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Showing papers on "Stochastic programming published in 2017"


Journal ArticleDOI
TL;DR: A comprehensive review of studies in the fields of SCND and reverse logistics network design under uncertainty and existing optimization techniques for dealing with uncertainty such as recourse-based stochastic programming, risk-averse stochastics, robust optimization, and fuzzy mathematical programming are explored.

442 citations


Journal ArticleDOI
TL;DR: In this article, the authors proposed a distributionally robust optimization model for solving unit commitment (UC) problems considering volatile wind power generation, where the uncertainty of wind power is captured by an ambiguity set that defines a family of renewable power distributions, and the expected total cost under the worst-case distribution is minimized.
Abstract: This paper proposes a distributionally robust optimization model for solving unit commitment (UC) problems considering volatile wind power generation. The uncertainty of wind power is captured by an ambiguity set that defines a family of wind power distributions, and the expected total cost under the worst-case distribution is minimized. Compared with stochastic programming, this method may have less dependence on the data of exact probability distributions. It should also outperform the conventional robust optimization methods because some distribution information can be incorporated into the ambiguity sets to generate less conservative results. In this paper, the UC model is formulated based on the typical two-stage framework, where the UC decisions are determined in a here-and-now manner, and the economic dispatch decisions are assumed to be wait-and-see , made after the observation of wind power outcomes. For computational tractability, the wait-and-see decisions are addressed by linear decision rule approximation, assuming that the economic dispatch decisions affinely depend on uncertain parameters as well as auxiliary random variables introduced to describe distributional characteristics of wind power generation. It is shown in case studies that this decision rule model tends to provide a tight approximation to the original two-stage problem, and the performance of UC solutions may be greatly improved by incorporating information on wind power distributions into the robust model.

277 citations


Journal ArticleDOI
01 May 2017-Energy
TL;DR: In this paper, a stochastic programming model is proposed to optimize the performance of a smart micro-grid in a short term to minimize operating costs and emissions with renewable sources.

223 citations


Journal ArticleDOI
TL;DR: It is shown that adding new source of heat energy for providing demand of consumers with market mechanism changes the optimal operation point of multi carrier energy system.

218 citations


Journal ArticleDOI
TL;DR: In this article, a multi-timescale coordinated stochastic voltage/var control method for high renewable-penetrated distribution networks is proposed, which utilizes multiple devices to counteract uncertain voltage fluctuation and deviation.
Abstract: This paper proposes a multi-timescale coordinated stochastic voltage/var control method for high renewable-penetrated distribution networks. It aims to utilize multiple devices to counteract uncertain voltage fluctuation and deviation. In the hourly timescale (first stage), capacitor banks and transformer tap changers are scheduled before stochastic renewable output and load variations are realized. In the 15-min timescale (second stage), inverters that interface the renewable energy resources provide var support to supplement the first-stage decision after uncertainty is observed. The coordination is model as a two-stage stochastic programming problem with scenario reduction. It is then converted to a deterministic mixed-integer quadratic programming equivalence model and solved by commercial solvers combined. Compared with existing methods, the proposed volt/var control can achieve lower expected energy loss and can sustain a secure voltage level under random load demand and renewable power injection. The proposed method is verified on the IEEE 33-bus distribution network and compared with existing practices.

210 citations


Journal ArticleDOI
TL;DR: In this paper, a stochastic bi-objective supply chain design model for the efficient (cost minimizing) and effective (delivery time minimizing) supply of blood in disasters is presented.

199 citations


Journal ArticleDOI
TL;DR: A two-stage stochastic programming model to design a green supply chain in a carbon trading environment is presented and it is found that the supply chain configuration can be highly sensitive to the probability distribution of the carbon credit price.
Abstract: This paper presents a two-stage stochastic programming model to design a green supply chain in a carbon trading environment. The model solves a discrete location problem and determines the optimal material flows and the number of carbon credits/allowances traded. The study contributes to the existing literature by incorporating uncertainty in carbon price and product demand. The proposed model is applied to a real world case study and the numerical results are carefully analyzed and interpreted. We find that the supply chain configuration can be highly sensitive to the probability distribution of the carbon credit price. More importantly, we observe that carbon price and budget availability for supply chain reconfiguration can both have a positive but nonlinear relationship with greening of the supply chain.

185 citations


Journal ArticleDOI
25 Jan 2017
TL;DR: In this article, the authors proposed to leverage day-ahead power market and time-of-use electricity, and uses stochastic programming to address the uncertainties in EV charging demand.
Abstract: Workplace electric vehicle (EV) charging is now supported by more and more companies to encourage EV adoption. In the meantime, renewable energies are becoming an important power source. To participate in the day-ahead power market, decisions have to be made before knowing the actual power demand. This paper addresses the challenges of energy scheduling in office buildings integrated with photovoltaic systems and workplace EV charging. It proposes to leverage day-ahead power market and time-of-use electricity, and uses stochastic programming to address the uncertainties in EV charging demand. Two computationally efficient control algorithms, stochastic programming and load forecasting for energy management with two stages (SPLET) and sample average approximation-based SPLET, are proposed. Both algorithms contain two stages: day-ahead scheduling and real-time operation. First, they try to find the amount of power to purchase from the day-ahead power market while leveraging the flexibility of the load. Then, the real-time demand is satisfied while incorporating the uncertainties realization. Case study based on real-world data shows the proposed two algorithms could provide 7.2% and 6.9% average cost reduction, respectively. Vehicle-to-building and stand-alone battery system can serve as countermeasures for the mismatch between the day-ahead scheduling and real-time demand to further reduce the operation cost.

172 citations


Journal ArticleDOI
TL;DR: In this paper, a two-stage stochastic programming model is proposed for defining optimal periodic review policies for red blood cells inventory management that focus on minimising operational costs, as well as blood shortage and wastage due to outdating, taking into account perishability and demand uncertainty.

161 citations


Journal ArticleDOI
01 Jan 2017-Energy
TL;DR: In this article, the problem of optimal scheduling problem of plug-in electric vehicle aggregators in electricity market considering the uncertainties of market prices, availability of vehicles and status of being called by the ISO in the reserve market is investigated.

157 citations


Journal ArticleDOI
TL;DR: This paper studies distributionally robust stochastic programming in a setting where there is a specified reference probability measure and the uncertainty set of probability measures consists of measures in some sense close to the reference measure.
Abstract: In this paper we study distributionally robust stochastic programming in a setting where there is a specified reference probability measure and the uncertainty set of probability measures consists of measures in some sense close to the reference measure. We discuss law invariance of the associated worst case functional and consider two basic constructions of such uncertainty sets. Finally we illustrate some implications of the property of law invariance.

Journal ArticleDOI
TL;DR: The stochastic MPC (SMPC) problem in the dual control paradigm is presented, where the control inputs to an uncertain system have a probing effect for active uncertainty learning and a directing effect for controlling the system dynamics.

Journal ArticleDOI
TL;DR: In this paper, a two-stage stochastic optimization problem suitable to solve strategic optimization problems of car-sharing systems that utilize electric cars is introduced and studied, and a time-dependent integer linear program and a heuristic algorithm for solving the considered optimization problem are developed and tested on real world instances from the city of Vienna, as well as on grid-graph-based instances.
Abstract: In this article, we introduce and study a two-stage stochastic optimization problem suitable to solve strategic optimization problems of car-sharing systems that utilize electric cars. By combining the individual advantages of car-sharing and electric vehicles, such electric car-sharing systems may help to overcome future challenges related to pollution, congestion, or shortage of fossil fuels. A time-dependent integer linear program and a heuristic algorithm for solving the considered optimization problem are developed and tested on real world instances from the city of Vienna, as well as on grid-graph-based instances. An analysis of the influence of different parameters on the overall performance and managerial insights are given. Results show that the developed exact approach is suitable for medium sized instances such as the ones obtained from the inner districts of Vienna. They also show that the heuristic can be used to tackle very-large-scale instances that cannot be approached successfully by the integer-programming-based method.

Proceedings Article
01 Mar 2017
TL;DR: The authors proposed an end-to-end approach for learning probabilistic machine learning models in a manner that directly captures the ultimate task-based objective for which they will be used, within the context of stochastic programming.
Abstract: With the increasing popularity of machine learning techniques, it has become common to see prediction algorithms operating within some larger process. However, the criteria by which we train these algorithms often differ from the ultimate criteria on which we evaluate them. This paper proposes an end-to-end approach for learning probabilistic machine learning models in a manner that directly captures the ultimate task-based objective for which they will be used, within the context of stochastic programming. We present three experimental evaluations of the proposed approach: a classical inventory stock problem, a real-world electrical grid scheduling task, and a real-world energy storage arbitrage task. We show that the proposed approach can outperform both traditional modeling and purely black-box policy optimization approaches in these applications.

Journal ArticleDOI
TL;DR: In this paper, the authors propose a novel approach for the offering strategy of a virtual power plant that participates in the day-ahead and the real-time energy markets, where the uncertainty in the wind-power production and in the market prices using confidence bounds and scenarios, respectively, allows them to formul-ate the strategic offering problem as a stochastic adaptive robust optimization model.
Abstract: This paper proposes a novel approach for the offering strategy of a virtual power plant that participates in the day-ahead and the real-time energy markets. The virtual power plant comprises a conventional power plant, a wind-power unit, a storage facility, and flexible demands, which participate in the day-ahead and the real-time markets as a single entity in order to optimize their energy resources. We model the uncertainty in the wind-power production and in the market prices using confidence bounds and scenarios, respectively, which allows us to formul-ate the strategic offering problem as a stochastic adaptive robust optimization model. Results of a case study are provided to show the applicability of the proposed approach.

Journal ArticleDOI
TL;DR: A risk-averse optimal bidding formulation for the resource aggregator at the demand side based on the conditional value-at-risk (VaR) theory is proposed, which outperforms the benchmark strategies in terms of hedging high regret risks, and results in computational efficiency and DA bidding costs that are comparable to the benchmarks.
Abstract: This paper first presents a generic model to characterize a variety of flexible demand-side resources (e.g., plug-in electric vehicles and distributed generation). Key sources of uncertainty affecting the modeling results are identified and are characterized via multiple stochastic scenarios. We then propose a risk-averse optimal bidding formulation for the resource aggregator at the demand side based on the conditional value-at-risk (VaR) theory. Specifically, this strategy seeks to minimize the expected regret value over a subset of worst-case scenarios whose collective probability is no more than a threshold value. Our approach ensures the robustness of the day-ahead (DA) bidding strategy while considering the uncertainties associated with the renewable generation, real-time price, and electricity demand. We carry out numerical simulations against three benchmark bidding strategies, including a VaR-based approach and a traditional scenario based stochastic programming approach. We find that the proposed strategy outperforms the benchmark strategies in terms of hedging high regret risks, and results in computational efficiency and DA bidding costs that are comparable to the benchmarks.

Journal ArticleDOI
TL;DR: In this paper, a robust model for unit commitment (UC) problem, minimizing the operating costs considering uncertainty of wind power generation, is proposed, where risk averse (RA) and opportunity seeker (OS) strategies are developed.

Journal ArticleDOI
TL;DR: A bilevel stochastic programming problem (BSPP) model of the decision-making of an energy hub manager is presented and conditional value at risk is used to reduce the unfavorable effects of the uncertainties.
Abstract: A bilevel stochastic programming problem (BSPP) model of the decision-making of an energy hub manager is presented. Hub managers seek ways to maximize their profit by selling electricity and heat. They have to make decisions about: 1) the level of involvement in forward contracts, electricity pool markets, and natural gas networks and 2) the electricity and heat offering prices to the clients. These decisions are made under uncertainty of pool prices, demands as well as the prices offered by rival hub managers. On the other hand, the clients try to minimize the total cost of energy procurement. This two-agent relationship is presented as a BSPP in which the hub manager is placed in the upper level and the clients in the lower one. The bilevel scheme is converted to its equivalent single-level scheme using the Karush–Kuhn–Tucker optimality conditions although there are two bilinear products related to electricity and heat. The heat bilinear product is replaced by a heat price-quota curve and the electricity bilinear product is linearized using the strong duality theorem. In addition, conditional value at risk is used to reduce the unfavorable effects of the uncertainties. The effectiveness of the proposed model is evaluated in various simulations of a realistic case study.

Journal ArticleDOI
TL;DR: In this paper, a general stochastic optimization and modeling framework for solving the wind integrated smart energy hub (SEH) scheduling problem was developed, where the electrical and thermal loads of the energy hub have been served in presence of demand response (DR) programs.

Journal ArticleDOI
TL;DR: In this article, the authors proposed a two-stage stochastic programming approach to incorporate the various possible scenarios for renewable energy generation and cost in the planning of microgrids to tackle uncertainty.

Journal ArticleDOI
TL;DR: A novel robust fuzzy stochastic programming approach is proposed that has significant advantages in terms of mean value and variability of the objective function and the performance of the proposed model is compared with that of other models in term of the mean cost and variability by simulation.

Journal ArticleDOI
TL;DR: In this article, a two-stage stochastic problem for energy resource scheduling is proposed to minimize the expected operational cost of the energy aggregator and is based on stochastically programming.

Journal ArticleDOI
TL;DR: In the proposed approach, optimal site, size, type, and time of distributed energy resources are determined along with optimal allocation of section switches to partitioning conventional distribution system into a number of interconnected MGs.
Abstract: This paper proposes a new stochastic multi-objective framework for optimal dynamic planning of interconnected microgrids (MGs) under uncertainty from economic, technical, reliability and environmental viewpoints. In the proposed approach, optimal site, size, type, and time of distributed energy resources are determined along with optimal allocation of section switches to partitioning conventional distribution system into a number of interconnected MGs. The uncertainties of the problem are considered using scenario modelling and backward scenario reduction technique is implemented to deal with computational burden. In addition, three different risk averse, risk neutral and risk seeker strategies are defined for distribution network operator. The proposed framework is considered as two unparalleled objective functions which the first objective minimizes the investment cost, operation and maintenance cost, power loss cost and pollutants emission cost and the second objective is defined to minimize energy not supplied in both connected and islanded modes of MGs. Finally, multi objective particle swarm optimization is applied to minimize the proposed bi-objective functions and subsequently fuzzy satisfying method is accomplished to select the best solution proportional to risk based strategies. Efficiency of the proposed framework is validated on 85-bus distribution system and obtained results are presented and discussed.

Journal ArticleDOI
TL;DR: In this article, a bilinear variant of the Benders decomposition method was proposed to solve the chance-constrained two-stage stochastic programming problem where the chance constraint is used to restrict the probability of load imbalance.
Abstract: In this paper, we study unit commitment (UC) problems considering the uncertainty of load and wind power generation. UC problem is formulated as a chance-constrained two-stage stochastic programming problem where the chance constraint is used to restrict the probability of load imbalance. In addition to the conventional mixed integer linear programming formulation using Big-M, we present the bilinear mixed integer formulation of chance constraint, and then derive its linear counterpart using the McCormick linearization method. Then, we develop a bilinear variant of the Benders decomposition method, which is an easy-to-implement algorithm, to solve the resulting large-scale linear counterpart. Our results on typical IEEE systems demonstrate that (i) the bilinear mixed integer programming formulation is stronger than the conventional one and (ii) the proposed Benders decomposition algorithm is generally an order of magnitude faster than using a professional solver to directly compute both linear and bilinear chance-constrained UC models.

Journal ArticleDOI
TL;DR: In this article, a stochastic accelerated mirror-prox (SAMP) method was proposed for solving a class of monotone variational inequalities (SVI), which is based on a multi-step acceleration scheme.
Abstract: We propose a novel stochastic method, namely the stochastic accelerated mirror-prox (SAMP) method, for solving a class of monotone stochastic variational inequalities (SVI). The main idea of the proposed algorithm is to incorporate a multi-step acceleration scheme into the stochastic mirror-prox method. The developed SAMP method computes weak solutions with the optimal iteration complexity for SVIs. In particular, if the operator in SVI consists of the stochastic gradient of a smooth function, the iteration complexity of the SAMP method can be accelerated in terms of their dependence on the Lipschitz constant of the smooth function. For SVIs with bounded feasible sets, the bound of the iteration complexity of the SAMP method depends on the diameter of the feasible set. For unbounded SVIs, we adopt the modified gap function introduced by Monteiro and Svaiter for solving monotone inclusion, and show that the iteration complexity of the SAMP method depends on the distance from the initial point to the set of strong solutions. It is worth noting that our study also significantly improves a few existing complexity results for solving deterministic variational inequality problems. We demonstrate the advantages of the SAMP method over some existing algorithms through our preliminary numerical experiments.

Journal ArticleDOI
TL;DR: Results show that the presented approach can be considered as an efficient tool for optimal energy exchange optimization of MGs.
Abstract: The inherent volatility and unpredictable nature of renewable generations and load demand pose considerable challenges for energy exchange optimization of microgrids (MG). To address these challenges, this paper proposes a new risk-based multi-objective energy exchange optimization for networked MGs from economic and reliability standpoints under load consumption and renewable power generation uncertainties. In so doing, three various risk-based strategies are distinguished by using conditional value at risk (CVaR) approach. The proposed model is specified as a two-distinct objective function. The first function minimizes the operation and maintenance costs, cost of power transaction between upstream network and MGs as well as power loss cost, whereas the second function minimizes the energy not supplied (ENS) value. Furthermore, the stochastic scenario-based approach is incorporated into the approach in order to handle the uncertainty. Also, Kantorovich distance scenario reduction method has been implemented to reduce the computational burden. Finally, non-dominated sorting genetic algorithm (NSGAII) is applied to minimize the objective functions simultaneously and the best solution is extracted by fuzzy satisfying method with respect to risk-based strategies. To indicate the performance of the proposed model, it is performed on the modified IEEE 33-bus distribution system and the obtained results show that the presented approach can be considered as an efficient tool for optimal energy exchange optimization of MGs.

Journal ArticleDOI
TL;DR: This paper addresses a multi-stage and multi-period supply chain network design problem in which multiple commodities should be produced through different subsequent levels of manufacturing processes, formulated as a two-stage stochastic program under stoChastic and highly time-variable demands.

Journal ArticleDOI
TL;DR: A compromise between the cost, and the equity of relief victims, is suggested in a stochastic linear mixed-integer programming model for integrated decisions in the preparedness and response stages in pre- and post-disaster operations.
Abstract: This paper proposes a stochastic linear mixed-integer programming model for integrated decisions in the preparedness and response stages in pre- and post-disaster operations, respectively. We develop a model for integrated decisions that considers three key areas of emergency logistics: facility and stock prepositioning, evacuation planning and relief vehicle planning. To develop a framework for effective relief operations, we consider not only a cost-based but also an equity-based solution approach in our multiple objectives model. Then a normalised weighted sum method is used to parameterise our multiple objective programming model. This paper suggests a compromise between the cost, and the equity of relief victims. The experiments also demonstrate how time restrictions and the availability of relief vehicles impact the two objective functions.

Journal ArticleDOI
TL;DR: A composite scenario tree is proposed that captures both types of uncertainty, and its unique structure is exploited to derive new theoretical properties that can drastically reduce the number of non-anticipativity constraints (NACs).

Journal ArticleDOI
TL;DR: Results show that the proposed approach allows the aggregator to reduce the charging costs in comparison with other charging strategies, and the solution obtained is robust in the sense that driving requirements of electric vehicle users are met.