Optimal Nonstationary Optimization Without Knowing Function Changes Nonstationary stochastic optimization plays a vital role in a number of computer science and operations research applications. It is known how to design and analyze algorithms that optimize a sequence of strongly convex/concave and smooth functions with access to only one-point noisy function values with the underlying function sequence subject to maximum magnitude of function changes. In recent work from Wang titled “Technical Note: On Adaptivity in Nonstationary Stochastic Optimization with Bandit Feedback,” an optimization algorithm is designed and analyzed without assuming the magnitude of function changes is known in advance. Optimality of the designed algorithm is demonstrated.
{"title":"Technical Note—On Adaptivity in Nonstationary Stochastic Optimization with Bandit Feedback","authors":"Yining Wang","doi":"10.1287/opre.2022.0576","DOIUrl":"https://doi.org/10.1287/opre.2022.0576","url":null,"abstract":"Optimal Nonstationary Optimization Without Knowing Function Changes Nonstationary stochastic optimization plays a vital role in a number of computer science and operations research applications. It is known how to design and analyze algorithms that optimize a sequence of strongly convex/concave and smooth functions with access to only one-point noisy function values with the underlying function sequence subject to maximum magnitude of function changes. In recent work from Wang titled “Technical Note: On Adaptivity in Nonstationary Stochastic Optimization with Bandit Feedback,” an optimization algorithm is designed and analyzed without assuming the magnitude of function changes is known in advance. Optimality of the designed algorithm is demonstrated.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"24 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78995857","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}
Call Center Staffing: On-Demand Is in Demand Traditional call centers face challenges in quickly adapting their service capacity to meet fluctuations in demand, even with short staffing periods. In their research article “Expanding Service Capabilities Through an On-Demand Workforce,” Sun and Liu propose a solution for call centers to improve service levels and reduce operating expenses. They develop a two-stage decision model that determines the optimal combination of permanent and on-demand staff, along with an optimal on-demand staffing and call scheduling policy that minimizes costs. By utilizing diffusion approximation, they derive approximate solutions for the second-stage problem. The optimal staffing rule employs switching boundaries to determine when to bring in or dismiss on-demand agents, while the scheduling rule employs a nested threshold rule that prioritizes customer urgency. Interestingly, the call scheduling rule exhibits an intriguing pattern arising from the interaction between on-demand staffing and call scheduling decisions. Their research findings highlight significant cost savings achievable through the implementation of an on-demand workforce.
{"title":"Expanding Service Capabilities Through an On-Demand Workforce","authors":"Xu Sun, Weiliang Liu","doi":"10.1287/opre.2021.0651","DOIUrl":"https://doi.org/10.1287/opre.2021.0651","url":null,"abstract":"Call Center Staffing: On-Demand Is in Demand Traditional call centers face challenges in quickly adapting their service capacity to meet fluctuations in demand, even with short staffing periods. In their research article “Expanding Service Capabilities Through an On-Demand Workforce,” Sun and Liu propose a solution for call centers to improve service levels and reduce operating expenses. They develop a two-stage decision model that determines the optimal combination of permanent and on-demand staff, along with an optimal on-demand staffing and call scheduling policy that minimizes costs. By utilizing diffusion approximation, they derive approximate solutions for the second-stage problem. The optimal staffing rule employs switching boundaries to determine when to bring in or dismiss on-demand agents, while the scheduling rule employs a nested threshold rule that prioritizes customer urgency. Interestingly, the call scheduling rule exhibits an intriguing pattern arising from the interaction between on-demand staffing and call scheduling decisions. Their research findings highlight significant cost savings achievable through the implementation of an on-demand workforce.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"17 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82148218","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 New Approach to Contract Design with Private Inventory Information In a typical decentralized supply chain, a downstream retailer privately observes its inventory level and has an informational advantage over the upstream supplier. In “A Stationary Infinite-Horizon Supply Contract Under Asymmetric Inventory Information” by Bensoussan, Sethi, and Wang, the authors study how to optimally design a stationary, truth-telling, long-term contract in such a setting. In contrast to the classic first order approach in literature, they formulate the contract design as an optimization over a functional space and develop a solution approach based on the calculus of variations. They further apply their necessary optimality condition to the class of batch-order contracts, which replenish a prespecified inventory quantity for a fixed payment in each period only when the retailer has zero inventory on hand.
{"title":"A Stationary Infinite-Horizon Supply Contract Under Asymmetric Inventory Information","authors":"A. Bensoussan, S. Sethi, Shouqiang Wang","doi":"10.1287/opre.2020.0495","DOIUrl":"https://doi.org/10.1287/opre.2020.0495","url":null,"abstract":"A New Approach to Contract Design with Private Inventory Information In a typical decentralized supply chain, a downstream retailer privately observes its inventory level and has an informational advantage over the upstream supplier. In “A Stationary Infinite-Horizon Supply Contract Under Asymmetric Inventory Information” by Bensoussan, Sethi, and Wang, the authors study how to optimally design a stationary, truth-telling, long-term contract in such a setting. In contrast to the classic first order approach in literature, they formulate the contract design as an optimization over a functional space and develop a solution approach based on the calculus of variations. They further apply their necessary optimality condition to the class of batch-order contracts, which replenish a prespecified inventory quantity for a fixed payment in each period only when the retailer has zero inventory on hand.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"4 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80319154","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}
Jonathan Eckstein, Jean-Paul Watson, David L. Woodruff
In “Projective Hedging Algorithms for Multistage Stochastic Programming, Supporting Distributed and Asynchronous Implementation,” Eckstein, Watson, and Woodruff derive a new class of decomposition methods for convex multistage stochastic programs defined on finite but potentially large scenario trees. These methods resemble Rockafellar and Wets’ now-classical progressive hedging (PH) method but are based on a flexible projective operator-splitting scheme instead of the standard alternating direction method of multipliers (ADMM). The new algorithms only need to reoptimize subproblems for a subset of the scenarios at each iteration, instead of all of them, and are also amenable to a form of asynchronous implementation, without the algorithm randomization or small step-size requirements usually imposed in such contexts. In the online appendix, the authors demonstrate significant computational gains over PH, applying hundreds or thousands of processor cores to problem instances with up to a million scenarios.
{"title":"Projective Hedging Algorithms for Multistage Stochastic Programming, Supporting Distributed and Asynchronous Implementation","authors":"Jonathan Eckstein, Jean-Paul Watson, David L. Woodruff","doi":"10.1287/opre.2022.0228","DOIUrl":"https://doi.org/10.1287/opre.2022.0228","url":null,"abstract":"In “Projective Hedging Algorithms for Multistage Stochastic Programming, Supporting Distributed and Asynchronous Implementation,” Eckstein, Watson, and Woodruff derive a new class of decomposition methods for convex multistage stochastic programs defined on finite but potentially large scenario trees. These methods resemble Rockafellar and Wets’ now-classical progressive hedging (PH) method but are based on a flexible projective operator-splitting scheme instead of the standard alternating direction method of multipliers (ADMM). The new algorithms only need to reoptimize subproblems for a subset of the scenarios at each iteration, instead of all of them, and are also amenable to a form of asynchronous implementation, without the algorithm randomization or small step-size requirements usually imposed in such contexts. In the online appendix, the authors demonstrate significant computational gains over PH, applying hundreds or thousands of processor cores to problem instances with up to a million scenarios.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"94 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79813521","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}
California Utility Firm Implements Innovative Model, Reducing Costs by 4% A California utility firm has successfully implemented a pioneering model to balance electricity demand and supply while minimizing costs. By utilizing direct load control contracts (DLCCs), the firm can reduce energy consumption during peak hours. Researchers developed an integer stochastic dynamic optimization problem that considers monthly and annual constraints, allowing for effective execution of DLCCs. Incorporating a “reduce-to-threshold” policy to flatten energy-consumption curves during high demand, the model was verified using real data from the California Independent System Operator. When implemented, the utility firm achieved an impressive cost reduction of approximately 4%. Sensitivity analysis was conducted to enhance customer experience and improve DLCC contract features. The success of this innovative model highlights the potential of DLCCs and advanced optimization techniques in the energy sector, offering a blueprint for other utility companies seeking to optimize grid stability and reduce costs.
{"title":"Flattening Energy-Consumption Curves by Monthly Constrained Direct Load Control Contracts","authors":"A. Fattahi, S. Ghodsi, S. Dasu, R. Ahmadi","doi":"10.1287/opre.2021.0638","DOIUrl":"https://doi.org/10.1287/opre.2021.0638","url":null,"abstract":"California Utility Firm Implements Innovative Model, Reducing Costs by 4% A California utility firm has successfully implemented a pioneering model to balance electricity demand and supply while minimizing costs. By utilizing direct load control contracts (DLCCs), the firm can reduce energy consumption during peak hours. Researchers developed an integer stochastic dynamic optimization problem that considers monthly and annual constraints, allowing for effective execution of DLCCs. Incorporating a “reduce-to-threshold” policy to flatten energy-consumption curves during high demand, the model was verified using real data from the California Independent System Operator. When implemented, the utility firm achieved an impressive cost reduction of approximately 4%. Sensitivity analysis was conducted to enhance customer experience and improve DLCC contract features. The success of this innovative model highlights the potential of DLCCs and advanced optimization techniques in the energy sector, offering a blueprint for other utility companies seeking to optimize grid stability and reduce costs.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"36 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89239430","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}
Solving realistic security-constrained optimal power flow problems In “A surrogate-based asynchronous decomposition technique for realistic security-constrained optimal power flow problems,” we propose a new algorithm for solving a classical problem in power grid operations: the security-constrained optimal power flow, considering its nonlinearities and realistic transitions between nominal and emergency post-contingency operations. Solving security-constrained optimal power flow problems accurately is a critical function, upon which depends the reliability, security, and efficiency of power systems as well as the correct functioning of other critical infrastructure dependent on electricity. The proposed algorithm was extensively tested against many state-of-the-art approaches using realistic and real instances in the ARPA-E Grid Optimization Competition Challenge 1, where it found the best-known solution for 58% of the instances, attained an average gap of less than 0.2%, and obtained the best overall scores, thereby winning all divisions of Challenge 1 with a very strong first place.
{"title":"A Surrogate-Based Asynchronous Decomposition Technique for Realistic Security-Constrained Optimal Power Flow Problems","authors":"C. Petra, I. Aravena","doi":"10.1287/opre.2022.0229","DOIUrl":"https://doi.org/10.1287/opre.2022.0229","url":null,"abstract":"Solving realistic security-constrained optimal power flow problems In “A surrogate-based asynchronous decomposition technique for realistic security-constrained optimal power flow problems,” we propose a new algorithm for solving a classical problem in power grid operations: the security-constrained optimal power flow, considering its nonlinearities and realistic transitions between nominal and emergency post-contingency operations. Solving security-constrained optimal power flow problems accurately is a critical function, upon which depends the reliability, security, and efficiency of power systems as well as the correct functioning of other critical infrastructure dependent on electricity. The proposed algorithm was extensively tested against many state-of-the-art approaches using realistic and real instances in the ARPA-E Grid Optimization Competition Challenge 1, where it found the best-known solution for 58% of the instances, attained an average gap of less than 0.2%, and obtained the best overall scores, thereby winning all divisions of Challenge 1 with a very strong first place.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"35 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85612412","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 major focus of the simulation literature is the study of optimal budget allocation. The goal is to divide a simulation budget between alternatives with unknown values in a manner that leads to efficient identification of the best alternative. Existing analytical techniques, based on large deviations theory, are limited to finite sets of alternatives, each of which is assigned a certain proportion of the budget. In “A New Rate-Optimal Sampling Allocation for Linear Belief Models,” Zhou and Ryzhov develop the first provably optimal budget allocation for a continuous problem where linear regression is used to model the value of a choice. The allocation is expressible in closed form and is simpler and easier to implement than analogous solutions for the discrete setting. This work bridges the emerging literature on contextual (regression-based) learning and the well-known statistical problem of optimal experimental design.
{"title":"Technical Note—A New Rate-Optimal Sampling Allocation for Linear Belief Models","authors":"Jiaqi Zhou, I. Ryzhov","doi":"10.1287/opre.2022.2337","DOIUrl":"https://doi.org/10.1287/opre.2022.2337","url":null,"abstract":"A major focus of the simulation literature is the study of optimal budget allocation. The goal is to divide a simulation budget between alternatives with unknown values in a manner that leads to efficient identification of the best alternative. Existing analytical techniques, based on large deviations theory, are limited to finite sets of alternatives, each of which is assigned a certain proportion of the budget. In “A New Rate-Optimal Sampling Allocation for Linear Belief Models,” Zhou and Ryzhov develop the first provably optimal budget allocation for a continuous problem where linear regression is used to model the value of a choice. The allocation is expressible in closed form and is simpler and easier to implement than analogous solutions for the discrete setting. This work bridges the emerging literature on contextual (regression-based) learning and the well-known statistical problem of optimal experimental design.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"19 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74186718","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 addresses decision making in multiple stages, where prior information is available and where consecutive and successive decisions are made. Risk measures assess the random outcome by taking various candidate probability measures into account. To justify decisions in multiple stages, it is essential to have conditional risk measures available, which respect the information, which was already revealed in the past. The paper addresses different variants of risk measures, discusses their properties in the specific context and their implications in multistage decision making. Various examples of risk measures on simple probability spaces with finite support illustrate the content. The Wasserstein and nested distance are involved to make decision making with numerous scenarios numerically tractalbe.
{"title":"Conditional Distributionally Robust Functionals","authors":"A. Shapiro, A. Pichler","doi":"10.1287/opre.2023.2470","DOIUrl":"https://doi.org/10.1287/opre.2023.2470","url":null,"abstract":"This paper addresses decision making in multiple stages, where prior information is available and where consecutive and successive decisions are made. Risk measures assess the random outcome by taking various candidate probability measures into account. To justify decisions in multiple stages, it is essential to have conditional risk measures available, which respect the information, which was already revealed in the past. The paper addresses different variants of risk measures, discusses their properties in the specific context and their implications in multistage decision making. Various examples of risk measures on simple probability spaces with finite support illustrate the content. The Wasserstein and nested distance are involved to make decision making with numerous scenarios numerically tractalbe.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"224 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86685745","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}
Optimizing State of Charge for Storage Resources Storage of generated energy has existed as a contributing resource within the power sector for more than a century in the case of pumped hydro storage. Even though most regional transmission organizations/independent system operators do not currently optimize state of charge (SOC) for storage, the SOC is an essential aspect of the operating characteristics of storage. This paper investigates the impact on computational performance of optimizing storage with explicit representation of SOC. To investigate the model, the paper considers two contexts, stand-alone and large-scale. Analysis of the stand-alone context helps to explain why the combination of features in the storage model results in a difficult problem. Numerical results for large-scale test cases verify that new tighter valid inequalities can improve the computation compared with the standard model in the literature.
{"title":"Optimization Formulations for Storage Devices with Disjoint Operating Modes","authors":"R. Baldick, Yonghong Chen, Bing Huang","doi":"10.1287/opre.2023.2482","DOIUrl":"https://doi.org/10.1287/opre.2023.2482","url":null,"abstract":"Optimizing State of Charge for Storage Resources Storage of generated energy has existed as a contributing resource within the power sector for more than a century in the case of pumped hydro storage. Even though most regional transmission organizations/independent system operators do not currently optimize state of charge (SOC) for storage, the SOC is an essential aspect of the operating characteristics of storage. This paper investigates the impact on computational performance of optimizing storage with explicit representation of SOC. To investigate the model, the paper considers two contexts, stand-alone and large-scale. Analysis of the stand-alone context helps to explain why the combination of features in the storage model results in a difficult problem. Numerical results for large-scale test cases verify that new tighter valid inequalities can improve the computation compared with the standard model in the literature.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"15 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88700229","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}
As well studied in the operations research literature, optimization of a mutual reserve system (e.g., federal reserves) and a nonmutual one such as regular inventory systems requires solving simultaneous systems of quasi-variational inequalities, of which analytical solutions in closed form remain unattainable and computational solutions are still intractable. Thus far, the studies of reserve optimization are of intra-nations (e.g., central bank reserves) as opposed to inter-nations (e.g., COVID vaccine reserves of the United Nations). In this paper, we advance a method of computational analytics for mutual reserve optimization, with an international perspective in response to the intensifying challenge on global medical reserves during the COVID pandemic. A solution algorithm is developed in the context of maritime mutual insurances (a long existent international mutual reserve system) and then tested through comprehensive numerical experiments.
{"title":"A Splitting Method for Band Control of Brownian Motion: With Application to Mutual Reserve Optimization","authors":"A. Bensoussan, John J. Liu, Jiguang Yuan","doi":"10.1287/opre.2011.0427","DOIUrl":"https://doi.org/10.1287/opre.2011.0427","url":null,"abstract":"As well studied in the operations research literature, optimization of a mutual reserve system (e.g., federal reserves) and a nonmutual one such as regular inventory systems requires solving simultaneous systems of quasi-variational inequalities, of which analytical solutions in closed form remain unattainable and computational solutions are still intractable. Thus far, the studies of reserve optimization are of intra-nations (e.g., central bank reserves) as opposed to inter-nations (e.g., COVID vaccine reserves of the United Nations). In this paper, we advance a method of computational analytics for mutual reserve optimization, with an international perspective in response to the intensifying challenge on global medical reserves during the COVID pandemic. A solution algorithm is developed in the context of maritime mutual insurances (a long existent international mutual reserve system) and then tested through comprehensive numerical experiments.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"35 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85625431","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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