In “Sequential Competitive Facility Location: Exact and Approximate Algorithms,” Qi et al. consider a competitive facility location problem (CFLP), where two firms sequentially open new facilities within their budgets and maximize their market shares of demand following a probabilistic choice model. They derive an equivalent, single-level mixed-integer nonlinear program (MINLP) reformulation of the bilevel MINLP and exploit the problem structures to derive valid inequalities based on submodularity and concave overestimation. They also develop an approximation algorithm with a constant approximation guarantee. They further study several extensions of CFLP that have general facility-opening costs, outside competitors, and diverse facility-planning decisions. Their approaches significantly accelerate the computation of CFLP on large-sized instances that have not been solved optimally or even heuristically by existing methods.
{"title":"Sequential Competitive Facility Location: Exact and Approximate Algorithms","authors":"Mingyao Qi, Ruiwei Jiang, Siqian Shen","doi":"10.1287/opre.2022.2339","DOIUrl":"https://doi.org/10.1287/opre.2022.2339","url":null,"abstract":"In “Sequential Competitive Facility Location: Exact and Approximate Algorithms,” Qi et al. consider a competitive facility location problem (CFLP), where two firms sequentially open new facilities within their budgets and maximize their market shares of demand following a probabilistic choice model. They derive an equivalent, single-level mixed-integer nonlinear program (MINLP) reformulation of the bilevel MINLP and exploit the problem structures to derive valid inequalities based on submodularity and concave overestimation. They also develop an approximation algorithm with a constant approximation guarantee. They further study several extensions of CFLP that have general facility-opening costs, outside competitors, and diverse facility-planning decisions. Their approaches significantly accelerate the computation of CFLP on large-sized instances that have not been solved optimally or even heuristically by existing methods.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"9 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75386495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An assumption that is pervasive in revenue management and economics is that buyers are perfect optimizers. However, in practice, buyers may be limited by their computational capabilities or lack of information and may not be able to perfectly optimize their response to a selling mechanism. This has motivated the introduction of approximate incentive compatibility as a solution concept for practical mechanisms. In “Mechanism Design under Approximate Incentive Compatibility,” Balseiro, Besbes, and Castro study, for the first time, the problem of designing optimal selling mechanisms when buyers are imperfect optimizers. Their work characterizes structural properties of approximate incentive compatible mechanisms and establishes fundamental bounds on how much revenue can be garnered by moving from exact to approximate incentive constraints. Their work brings a new perspective to the theory of mechanism design by shedding light on a novel class of optimization problems, techniques, and challenges that emerge when relaxing incentive constraints.
{"title":"Mechanism Design Under Approximate Incentive Compatibility","authors":"S. Balseiro, Omar Besbes, Francisco Castro","doi":"10.1287/opre.2022.2359","DOIUrl":"https://doi.org/10.1287/opre.2022.2359","url":null,"abstract":"An assumption that is pervasive in revenue management and economics is that buyers are perfect optimizers. However, in practice, buyers may be limited by their computational capabilities or lack of information and may not be able to perfectly optimize their response to a selling mechanism. This has motivated the introduction of approximate incentive compatibility as a solution concept for practical mechanisms. In “Mechanism Design under Approximate Incentive Compatibility,” Balseiro, Besbes, and Castro study, for the first time, the problem of designing optimal selling mechanisms when buyers are imperfect optimizers. Their work characterizes structural properties of approximate incentive compatible mechanisms and establishes fundamental bounds on how much revenue can be garnered by moving from exact to approximate incentive constraints. Their work brings a new perspective to the theory of mechanism design by shedding light on a novel class of optimization problems, techniques, and challenges that emerge when relaxing incentive constraints.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"2020 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87832937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Kilian Schindler, Napat Rujeerapaiboon, D. Kuhn, W. Wiesemann
Multimarket Multireservoir Hydro Scheduling Peak/off-peak spreads on European electricity forward and spot markets are eroding due to the ongoing nuclear phaseout in Germany and the steady growth in photovoltaic capacity. The reduced profitability of peak/off-peak arbitrage forces hydropower producers to recover part of their original profitability on the reserve markets. In their paper titled “A Planner-Trader Decomposition for Multimarket Hydro Scheduling” Schindler, Rujeerapaiboon, Kuhn, and Wiesemann propose a bi-layer stochastic programming framework that jointly optimizes the trading strategies on the spot and reserve markets. The model faithfully accounts for uncertainty in electricity prices, water inflows, and reserve activations, and it ensures that the hydropower producers can fulfill their market commitments under any circumstances. The model is numerically challenging due to the various sources of uncertainty that are revealed at different time scales and that affect the problem's objective function and constraints, and the authors propose a new planner-trader decomposition and an information restriction for its solution. A case study based on real data from Austria reveals significant benefits of simultaneously participating in the spot and the reserve markets.
由于德国核电的逐步淘汰和光伏发电容量的稳步增长，欧洲电力远期和现货市场的高峰/非高峰价差正在下降。峰/非峰套利盈利能力的降低，迫使水电生产商在储备市场上恢复部分原有盈利能力。Schindler, Rujeerapaiboon, Kuhn, and Wiesemann在他们题为“多市场水电调度的计划者-交易者分解”的论文中提出了一个双层随机规划框架，该框架共同优化了现货市场和储备市场的交易策略。该模型忠实地考虑了电价、水流入和备用激活的不确定性，并确保水电生产商在任何情况下都能履行其市场承诺。由于在不同的时间尺度上揭示的各种不确定性来源会影响问题的目标函数和约束，该模型在数值上具有挑战性，作者提出了一种新的计划者-交易者分解和求解的信息限制。一项基于奥地利真实数据的案例研究揭示了同时参与现货和储备市场的显著好处。
{"title":"A Planner-Trader Decomposition for Multimarket Hydro Scheduling","authors":"Kilian Schindler, Napat Rujeerapaiboon, D. Kuhn, W. Wiesemann","doi":"10.1287/opre.2023.2456","DOIUrl":"https://doi.org/10.1287/opre.2023.2456","url":null,"abstract":"Multimarket Multireservoir Hydro Scheduling Peak/off-peak spreads on European electricity forward and spot markets are eroding due to the ongoing nuclear phaseout in Germany and the steady growth in photovoltaic capacity. The reduced profitability of peak/off-peak arbitrage forces hydropower producers to recover part of their original profitability on the reserve markets. In their paper titled “A Planner-Trader Decomposition for Multimarket Hydro Scheduling” Schindler, Rujeerapaiboon, Kuhn, and Wiesemann propose a bi-layer stochastic programming framework that jointly optimizes the trading strategies on the spot and reserve markets. The model faithfully accounts for uncertainty in electricity prices, water inflows, and reserve activations, and it ensures that the hydropower producers can fulfill their market commitments under any circumstances. The model is numerically challenging due to the various sources of uncertainty that are revealed at different time scales and that affect the problem's objective function and constraints, and the authors propose a new planner-trader decomposition and an information restriction for its solution. A case study based on real data from Austria reveals significant benefits of simultaneously participating in the spot and the reserve markets.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"3 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74934734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stochastic root-finding problems are fundamental in the fields of operations research and data science. However, when the root-finding problem involves rare events, crude Monte Carlo can be prohibitively inefficient. Importance sampling (IS) is a commonly used approach, but selecting a good IS parameter requires knowledge of the problem’s solution, which creates a circular challenge. In “Adaptive Importance Sampling for Efficient Stochastic Root Finding and Quantile Estimation,” He, Jiang, Lam, and Fu propose an adaptive IS approach to untie this circularity. The adaptive IS simultaneously estimates the root and the IS parameters, and can be embedded in sample average approximation–type algorithms and stochastic approximation–type algorithms. They provide theoretical analysis on strong consistency and asymptotic normality of the resulting estimators, and show the benefit of adaptivity from a worst-case perspective. They also provide specialized analyses on extreme quantile estimation under milder conditions.
{"title":"Adaptive Importance Sampling for Efficient Stochastic Root Finding and Quantile Estimation","authors":"Shengyi He, Guangxin Jiang, H. Lam, M. Fu","doi":"10.1287/opre.2023.2484","DOIUrl":"https://doi.org/10.1287/opre.2023.2484","url":null,"abstract":"Stochastic root-finding problems are fundamental in the fields of operations research and data science. However, when the root-finding problem involves rare events, crude Monte Carlo can be prohibitively inefficient. Importance sampling (IS) is a commonly used approach, but selecting a good IS parameter requires knowledge of the problem’s solution, which creates a circular challenge. In “Adaptive Importance Sampling for Efficient Stochastic Root Finding and Quantile Estimation,” He, Jiang, Lam, and Fu propose an adaptive IS approach to untie this circularity. The adaptive IS simultaneously estimates the root and the IS parameters, and can be embedded in sample average approximation–type algorithms and stochastic approximation–type algorithms. They provide theoretical analysis on strong consistency and asymptotic normality of the resulting estimators, and show the benefit of adaptivity from a worst-case perspective. They also provide specialized analyses on extreme quantile estimation under milder conditions.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"46 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80022123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper investigates a model-free algorithm of broad interest in reinforcement learning, namely, Q-learning. Whereas substantial progress had been made toward understanding the sample efficiency of Q-learning in recent years, it remained largely unclear whether Q-learning is sample-optimal and how to sharpen the sample complexity analysis of Q-learning. In this paper, we settle these questions: (1) When there is only a single action, we show that Q-learning (or, equivalently, TD learning) is provably minimax optimal. (2) When there are at least two actions, our theory unveils the strict suboptimality of Q-learning and rigorizes the negative impact of overestimation in Q-learning. Our theory accommodates both the synchronous case (i.e., the case in which independent samples are drawn) and the asynchronous case (i.e., the case in which one only has access to a single Markovian trajectory).
{"title":"Is Q-Learning Minimax Optimal? A Tight Sample Complexity Analysis","authors":"Gen Li, Ee, Changxiao Cai, Yuting Wei","doi":"10.1287/opre.2023.2450","DOIUrl":"https://doi.org/10.1287/opre.2023.2450","url":null,"abstract":"This paper investigates a model-free algorithm of broad interest in reinforcement learning, namely, Q-learning. Whereas substantial progress had been made toward understanding the sample efficiency of Q-learning in recent years, it remained largely unclear whether Q-learning is sample-optimal and how to sharpen the sample complexity analysis of Q-learning. In this paper, we settle these questions: (1) When there is only a single action, we show that Q-learning (or, equivalently, TD learning) is provably minimax optimal. (2) When there are at least two actions, our theory unveils the strict suboptimality of Q-learning and rigorizes the negative impact of overestimation in Q-learning. Our theory accommodates both the synchronous case (i.e., the case in which independent samples are drawn) and the asynchronous case (i.e., the case in which one only has access to a single Markovian trajectory).","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"99 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76595014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bounded Regret for LP-Based Revenue-Management Problems In “An Improved Analysis of LP-Based Control for Revenue Management,” Chen, Li, and Ye study a class of quantity-based network revenue-management problems. The authors consider a stochastic setting where all the orders are i.i.d. sampled and the customers are of finite type. They focus on the classic LP-based adaptive algorithm and consider regret as the performance measure. They found that when the underlying LP is nondegenerate, the algorithm achieves a problem-dependent regret upper bound that is independent of the horizon/number of time periods T; when the underlying LP is degenerate, the algorithm achieves a tight regret upper bound that scales on the order of T log(T) and matches the lower bound up to a logarithmic order.
{"title":"An Improved Analysis of LP-Based Control for Revenue Management","authors":"Guanting Chen, Xiaocheng Li, Y. Ye","doi":"10.1287/opre.2022.2358","DOIUrl":"https://doi.org/10.1287/opre.2022.2358","url":null,"abstract":"Bounded Regret for LP-Based Revenue-Management Problems In “An Improved Analysis of LP-Based Control for Revenue Management,” Chen, Li, and Ye study a class of quantity-based network revenue-management problems. The authors consider a stochastic setting where all the orders are i.i.d. sampled and the customers are of finite type. They focus on the classic LP-based adaptive algorithm and consider regret as the performance measure. They found that when the underlying LP is nondegenerate, the algorithm achieves a problem-dependent regret upper bound that is independent of the horizon/number of time periods T; when the underlying LP is degenerate, the algorithm achieves a tight regret upper bound that scales on the order of T log(T) and matches the lower bound up to a logarithmic order.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"106 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87833018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
F. Kılınç-Karzan, Simge Küçükyavuz, Dabeen Lee, Soroosh Shafieezadeh-Abadeh
A Unifying Framework for the Convexification of Mixed-Integer Conic Binary Sets The paper “Conic Mixed-Binary Sets: Convex Hull Characterizations and Applications,” by Fatma Kilinc-Karzan, Simge Kucukyavuz, Dabeen Lee, and Soroosh Shafieezadeh-Abadeh, develops a unifying framework for convexifying mixed-integer conic binary sets. Many applications in machine-learning and operations research give rise to integer programming models with nonlinear structures and binary variables. The paper develops general methods for generating strong valid inequalities that take into account multiple conic constraints at the same time. The authors demonstrate that their framework applies to conic quadratic programming with binary variables, fractional programming, best subset selection, distributionally robust optimization, and sparse approximation of positive semidefinite matrices.
{"title":"Conic Mixed-Binary Sets: Convex Hull Characterizations and Applications","authors":"F. Kılınç-Karzan, Simge Küçükyavuz, Dabeen Lee, Soroosh Shafieezadeh-Abadeh","doi":"10.1287/opre.2020.0827","DOIUrl":"https://doi.org/10.1287/opre.2020.0827","url":null,"abstract":"A Unifying Framework for the Convexification of Mixed-Integer Conic Binary Sets The paper “Conic Mixed-Binary Sets: Convex Hull Characterizations and Applications,” by Fatma Kilinc-Karzan, Simge Kucukyavuz, Dabeen Lee, and Soroosh Shafieezadeh-Abadeh, develops a unifying framework for convexifying mixed-integer conic binary sets. Many applications in machine-learning and operations research give rise to integer programming models with nonlinear structures and binary variables. The paper develops general methods for generating strong valid inequalities that take into account multiple conic constraints at the same time. The authors demonstrate that their framework applies to conic quadratic programming with binary variables, fractional programming, best subset selection, distributionally robust optimization, and sparse approximation of positive semidefinite matrices.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"67 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83849307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Contextual simulation optimization problems have attracted great attention in the healthcare, commercial, and financial fields because of the need for personalized decision making. Besides randomness in simulation outputs, larger solution space makes learning and optimization more challenging. In the current work, Li, Lam, and Peng use a Gaussian mixture model (GMM) as a basic technique to deal with this difficulty. To address the computational challenge in updating GMM-based Bayesian posterior, they present a computationally efficient approximation method that can reduce the computational complexity from an exponential rate to a linear rate with respect to the problem scale. For sample allocation decision making, they propose a dynamic sampling policy to efficiently utilize both global clustering information and local performance information. The proposed sampling policy is proved to be consistent, be implementable, and achieve the asymptotically optimal sampling ratio. Numerical experiments show that the proposed sampling policy significantly improves the efficiency in contextual simulation optimization.
{"title":"Efficient Learning for Clustering and Optimizing Context-Dependent Designs","authors":"Haidong Li, H. Lam, Yijie Peng","doi":"10.1287/opre.2022.2368","DOIUrl":"https://doi.org/10.1287/opre.2022.2368","url":null,"abstract":"Contextual simulation optimization problems have attracted great attention in the healthcare, commercial, and financial fields because of the need for personalized decision making. Besides randomness in simulation outputs, larger solution space makes learning and optimization more challenging. In the current work, Li, Lam, and Peng use a Gaussian mixture model (GMM) as a basic technique to deal with this difficulty. To address the computational challenge in updating GMM-based Bayesian posterior, they present a computationally efficient approximation method that can reduce the computational complexity from an exponential rate to a linear rate with respect to the problem scale. For sample allocation decision making, they propose a dynamic sampling policy to efficiently utilize both global clustering information and local performance information. The proposed sampling policy is proved to be consistent, be implementable, and achieve the asymptotically optimal sampling ratio. Numerical experiments show that the proposed sampling policy significantly improves the efficiency in contextual simulation optimization.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"24 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81636723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Much like higher-order Taylor expansions allow one to approximate functions to a higher degree of accuracy, we demonstrate that, by accounting for higher-order terms in the Taylor expansion of a Markov process generator, one can derive novel diffusion approximations that achieve a higher degree of accuracy compared with the classical ones used in the literature over the last 50 years.
{"title":"High-Order Steady-State Diffusion Approximations","authors":"Anton Braverman, Jim Dai, Xiao Fang","doi":"10.1287/opre.2022.2362","DOIUrl":"https://doi.org/10.1287/opre.2022.2362","url":null,"abstract":"Much like higher-order Taylor expansions allow one to approximate functions to a higher degree of accuracy, we demonstrate that, by accounting for higher-order terms in the Taylor expansion of a Markov process generator, one can derive novel diffusion approximations that achieve a higher degree of accuracy compared with the classical ones used in the literature over the last 50 years.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"6 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78421022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Radhakrishna Tumbalam Gooty, R. Agrawal, Mohit Tawarmalani
Separation of mixtures of chemicals, ubiquitous in chemical and petrochemical industries, by distillation is energy intensive. Nearly 3% of the overall energy is used for distillation in the United States. Improving the distillation process is crucial for making chemical industries more sustainable. However, designing distillation sequences is challenging because the choice set is vast, and the equations governing the physical process are highly nonconvex. Traditional design practices rely on heuristics and often result in suboptimal solutions. Tumbalam Gooty et al. present the first approach that reliably identifies the distillation sequence that requires the least energy for a given separation. By embedding convex hulls of substructures and adapting the reformulation-linearization technique to fractions of polynomials, they demonstrated that their approach outperforms the state-of-the-art. Their work will help the chemical industry reduce greenhouse gas emissions associated with distillation.
{"title":"Advances in MINLP to Identify Energy-Efficient Distillation Configurations","authors":"Radhakrishna Tumbalam Gooty, R. Agrawal, Mohit Tawarmalani","doi":"10.1287/opre.2022.2340","DOIUrl":"https://doi.org/10.1287/opre.2022.2340","url":null,"abstract":"Separation of mixtures of chemicals, ubiquitous in chemical and petrochemical industries, by distillation is energy intensive. Nearly 3% of the overall energy is used for distillation in the United States. Improving the distillation process is crucial for making chemical industries more sustainable. However, designing distillation sequences is challenging because the choice set is vast, and the equations governing the physical process are highly nonconvex. Traditional design practices rely on heuristics and often result in suboptimal solutions. Tumbalam Gooty et al. present the first approach that reliably identifies the distillation sequence that requires the least energy for a given separation. By embedding convex hulls of substructures and adapting the reformulation-linearization technique to fractions of polynomials, they demonstrated that their approach outperforms the state-of-the-art. Their work will help the chemical industry reduce greenhouse gas emissions associated with distillation.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"34 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74608275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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