{"title":"Minimum-cardinality global defensive alliances in general graphs","authors":"André Rossi, Alok Singh","doi":"10.1007/s10479-025-06571-2","DOIUrl":"10.1007/s10479-025-06571-2","url":null,"abstract":"<div><p>A subset <i>S</i> of vertices of an undirected graph <i>G</i> is a defensive alliance if at least half of the vertices in the closed neighborhood of each vertex of <i>S</i> are in <i>S</i>. A defensive alliance is a global defensive alliance if it is also a dominating set of <i>G</i>. This paper addresses the problem of finding minimum-cardinality global defensive alliances for general graphs. Two integer linear programming formulations are proposed to address this problem, the second one being an improved version of the first one in which the constraints are attempted for tightening with a cubing-time algorithm. Two new lower bounds on the cardinality of a defensive global alliance are proposed: the first one is based on a linear time algorithm and is shown to be tighter than three of the four lower bounds from the literature, and the second one is derived from the linear programming relaxation of the aforementioned integer linear programming formulations of the problem. An upper bound on the global defensive alliance number is obtained using a greedy peeling algorithm that is shown to be at least as good as an upper bound of the literature, however it is also shown that the proposed algorithm may be unable to find an optimal solution for some graphs. Finally, numerical experiments are carried out on the 78 DIMACS instances and on 75 Erdős-Rényi graphs with up to 10,000 vertices in order to show the effectiveness of the proposed approaches.</p></div>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"349 3","pages":"1891 - 1931"},"PeriodicalIF":4.5,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimal firm behavior under pollution irreversibility risk, and distance to irreversibility thresholds","authors":"R. Boucekkine, W. Ruan, B. Zou","doi":"10.1007/s10479-025-06566-z","DOIUrl":"10.1007/s10479-025-06566-z","url":null,"abstract":"<div><p>We study optimal firm behavior under irreversible pollution risk for a general class of models with irreversible local pollution. Irreversibility comes from the decay rate of pollution dropping to zero above a pollution level featuring non-convexity. In addition, the firm can instantaneously move from a reversible to an irreversible pollution mode, following a Poisson process. First, we prove for the general class of models that for any value of the Poisson probability, the optimal emission policy leads to more pollution with the irreversibility risk than without in a neighborhood of the irreversibility threshold. It’s shown that the extent of uncertainty (as captured by the Poisson arrival rate) is second-order in this neighborhood. Next we study the robustness of the latter result at any pollution level in the case of linear-quadratic objective functions. We find that the general local result does not necessarily hold if actual pollution is far enough from the irreversibility threshold.\u0000</p></div>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"349 3","pages":"1471 - 1500"},"PeriodicalIF":4.5,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Joseph Farrington, Wai Keong Wong, Kezhi Li, Martin Utley
{"title":"Going faster to see further: graphics processing unit-accelerated value iteration and simulation for perishable inventory control using JAX","authors":"Joseph Farrington, Wai Keong Wong, Kezhi Li, Martin Utley","doi":"10.1007/s10479-025-06551-6","DOIUrl":"10.1007/s10479-025-06551-6","url":null,"abstract":"<div><p>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 graphics processing units (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 interface, 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.</p></div>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"349 3","pages":"1609 - 1638"},"PeriodicalIF":4.5,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12350524/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144871103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"N-player and mean field games among fund managers considering excess logarithmic returns","authors":"Guohui Guan, Jiaqi Hu, Zongxia Liang","doi":"10.1007/s10479-025-06576-x","DOIUrl":"10.1007/s10479-025-06576-x","url":null,"abstract":"<div><p>This paper studies the competition among multiple fund managers with relative performance over the excess logarithmic return. Fund managers compete with each other and have expected utility or mean-variance criteria for excess logarithmic return. Each fund manager possesses a unique risky asset, and all fund managers can also invest in a public risk-free asset and a public risk asset. We construct both an <i>n</i>-player game and a mean field game (MFG) to address the competition problem under these two criteria. We explicitly define and rigorously solve the equilibrium and mean field equilibrium (MFE) for each criteria. In the four models, the excess logarithmic return as the evaluation criterion of the fund leads to the allocation fractions being constant. The introduction of the public risky asset yields different outcomes, with competition primarily affecting the investment in public assets, particularly evident in the MFG. We demonstrate that the MFE of the MFG represents the limit of the <i>n</i>-player game’s equilibrium as the competitive scale <i>n</i> approaches infinity. Finally, the sensitivity analyses of the equilibrium are given.</p></div>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"349 3","pages":"1663 - 1691"},"PeriodicalIF":4.5,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Francesca Maggioni, Fabrizio Dabbene, Georg Ch. Pflug
{"title":"Sampling methods for multi-stage robust optimization problems","authors":"Francesca Maggioni, Fabrizio Dabbene, Georg Ch. Pflug","doi":"10.1007/s10479-025-06545-4","DOIUrl":"10.1007/s10479-025-06545-4","url":null,"abstract":"<div><p>In this paper, we consider multi-stage robust optimization problems of the minimax type. We assume that the total uncertainty set is the cartesian product of stagewise compact uncertainty sets and approximate the given problem by a sampled subproblem. Instead of looking for the worst case among the infinite and typically uncountable set of uncertain parameters, we consider only the worst case among a randomly selected subset of parameters. By adopting such a strategy, two main questions arise: (1) Can we quantify the error committed by the random approximation, especially as a function of the sample size? (2) If the sample size tends to infinity, does the optimal value converge to the “true” optimal value? Both questions will be answered in this paper. An explicit bound on the probability of violation is given and chain of lower bounds on the original multi-stage robust optimization problem provided. Numerical results dealing with a multi-stage inventory management problem show that the proposed approach works well for problems with two or three time periods while for larger ones the number of required samples is prohibitively large for computational tractability. Despite this, we believe that our results can be useful for problems with such small number of time periods, and it sheds some light on the challenge for problems with more time periods.</p></div>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"347 3","pages":"1385 - 1423"},"PeriodicalIF":4.4,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10479-025-06545-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Małgorzata M. O’Reilly, Sebastian Krasnicki, James Montgomery, Mojtaba Heydar, Richard Turner, Pieter Van Dam, Peter Maree
{"title":"Markov decision process and approximate dynamic programming for a patient assignment scheduling problem","authors":"Małgorzata M. O’Reilly, Sebastian Krasnicki, James Montgomery, Mojtaba Heydar, Richard Turner, Pieter Van Dam, Peter Maree","doi":"10.1007/s10479-025-06553-4","DOIUrl":"10.1007/s10479-025-06553-4","url":null,"abstract":"<div><p>We study the patient assignment scheduling (PAS) problem in a random environment that arises in the management of patient flow in hospital systems, due to the stochastic nature of the arrivals as well as the length of stay (LoS) distribution. At the start of each time period, emergency patients in the waiting area of a hospital system need to be admitted to relevant wards. Decisions may involve allocation to less suitable wards, or transfers of the existing inpatients to accommodate higher priority cases when wards are at full capacity. However, the LoS for patients in non-primary wards may increase, potentially leading to long-term congestion. To assist with decision-making in this PAS problem, we construct a discrete-time Markov decision process over an infinite horizon, with multiple patient types and multiple wards. Since the instances of realistic size of this problem are not easy to solve, we develop numerical methods based on approximate dynamic programming. We demonstrate the application potential of our methodology under practical considerations with numerical examples, using parameters obtained from data at a tertiary referral hospital in Australia. We gain valuable insights, such as the number of patients in non-primary wards, the number of transferred patients, and the number of patients redirected to other facilities, under different policies that enhance the system’s performance. This approach allows for more realistic assumptions and can also help determine the appropriate size of wards for different patient types within the hospital system.</p></div>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"347 3","pages":"1493 - 1531"},"PeriodicalIF":4.4,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10479-025-06553-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mixed frequency data and portfolio selection: A novel approach integrating DEA with\u0000mixed frequency data sources","authors":"Weiqing Wang, Shuhao Liang, Liukai Wang, Yu Xiong","doi":"10.1007/s10479-025-06529-4","DOIUrl":"10.1007/s10479-025-06529-4","url":null,"abstract":"<div><p>This paper presents an innovative approach to portfolio optimization by integrating key elements of asset selection, risk management, and portfolio rebalancing. We first employ the Mixed Data Sampling (MIDAS) model to accurately measure Expected Shortfall (ES). Then, the Range Directional Measure-based Data Envelopment Analysis is considered to assess the portfolio efficiency, which integrates ES, asset returns, and inter-asset correlations for asset selection. Finally, utilizing the mixed frequency data from the metal futures market, we compared the portfolio performance of the Global Minimum ES strategy and the Market Neutral strategy, which reveals that our framework always outperforms traditional benchmarks in multiple aspects. Our findings indicate that, under the comprehensive risk management, a weekly rebalancing strategy is more effective compared to a daily rebalancing scheme. Furthermore, our study demonstrates that stringent asset selection, as opposed to loose selection or non-selection, significantly enhances the overall portfolio performance under the comprehensive risk management. Collectively, this research underscores the necessity of judicious asset selection and rebalance strategies in the modern portfolio management, and validates the practical utility of the portfolio efficiency with DEA and the mixed frequency data sources with MIDAS scheme.</p></div>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"347 3","pages":"1533 - 1565"},"PeriodicalIF":4.4,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}