Joint chance constraints(JCCs)can ensure the consistency and correlation of stochastic variables when participating in decision-making.Sample average approximation(SAA)is the most popular method for solving JCCs in un...Joint chance constraints(JCCs)can ensure the consistency and correlation of stochastic variables when participating in decision-making.Sample average approximation(SAA)is the most popular method for solving JCCs in unit commitment(UC)problems.However,the typical SAA requires large Monte Carlo(MC)samples to ensure the solution accuracy,which results in large-scale mixed-integer programming(MIP)problems.To address this problem,this paper presents the partial sample average approximation(PSAA)to deal with JCCs in UC problems in multi-area power systems with wind power.PSAA partitions the stochastic variables and historical dataset,and the historical dataset is then partitioned into non-sampled and sampled sets.When approximating the expectation of stochastic variables,PSAA replaces the big-M formulation with the cumulative distribution function of the non-sampled set,thus preventing binary variables from being introduced.Finally,PSAA can transform the chance constraints to deterministic constraints with only continuous variables,avoiding the large-scale MIP problem caused by SAA.Simulation results demonstrate that PSAA has significant advantages in solution accuracy and efficiency compared with other existing methods including traditional SAA,SAA with improved big-M,SAA with Latin hypercube sampling(LHS),and the multi-stage robust optimization methods.展开更多
This paper considers a class of stochastic variational inequality problems. As proposed by Jiang and Xu （2008）, by using the so-called regularized gap function, the authors formulate the problems as constrained opti...This paper considers a class of stochastic variational inequality problems. As proposed by Jiang and Xu （2008）, by using the so-called regularized gap function, the authors formulate the problems as constrained optimization problems and then propose a sample average approximation method for solving the problems. Under some moderate conditions, the authors investigate the limiting behavior of the optimal values and the optimal solutions of the approximation problems. Finally, some numerical results are reported to show efficiency of the proposed method.展开更多
This study aims to solve a typical long-term strategic decision problem on supply chain network design with consideration to uncertain demands. Existing methods for these problems are either deterministic or limited i...This study aims to solve a typical long-term strategic decision problem on supply chain network design with consideration to uncertain demands. Existing methods for these problems are either deterministic or limited in scale. We analyze the impact of uncertainty on demand based on actual large data from industrial companies.Deterministic equivalent model with nonanticipativity constraints, branch-and-fix coordination, sample average approximation(SAA) with Bayesian bootstrap, and Latin hypercube sampling were adopted to analyze stochastic demands. A computational study of supply chain network with front-ends in Europe and back-ends in Asia is presented to highlight the importance of stochastic factors in these problems and the efficiency of our proposed solution approach.展开更多
Recently,one of the main challenges facing the smart grid is insufficient computing resources and intermittent energy supply for various distributed components(such as monitoring systems for renewable energy power sta...Recently,one of the main challenges facing the smart grid is insufficient computing resources and intermittent energy supply for various distributed components(such as monitoring systems for renewable energy power stations).To solve the problem,we propose an energy harvesting based task scheduling and resource management framework to provide robust and low-cost edge computing services for smart grid.First,we formulate an energy consumption minimization problem with regard to task offloading,time switching,and resource allocation for mobile devices,which can be decoupled and transformed into a typical knapsack problem.Then,solutions are derived by two different algorithms.Furthermore,we deploy renewable energy and energy storage units at edge servers to tackle intermittency and instability problems.Finally,we design an energy management algorithm based on sampling average approximation for edge computing servers to derive the optimal charging/discharging strategies,number of energy storage units,and renewable energy utilization.The simulation results show the efficiency and superiority of our proposed framework.展开更多
This paper extends the quantitative stability results to a more general class of two-stage stochastic variational inequality problems(TSVIP).The existence of solutions to the TSVIP is discussed,and the quantitative re...This paper extends the quantitative stability results to a more general class of two-stage stochastic variational inequality problems(TSVIP).The existence of solutions to the TSVIP is discussed,and the quantitative relationship between the TSVIP and its distribution perturbed problem is derived.展开更多
Airlines adjust their flight schedules to satisfy more stringent airport capacity constraints caused by inclement weather or other unexpected disruptions.The problem will be more important and complicated if uncertain...Airlines adjust their flight schedules to satisfy more stringent airport capacity constraints caused by inclement weather or other unexpected disruptions.The problem will be more important and complicated if uncertain disruptions occur in hub airports.A two-stage stochastic programming model was established to deal with the realtime flight schedule recovery and passenger re-accommodation problem.The first-stage model represents the flight re-timing and re-fleeting decision in current time period when capacity information is deterministic,while the second-stage recourse model evaluates the passenger delay given the first-stage solutions when one future scenario is realized.Aiming at the large size of the problem and requirement for quick response,an algorithmic framework combining the sample average approximation and heuristic method was proposed.The computational results indicated of that the proposed method could obtain solutions with around 5% optimal gaps,and the computing time was linearly positive to the sample size.展开更多
In this paper, we study the p-order cone constraint stochastic variational inequality problem. We first take the sample average approximation method to deal with the expectation and gain an approximation problem, furt...In this paper, we study the p-order cone constraint stochastic variational inequality problem. We first take the sample average approximation method to deal with the expectation and gain an approximation problem, further the rationality is given. When the underlying function is Lipschitz continuous, we acquire a projection and contraction algorithm to solve the approximation problem. In the end, the method is applied to some numerical experiments and the effectiveness of the algorithm is verified.展开更多
The issues of uncertainty and frequency security become significantly serious in power systems with the high penetration of volatile inverter-based renewables(IBRs),which makes it necessary to consider the uncertainty...The issues of uncertainty and frequency security become significantly serious in power systems with the high penetration of volatile inverter-based renewables(IBRs),which makes it necessary to consider the uncertainty and frequency-related constraints in the economic dispatch(ED)programs.However,existing ED studies rarely proactively optimize the control parameters of inverter-based resources related to fast regulation(e.g.,virtual inertia and droop coefficients)in cooperation with other dispatchable resources to improve the system frequency security and dispatch reliability.This paper proposes a joint chance-constrained economic dispatch model that jointly optimizes the frequency-related inverter control,the system up/down reserves,and base-point power for the minimal total operational cost.In the proposed model,multiple dispatchable resources,including thermal units,dispatchable IBRs,and energy storage,are considered,and the(virtual)inertias,the regulation reserve allocations,and base-point power are coordinated.To ensure the system reliability,the joint chance-constraint formulation is also adopted.Additionally,since the traditional sample average approximation(SAA)method imposes a huge computational burden,a novel mix-SAA(MSAA)method is proposed to transform the original intractable model into a linear model that can be efficiently solved via commercial solvers.The case studies validate the satisfactory efficacy of the proposed ED model and demonstrate that the MSAA can save nearly 90%calculation time compared with the traditional SAA.展开更多
A stochastic programming model on the combination of aircraft landing problem and terminal traffic flow management under uncertainty is proposed in this work.In reality,various kinds of uncertainties,including adverse...A stochastic programming model on the combination of aircraft landing problem and terminal traffic flow management under uncertainty is proposed in this work.In reality,various kinds of uncertainties,including adverse weather events,occur more frequently and interrupt air traffic operations.Some of these uncertain events can appear and disappear in a short period.Furthermore,the occurrence of these events affects the flights significantly,delaying the flights or event harming the safety of passengers.Thus,it is essential to respond to these uncertainties to ensure the level of safety at runtime.Runway operation may cease due to strong wind shear,turbulence,microburst or other extreme weather scenarios,is limited due to the restricted airspace capacity,and we extend the problem covering the terminal airspace.The proposed model can significantly reduce the total delay time of aircraft in the computations.展开更多
Purpose-Human resources are one of the most important and effective elements for companies.In other words,employees are a competitive advantage.This issue is more vital in the supply chains and production systems,beca...Purpose-Human resources are one of the most important and effective elements for companies.In other words,employees are a competitive advantage.This issue is more vital in the supply chains and production systems,because of high need for manpower in the different specification.Therefore,manpower planning is an important,essential and complex task.The purpose of this paper is to present a manpower planning model for production departments.The authors consider workforce with individual and hierarchical skills with skill substitution in the planning.Assuming workforce demand as a factor of uncertainty,a two-stage stochastic model is proposed.Design/methodology/approach–To solve the proposed mixed-integer model in the real-world cases and large-scale problems,a Benders’decomposition algorithm is introduced.Some test instances are solved,with scenarios generated by Monte Carlo method.For some test instances,to find the number of suitable scenarios,the authors use the sample average approximation method and to generate scenarios,the authors use Latin hypercube sampling method.Findings–The results show a reasonable performance in terms of both quality and solution time.Finally,the paper concludes with some analysis of the results and suggestions for further research.Originality/value–Researchers have attracted to other uncertainty factors such as costs and products demand in the literature,and have little attention to workforce demand as an uncertainty factor.Furthermore,most of the time,researchers assume that there is no difference between the education level and skill,while they are not necessarily equivalent.Hence,this paper enters these elements into decision making.展开更多
基金supported by the National Natural Science Foundation of China(No.51977042)。
文摘Joint chance constraints(JCCs)can ensure the consistency and correlation of stochastic variables when participating in decision-making.Sample average approximation(SAA)is the most popular method for solving JCCs in unit commitment(UC)problems.However,the typical SAA requires large Monte Carlo(MC)samples to ensure the solution accuracy,which results in large-scale mixed-integer programming(MIP)problems.To address this problem,this paper presents the partial sample average approximation(PSAA)to deal with JCCs in UC problems in multi-area power systems with wind power.PSAA partitions the stochastic variables and historical dataset,and the historical dataset is then partitioned into non-sampled and sampled sets.When approximating the expectation of stochastic variables,PSAA replaces the big-M formulation with the cumulative distribution function of the non-sampled set,thus preventing binary variables from being introduced.Finally,PSAA can transform the chance constraints to deterministic constraints with only continuous variables,avoiding the large-scale MIP problem caused by SAA.Simulation results demonstrate that PSAA has significant advantages in solution accuracy and efficiency compared with other existing methods including traditional SAA,SAA with improved big-M,SAA with Latin hypercube sampling(LHS),and the multi-stage robust optimization methods.
基金This research is partly supported by the National Natural Science Foundation of China under Grant Nos. 71171027 and 11071028, the Fundamental Research Funds for the Central Universities under Grant No. DUT11SX11, and the Key Project of the National Natural Science Foundation of China under Grant No. 71031002.
文摘This paper considers a class of stochastic variational inequality problems. As proposed by Jiang and Xu （2008）, by using the so-called regularized gap function, the authors formulate the problems as constrained optimization problems and then propose a sample average approximation method for solving the problems. Under some moderate conditions, the authors investigate the limiting behavior of the optimal values and the optimal solutions of the approximation problems. Finally, some numerical results are reported to show efficiency of the proposed method.
文摘This study aims to solve a typical long-term strategic decision problem on supply chain network design with consideration to uncertain demands. Existing methods for these problems are either deterministic or limited in scale. We analyze the impact of uncertainty on demand based on actual large data from industrial companies.Deterministic equivalent model with nonanticipativity constraints, branch-and-fix coordination, sample average approximation(SAA) with Bayesian bootstrap, and Latin hypercube sampling were adopted to analyze stochastic demands. A computational study of supply chain network with front-ends in Europe and back-ends in Asia is presented to highlight the importance of stochastic factors in these problems and the efficiency of our proposed solution approach.
基金supported in part by the National Natural Science Foundation of China under Grant No.61473066in part by the Natural Science Foundation of Hebei Province under Grant No.F2021501020+2 种基金in part by the S&T Program of Qinhuangdao under Grant No.202401A195in part by the Science Research Project of Hebei Education Department under Grant No.QN2025008in part by the Innovation Capability Improvement Plan Project of Hebei Province under Grant No.22567637H
文摘Recently,one of the main challenges facing the smart grid is insufficient computing resources and intermittent energy supply for various distributed components(such as monitoring systems for renewable energy power stations).To solve the problem,we propose an energy harvesting based task scheduling and resource management framework to provide robust and low-cost edge computing services for smart grid.First,we formulate an energy consumption minimization problem with regard to task offloading,time switching,and resource allocation for mobile devices,which can be decoupled and transformed into a typical knapsack problem.Then,solutions are derived by two different algorithms.Furthermore,we deploy renewable energy and energy storage units at edge servers to tackle intermittency and instability problems.Finally,we design an energy management algorithm based on sampling average approximation for edge computing servers to derive the optimal charging/discharging strategies,number of energy storage units,and renewable energy utilization.The simulation results show the efficiency and superiority of our proposed framework.
基金Supported by the Guangxi Natural Science Foundation (2024GXNSFBA010345)the Innovation and Entrepreneurship Training Program of Guangxi Minzu University (S202310608001)。
文摘This paper extends the quantitative stability results to a more general class of two-stage stochastic variational inequality problems(TSVIP).The existence of solutions to the TSVIP is discussed,and the quantitative relationship between the TSVIP and its distribution perturbed problem is derived.
基金supported by the National Natural Science Foundation of China(Nos.61079014,71171111)the Funding of Outstanding Doctoral Dissertation in Nanjing University of Aeronautics and Astronautics(No.BCXJ1314)the Funding of Jiangsu Innovation Program for Graduate Education(No.CXZZ13_0174)
文摘Airlines adjust their flight schedules to satisfy more stringent airport capacity constraints caused by inclement weather or other unexpected disruptions.The problem will be more important and complicated if uncertain disruptions occur in hub airports.A two-stage stochastic programming model was established to deal with the realtime flight schedule recovery and passenger re-accommodation problem.The first-stage model represents the flight re-timing and re-fleeting decision in current time period when capacity information is deterministic,while the second-stage recourse model evaluates the passenger delay given the first-stage solutions when one future scenario is realized.Aiming at the large size of the problem and requirement for quick response,an algorithmic framework combining the sample average approximation and heuristic method was proposed.The computational results indicated of that the proposed method could obtain solutions with around 5% optimal gaps,and the computing time was linearly positive to the sample size.
文摘In this paper, we study the p-order cone constraint stochastic variational inequality problem. We first take the sample average approximation method to deal with the expectation and gain an approximation problem, further the rationality is given. When the underlying function is Lipschitz continuous, we acquire a projection and contraction algorithm to solve the approximation problem. In the end, the method is applied to some numerical experiments and the effectiveness of the algorithm is verified.
基金supported by the National Natural Science Foundation of China under Grant 52377107.
文摘The issues of uncertainty and frequency security become significantly serious in power systems with the high penetration of volatile inverter-based renewables(IBRs),which makes it necessary to consider the uncertainty and frequency-related constraints in the economic dispatch(ED)programs.However,existing ED studies rarely proactively optimize the control parameters of inverter-based resources related to fast regulation(e.g.,virtual inertia and droop coefficients)in cooperation with other dispatchable resources to improve the system frequency security and dispatch reliability.This paper proposes a joint chance-constrained economic dispatch model that jointly optimizes the frequency-related inverter control,the system up/down reserves,and base-point power for the minimal total operational cost.In the proposed model,multiple dispatchable resources,including thermal units,dispatchable IBRs,and energy storage,are considered,and the(virtual)inertias,the regulation reserve allocations,and base-point power are coordinated.To ensure the system reliability,the joint chance-constraint formulation is also adopted.Additionally,since the traditional sample average approximation(SAA)method imposes a huge computational burden,a novel mix-SAA(MSAA)method is proposed to transform the original intractable model into a linear model that can be efficiently solved via commercial solvers.The case studies validate the satisfactory efficacy of the proposed ED model and demonstrate that the MSAA can save nearly 90%calculation time compared with the traditional SAA.
基金supported by grants from the Research Grants Council,the Hong Kong Government(Grant No.PolyU25218321,PolyU15201423)Department of Aeronautical and Aviation Engineering,The Hong Kong Polytechnic University,Hong Kong SAR(RJTT,RJ85,RJJ9)the National Natural Science Foun-dation of China(Grant number:72301229).
文摘A stochastic programming model on the combination of aircraft landing problem and terminal traffic flow management under uncertainty is proposed in this work.In reality,various kinds of uncertainties,including adverse weather events,occur more frequently and interrupt air traffic operations.Some of these uncertain events can appear and disappear in a short period.Furthermore,the occurrence of these events affects the flights significantly,delaying the flights or event harming the safety of passengers.Thus,it is essential to respond to these uncertainties to ensure the level of safety at runtime.Runway operation may cease due to strong wind shear,turbulence,microburst or other extreme weather scenarios,is limited due to the restricted airspace capacity,and we extend the problem covering the terminal airspace.The proposed model can significantly reduce the total delay time of aircraft in the computations.
文摘Purpose-Human resources are one of the most important and effective elements for companies.In other words,employees are a competitive advantage.This issue is more vital in the supply chains and production systems,because of high need for manpower in the different specification.Therefore,manpower planning is an important,essential and complex task.The purpose of this paper is to present a manpower planning model for production departments.The authors consider workforce with individual and hierarchical skills with skill substitution in the planning.Assuming workforce demand as a factor of uncertainty,a two-stage stochastic model is proposed.Design/methodology/approach–To solve the proposed mixed-integer model in the real-world cases and large-scale problems,a Benders’decomposition algorithm is introduced.Some test instances are solved,with scenarios generated by Monte Carlo method.For some test instances,to find the number of suitable scenarios,the authors use the sample average approximation method and to generate scenarios,the authors use Latin hypercube sampling method.Findings–The results show a reasonable performance in terms of both quality and solution time.Finally,the paper concludes with some analysis of the results and suggestions for further research.Originality/value–Researchers have attracted to other uncertainty factors such as costs and products demand in the literature,and have little attention to workforce demand as an uncertainty factor.Furthermore,most of the time,researchers assume that there is no difference between the education level and skill,while they are not necessarily equivalent.Hence,this paper enters these elements into decision making.
