Strict priority policies in a stochastic system with abandonment In the technical note “Stochastic scheduling with abandonment: Necessary and sufficient conditions for the optimality of a strict priority policy,” Chen, Gayon, and Lemaire consider a stochastic scheduling problem in which jobs abandon when their waiting time exceeds their lifetime. Such a problem arises, for example, in call centers or emergency systems. It is known that the optimal policy is a strict priority policy under some sets of conditions. The authors provide the first set of necessary and sufficient conditions for a problem with two types of jobs. They also provide conjectures to guide toward generalizations of the proposed conditions.
{"title":"Stochastic Scheduling with Abandonment: Necessary and Sufficient Conditions for the Optimality of a Strict Priority Policy","authors":"Gang Chen, J. Gayon, Pierre Lemaire","doi":"10.1287/opre.2022.2285","DOIUrl":"https://doi.org/10.1287/opre.2022.2285","url":null,"abstract":"Strict priority policies in a stochastic system with abandonment In the technical note “Stochastic scheduling with abandonment: Necessary and sufficient conditions for the optimality of a strict priority policy,” Chen, Gayon, and Lemaire consider a stochastic scheduling problem in which jobs abandon when their waiting time exceeds their lifetime. Such a problem arises, for example, in call centers or emergency systems. It is known that the optimal policy is a strict priority policy under some sets of conditions. The authors provide the first set of necessary and sufficient conditions for a problem with two types of jobs. They also provide conjectures to guide toward generalizations of the proposed conditions.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"39 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77155675","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}
Online retail has become more prominent around the world in the last decade. As a result, online retailers' website performance is increasingly important. Previous literature has extensively studied customer sensitivity to service speed and wait times in offline services. In “Need for Speed: The Impact of In-Process Delays on Customer Behavior in Online Retail,” Gallino, Karacaoglu, and Moreno extend this literature to online retail. They study the impact of delays in online retail on customer behavior. They estimate sizable negative effects of website slowdowns on online sales and conversion rates. Moreover, they explore how customer sensitivity to online delays varies throughout customers' shopping journeys. They find that the impact of waiting times varies along the different stages of the shopping journey, with customers becoming more sensitive to slowdowns at the checkout stage. Their findings have implications for website design decisions. This research is especially relevant in the current regulatory environment with ongoing policy debates about net neutrality.
{"title":"Need for Speed: The Impact of In-Process Delays on Customer Behavior in Online Retail","authors":"Santiago Gallino, Nil Karacaoglu, Antonio Moreno","doi":"10.1287/opre.2022.2262","DOIUrl":"https://doi.org/10.1287/opre.2022.2262","url":null,"abstract":"Online retail has become more prominent around the world in the last decade. As a result, online retailers' website performance is increasingly important. Previous literature has extensively studied customer sensitivity to service speed and wait times in offline services. In “Need for Speed: The Impact of In-Process Delays on Customer Behavior in Online Retail,” Gallino, Karacaoglu, and Moreno extend this literature to online retail. They study the impact of delays in online retail on customer behavior. They estimate sizable negative effects of website slowdowns on online sales and conversion rates. Moreover, they explore how customer sensitivity to online delays varies throughout customers' shopping journeys. They find that the impact of waiting times varies along the different stages of the shopping journey, with customers becoming more sensitive to slowdowns at the checkout stage. Their findings have implications for website design decisions. This research is especially relevant in the current regulatory environment with ongoing policy debates about net neutrality.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"16 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89017548","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}
When optimizing electric power system operational decisions, it is of great importance to prevent potential failures in both the system operation and the optimization algorithm. In “An Alternating Direction Method of Multipliers-Based Distributed Optimization Method for Solving Security-Constrained Alternating Current Optimal Power Flow,” Gholami, Sun, Zhang, and Sun propose a novel two-level algorithm that (1) effectively prevents power system operational failures through consideration of impactful contingencies and (2) guarantees convergence when parallelized on a computing cluster with multiple nodes. Extensive numerical experiments suggest that the proposed algorithm is able to provide high-quality feasible solutions under the time limit of 10–45 minutes for various synthetic and industrial networks with up to 30,000 buses and 22,000 contingencies, comparable with the size of the U.S. power grid.
{"title":"An Alternating Direction Method of Multipliers-Based Distributed Optimization Method for Solving Security-Constrained Alternating Current Optimal Power Flow","authors":"A. Gholami, Kaizhao Sun, Shixu Zhang, X. Sun","doi":"10.1287/opre.2023.2486","DOIUrl":"https://doi.org/10.1287/opre.2023.2486","url":null,"abstract":"When optimizing electric power system operational decisions, it is of great importance to prevent potential failures in both the system operation and the optimization algorithm. In “An Alternating Direction Method of Multipliers-Based Distributed Optimization Method for Solving Security-Constrained Alternating Current Optimal Power Flow,” Gholami, Sun, Zhang, and Sun propose a novel two-level algorithm that (1) effectively prevents power system operational failures through consideration of impactful contingencies and (2) guarantees convergence when parallelized on a computing cluster with multiple nodes. Extensive numerical experiments suggest that the proposed algorithm is able to provide high-quality feasible solutions under the time limit of 10–45 minutes for various synthetic and industrial networks with up to 30,000 buses and 22,000 contingencies, comparable with the size of the U.S. power grid.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"55 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78602983","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}
Optimization under uncertainty and risk is ubiquitous in business, engineering, and finance. Typically, we use observed or simulated data in our decision models, which aim to control risk, and result in composite risk functionals. The paper addresses the stability of the decision problems when the composite risk functionals are subjected to measure perturbations at multiple levels of potentially different nature. We analyze data-driven formulations with empirical or smoothing estimators such as kernels or wavelets applied to some or to all functions of the compositions and establish laws of large numbers and consistency of the optimal values and solutions. This is the first study to propose and analyze smoothing in data-driven composite optimization problems. It is shown that kernel-based and wavelet estimation provide less biased estimation of the risk compared with the empirical plug-in estimators under some assumptions.
{"title":"Stability and Sample-Based Approximations of Composite Stochastic Optimization Problems","authors":"D. Dentcheva, Yang Lin, S. Penev","doi":"10.1287/opre.2022.2308","DOIUrl":"https://doi.org/10.1287/opre.2022.2308","url":null,"abstract":"Optimization under uncertainty and risk is ubiquitous in business, engineering, and finance. Typically, we use observed or simulated data in our decision models, which aim to control risk, and result in composite risk functionals. The paper addresses the stability of the decision problems when the composite risk functionals are subjected to measure perturbations at multiple levels of potentially different nature. We analyze data-driven formulations with empirical or smoothing estimators such as kernels or wavelets applied to some or to all functions of the compositions and establish laws of large numbers and consistency of the optimal values and solutions. This is the first study to propose and analyze smoothing in data-driven composite optimization problems. It is shown that kernel-based and wavelet estimation provide less biased estimation of the risk compared with the empirical plug-in estimators under some assumptions.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"18 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84385147","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}
Linear programming is a very important class of problems, both algorithmically and combinatorially. Linear programming has many applications. From an algorithmic point-of-view, the simplex was proposed in the forties (soon after the war, and was motivated by military applications) and, although it has performed very well in practice, is known to run in exponential time in the worst-case. On the other hand, since the early seventies when the classes P and NP were defined, it was observed that linear programming is in NP∩ co-NP although no polynomial-time algorithm was known at that time. The first polynomial-time algorithm, the ellipsoid algorithm, was only discovered at the end of the seventies. Karmarkar’s algorithm in the mid-eighties lead to very active research in the area of interior-point methods for linear programming. We shall present one of the numerous variations of interior-point methods in class. From a combinatorial perspective, systems of linear inequalities were already studied at the end of the last century by Farkas and Minkovsky. Linear programming, and especially the notion of duality, is very important as a proof technique. We shall illustrate its power when discussing approximation algorithms. We shall also talk about network flow algorithms where linear programming plays a crucial role both algorithmically and combinatorially. For a more in-depth coverage of linear programming, we refer the reader to [1, 4, 7, 8, 5]. A linear program is the problem of optimizing a linear objective function in the decision variables, x1 . . . xn, subject to linear equality or inequality constraints on the xi’s. In standard form, it is expressed as:
{"title":"Linear Programming","authors":"M. Goemans","doi":"10.2307/3006986","DOIUrl":"https://doi.org/10.2307/3006986","url":null,"abstract":"Linear programming is a very important class of problems, both algorithmically and combinatorially. Linear programming has many applications. From an algorithmic point-of-view, the simplex was proposed in the forties (soon after the war, and was motivated by military applications) and, although it has performed very well in practice, is known to run in exponential time in the worst-case. On the other hand, since the early seventies when the classes P and NP were defined, it was observed that linear programming is in NP∩ co-NP although no polynomial-time algorithm was known at that time. The first polynomial-time algorithm, the ellipsoid algorithm, was only discovered at the end of the seventies. Karmarkar’s algorithm in the mid-eighties lead to very active research in the area of interior-point methods for linear programming. We shall present one of the numerous variations of interior-point methods in class. From a combinatorial perspective, systems of linear inequalities were already studied at the end of the last century by Farkas and Minkovsky. Linear programming, and especially the notion of duality, is very important as a proof technique. We shall illustrate its power when discussing approximation algorithms. We shall also talk about network flow algorithms where linear programming plays a crucial role both algorithmically and combinatorially. For a more in-depth coverage of linear programming, we refer the reader to [1, 4, 7, 8, 5]. A linear program is the problem of optimizing a linear objective function in the decision variables, x1 . . . xn, subject to linear equality or inequality constraints on the xi’s. In standard form, it is expressed as:","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"63 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72640747","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}
What is the relation between the notion of Nash equilibria and Pareto-optimal points? It is well known that Nash equilibria do not need to be Pareto optimal, and Pareto points do not need to be Nash equilibria. However, the paper “Characterizing and Computing the Set of Nash Equilibria via Vector Optimization” by Feinstein and Rudloff takes a deeper look at the relation. It is shown that it is possible to characterize the set of all Nash equilibria as the set of all Pareto-optimal solutions of a certain vector optimization problem. This is accomplished by carefully designing the objective function and the ordering cone of the vector optimization problem such that both notions coincide. This characterization holds for all noncooperative games (nonconvex, convex, linear). It opens up a new way of computing Nash equilibria, as one can now use techniques and algorithms from vector optimization to compute the set of all Nash equilibria, which is in contrast to the classical fixed-point iterations that find just a single Nash equilibrium.
{"title":"Characterizing and Computing the Set of Nash Equilibria via Vector Optimization","authors":"Zachary Feinstein, Birgit Rudloff","doi":"10.1287/opre.2023.2457","DOIUrl":"https://doi.org/10.1287/opre.2023.2457","url":null,"abstract":"What is the relation between the notion of Nash equilibria and Pareto-optimal points? It is well known that Nash equilibria do not need to be Pareto optimal, and Pareto points do not need to be Nash equilibria. However, the paper “Characterizing and Computing the Set of Nash Equilibria via Vector Optimization” by Feinstein and Rudloff takes a deeper look at the relation. It is shown that it is possible to characterize the set of all Nash equilibria as the set of all Pareto-optimal solutions of a certain vector optimization problem. This is accomplished by carefully designing the objective function and the ordering cone of the vector optimization problem such that both notions coincide. This characterization holds for all noncooperative games (nonconvex, convex, linear). It opens up a new way of computing Nash equilibria, as one can now use techniques and algorithms from vector optimization to compute the set of all Nash equilibria, which is in contrast to the classical fixed-point iterations that find just a single Nash equilibrium.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"52 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76727924","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}
Optimal Auction Duration in Financial Markets In the considered auction market, market makers fill the order book during a given time period while some other investors send market orders. The clearing price is set to maximize the exchanged volume at the clearing time according to the supply and demand of each market participant. The error made between this clearing price and the efficient price is derived as a function of the auction duration. We study the impact of the behavior of market takers on this error to minimize their transaction costs. We compute the optimal duration of the auctions for 77 stocks traded on Euronext and compare the quality of the price formation process under this optimal value to the case of a continuous limit order book. Continuous limit order books are usually found to be suboptimal. Order of magnitude of optimal auction durations is from 2–10 minutes.
{"title":"Optimal Auction Duration: A Price Formation Viewpoint","authors":"Jusselin Paul, M. Thibaut, Rosenbaum Mathieu","doi":"10.1287/opre.2021.2113","DOIUrl":"https://doi.org/10.1287/opre.2021.2113","url":null,"abstract":"Optimal Auction Duration in Financial Markets In the considered auction market, market makers fill the order book during a given time period while some other investors send market orders. The clearing price is set to maximize the exchanged volume at the clearing time according to the supply and demand of each market participant. The error made between this clearing price and the efficient price is derived as a function of the auction duration. We study the impact of the behavior of market takers on this error to minimize their transaction costs. We compute the optimal duration of the auctions for 77 stocks traded on Euronext and compare the quality of the price formation process under this optimal value to the case of a continuous limit order book. Continuous limit order books are usually found to be suboptimal. Order of magnitude of optimal auction durations is from 2–10 minutes.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"19 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74954459","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}
A fundamental NP-hard combinatorial-optimization in the area of statistical designs is the maximum-entropy sampling problem (MESP), which seeks to maximize Shannon's “differential entropy” over all subsets of a prespecified cardinality from a set of n Gaussian random variables. This problem has applications in many areas, such as the redesign of environmental-monitoring networks. Most algorithms for exact solution of MESP are branch-and-bound based, and one of the best upper bounds is based on Anstrecher's recent concave “linx relaxation” of differential entropy. A key paradigm for improving bounds is by “masking” the covariance of the random variables with a correlation matrix. The main result establishes that in the best case, the linx bound can be improved by an amount that is at least linear in n by masking. These and other recent results on the hot topic of MESP are leading to practical algorithms for exact solution of meaningful design problems in applied areas such as environmental statistics.
{"title":"Technical Note—Masking Anstreicher’s linx Bound for Improved Entropy Bounds","authors":"Zhongzhu Chen, M. Fampa, Jon Lee","doi":"10.1287/opre.2022.2324","DOIUrl":"https://doi.org/10.1287/opre.2022.2324","url":null,"abstract":"A fundamental NP-hard combinatorial-optimization in the area of statistical designs is the maximum-entropy sampling problem (MESP), which seeks to maximize Shannon's “differential entropy” over all subsets of a prespecified cardinality from a set of n Gaussian random variables. This problem has applications in many areas, such as the redesign of environmental-monitoring networks. Most algorithms for exact solution of MESP are branch-and-bound based, and one of the best upper bounds is based on Anstrecher's recent concave “linx relaxation” of differential entropy. A key paradigm for improving bounds is by “masking” the covariance of the random variables with a correlation matrix. The main result establishes that in the best case, the linx bound can be improved by an amount that is at least linear in n by masking. These and other recent results on the hot topic of MESP are leading to practical algorithms for exact solution of meaningful design problems in applied areas such as environmental statistics.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"12 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91059237","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}
The common setting of a queueing-game model consists of a stochastic stream of customers arriving at a queueing system one by one, each customer strategically chooses an action that may depend on information they receive regarding the system state. The aggregate customer decision profile gives rise to a system steady state, and, provided customers arrive at said steady state, if their decision is utility maximizing (ex ante), then this aggregate decision profile constitutes a Nash equilibrium. However, expressing the steady-state distribution for a given decision profile is very often a difficult task, and in such a case, an attempt to find a Nash equilibrium via direct analysis is futile. In the article “Stochastic Approximation of Symmetric Nash Equilibria in Queueing Games,” Ravner and Snitkovsky suggest a novel stochastic algorithm that learns the Nash equilibrium in a class of queueing games, based on a single adaptive simulation. The method is robust and is easy to implement, offering a practical solution to queueing-game models that classical queueing-analytic methods prove inadequate.
{"title":"Stochastic Approximation of Symmetric Nash Equilibria in Queueing Games","authors":"L. Ravner, Ran I. Snitkovsky","doi":"10.1287/opre.2021.0306","DOIUrl":"https://doi.org/10.1287/opre.2021.0306","url":null,"abstract":"The common setting of a queueing-game model consists of a stochastic stream of customers arriving at a queueing system one by one, each customer strategically chooses an action that may depend on information they receive regarding the system state. The aggregate customer decision profile gives rise to a system steady state, and, provided customers arrive at said steady state, if their decision is utility maximizing (ex ante), then this aggregate decision profile constitutes a Nash equilibrium. However, expressing the steady-state distribution for a given decision profile is very often a difficult task, and in such a case, an attempt to find a Nash equilibrium via direct analysis is futile. In the article “Stochastic Approximation of Symmetric Nash Equilibria in Queueing Games,” Ravner and Snitkovsky suggest a novel stochastic algorithm that learns the Nash equilibrium in a class of queueing games, based on a single adaptive simulation. The method is robust and is easy to implement, offering a practical solution to queueing-game models that classical queueing-analytic methods prove inadequate.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"7 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90354833","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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