-of-the-art exact method, and in the case of SMKP, the same figure is 20%. Average optimality gaps are, in most cases, less than 0.1%. History: Accepted by Alice Smith, Area Editor (for this paper) for Design and Analysis of Algorithms–Discrete. Funding: Financial support from the Institut de Valorisation des Données (IVADO) Fundamental Research Project Grants [project entitled "Machine Learning for (Discrete) Optimization"]; Canada Research Chairs; the Natural Sciences and Engineering Research Council of Canada [Collaborative Research and Development Grant CRD-477938-14]; and the Canadian National Railway Company Chair in Optimization of Railway Operations at Université de Montréal is gratefully acknowledged. E. Frejinger holds a Canada Research Chair. Computations were made on the supercomputer Béluga, managed by Calcul Québec and Digital Research Alliance of Canada. The operation of this supercomputer is funded by the Canada Foundation for Innovation; the Ministère de l'Économie, de la Science et de l'Innovation du Québec; and the Fonds de Recherche du Québec – Nature et Technologies. [ABSTRACT FROM AUTHOR]

In this paper, we study adjustable robust optimization (ARO) problems with discrete uncertainty. Under a very general modeling framework, we show that such two-stage robust problems can be exactly reformulated as ARO problems with objective uncertainty only. This reformulation is valid with and without the fixed recourse assumption and is not limited to continuous wait-and-see decision variables unlike most of the existing literature. Additionally, we extend an enumerative algorithm akin to a branch-and-cut scheme for which we study the asymptotic convergence. We discuss how to apply the reformulation on two variants of well-known optimization problems, a facility location problem in which uncertainty may affect the capacity values and a multiple knapsack problem with uncertain weights, and we report extensive computational results demonstrating the effectiveness of the approach. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: This work was supported by the Air Force Office of Scientific Research [Grants FA8655-20-1-7012, FA8655-20-1-7019]. [ABSTRACT FROM AUTHOR]