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Showing papers on "Stochastic programming published in 2018"


Journal ArticleDOI
TL;DR: In this paper, the authors consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset and use the Wasserstein metric to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples.
Abstract: We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete) probability distributions centered at the uniform distribution on the training samples, and we seek decisions that perform best in view of the worst-case distribution within this Wasserstein ball. The state-of-the-art methods for solving the resulting distributionally robust optimization problems rely on global optimization techniques, which quickly become computationally excruciating. In this paper we demonstrate that, under mild assumptions, the distributionally robust optimization problems over Wasserstein balls can in fact be reformulated as finite convex programs—in many interesting cases even as tractable linear programs. Leveraging recent measure concentration results, we also show that their solutions enjoy powerful finite-sample performance guarantees. Our theoretical results are exemplified in mean-risk portfolio optimization as well as uncertainty quantification.

913 citations


Journal ArticleDOI
TL;DR: A stochastic dynamic programming framework for the optimal energy management of a smart home with plug-in electric vehicle (PEV) energy storage is proposed, to minimize electricity ratepayer cost, while satisfying home power demand and PEV charging requirements.
Abstract: This paper proposes a stochastic dynamic programming framework for the optimal energy management of a smart home with plug-in electric vehicle (PEV) energy storage. This paper is motivated by the challenges associated with intermittent renewable energy supplies and the local energy storage opportunity presented by vehicle electrification. This paper seeks to minimize electricity ratepayer cost, while satisfying home power demand and PEV charging requirements. First, various operating modes are defined, including vehicle-to-grid, vehicle-to-home, and grid-to-vehicle. Second, we use equivalent circuit PEV battery models and probabilistic models of trip time and trip length to formulate the PEV to smart home energy management stochastic optimization problem. Finally, based on time-varying electricity price and time-varying home power demand, we examine the performance of the three operating modes for typical weekdays.

239 citations


Journal ArticleDOI
TL;DR: In this article, a stochastic multi-objective linear programming problem is formulated to find the optimized operation strategies of the DER system to reduce the expected energy costs and CO2 emissions, while satisfying the time-varying user demand.

190 citations


Journal ArticleDOI
TL;DR: A modified and computationally efficient progressive hedging algorithm with scenario bundling is introduced for resilience-oriented design to protect distribution grids against high-impact but low-probability extreme weather events.
Abstract: This paper proposes a resilience-oriented design (ROD) technique to protect distribution grids against high-impact but low-probability extreme weather events. The problem is formulated as a two-stage stochastic mixed integer problem. The first stage is to make ROD decisions, i.e., hardening existing distribution lines and deploying ROD resources such as back-up distributed generators and automatic switches. The second stage evaluates the system operation cost during a realized extreme weather event and repair cost after the event. A novel modeling strategy is proposed to deal with the decision-dependent uncertainty of distribution line damage status, which is affected by the first-stage hardening decisions. As both stages have binary variables, a modified and computationally efficient progressive hedging algorithm with scenario bundling is introduced. The algorithm performance is evaluated by calculating lower bounds of solutions. The proposed model and algorithms are demonstrated on 34-bus and 123-bus test feeders.

168 citations


Journal ArticleDOI
TL;DR: A novel model to decide the joint expansion planning of distributed generation and the distribution network considering the impact of ESS and price-dependent DR programs is presented.
Abstract: The first part of this two-paper series describes the incorporation of demand response (DR) and energy storage systems (ESSs) in the joint distribution and generation expansion planning for isolated systems. The role of DR and ESS has recently attracted an increasing interest in power systems. However, previous models have not been completely adapted in order to treat DR and ESS on an equal footing. The model presented includes DR and ESS in the planning of insular distribution systems. Hence, this paper presents a novel model to decide the joint expansion planning of distributed generation and the distribution network considering the impact of ESS and price-dependent DR programs. The problem is formulated as a stochastic-programming-based model driven by the maximization of the net social benefit. The associated deterministic equivalent is formulated as a mixed-integer linear program suitable for commercially available software. The outcomes of the model are the location and size of new generation and storage units and the distribution assets to be installed, reinforced or replaced. In the second companion paper, an insular case study (La Graciosa, Canary Islands, Spain) is provided illustrating the effects of DR and ESS on social welfare.

162 citations


Journal ArticleDOI
TL;DR: In this article, a multi-stage stochastic programming model is proposed for the expansion coplanning of gas and power networks considering the uncertainties in net load demand, and non-anticipativity constraints are taken into account to guarantee the decisions should only depend on the information of realized uncertainties up to the present stage.
Abstract: A novel multi-stage stochastic programming model is proposed for the expansion coplanning of gas and power networks considering the uncertainties in net load demand. Meanwhile, the nonanticipativity constraints are taken into account to guarantee the decisions should only depend on the information of realized uncertainties up to the present stage. Compared with the traditional two-stage stochastic programming model, the proposed multi-stage stochastic programming model yields sequential investment decisions with the uncertainties revealed gradually over time, such that the investment decisions are capable of keeping future options open and can shift from “never be changed” decisions to a flexible “wait and see” decisions. The test on three systems shows the effectiveness of the proposed multi-stage stochastic programming model.

157 citations


Journal ArticleDOI
01 Oct 2018-Energy
TL;DR: Two-stage stochastic programming approach is used to minimize the operational cost in microgrid energy management and a scenario reduction method based on mixed-integer linear optimization is obtained.

149 citations


Journal ArticleDOI
TL;DR: In this article, a stochastic programming approach for increasing resiliency of a distribution system exposed to an approaching wildfire is proposed, where the uncertainties associated with solar radiation, wind speed, and wind direction are taken into account.
Abstract: Natural disasters can cause significant damage to power grids. During summer, in countries with high temperatures, distribution systems passing through forested areas are prone to wildfires. This paper proposes a stochastic programming approach for increasing resiliency of a distribution system exposed to an approaching wildfire. Dynamic line rating of the overhead lines is considered in order to model the impact of the wildfire on conductor temperature and flowing current. The uncertainties associated with solar radiation, wind speed, and wind direction that affect the progression of the wildfire and the production of stochastic distributed generators are taken into account. A scenario reduction algorithm is applied to reduce the number of scenarios in a tractable size and subsequently the computational burden. The proposed model is transformed to a mixed-integer problem with quadratic constraints, which provides effective solution to the operation of a distribution system against an approaching wildfire. A modified IEEE 33-bus distribution system is used to illustrate the applicability of the proposed approach.

144 citations


Journal ArticleDOI
TL;DR: A stochastic dynamic programming approach to optimally operate an energy storage system across a receding horizon and demonstrates that an optimally operated system returns a lifetime value which is 160% more, on average, than that of the same system operated using a set-point-based method today.
Abstract: Energy storage systems have the potential to deliver value in multiple ways, and these must be traded off against one another. An operational strategy that aims to maximize the returned value of such a system can often be significantly improved with the use of forecasting—of demand, generation, and pricing—but consideration of battery degradation is important too. This paper proposes a stochastic dynamic programming approach to optimally operate an energy storage system across a receding horizon. The method operates an energy storage asset to deliver maximal lifetime value, by using available forecasts and by applying a multi-factor battery degradation model that takes into account operational impacts on system degradation. Applying the method to a dataset of a residential Australian customer base demonstrates that an optimally operated system returns a lifetime value which is 160% more, on average, than that of the same system operated using a set-point-based method applied in many settings today.

142 citations


Journal ArticleDOI
TL;DR: A model for optimal DES design under uncertainty is presented and is formulated as a Two-stage Stochastic Mixed-Integer Linear Program that contrasts in terms of technology selection and energy consumption shares among fossil fuels, grid electricity and renewable energy.

139 citations


Journal ArticleDOI
TL;DR: The approach adopted in this paper applies not only to optimization, but also to generic decision problems where the solution is obtained according to a rule that is not necessarily the optimization of a cost function.
Abstract: The scenario approach is a general methodology for data-driven optimization that has attracted a great deal of attention in the past few years. It prescribes that one collects a record of previous cases (scenarios) from the same setup in which optimization is being conducted and makes a decision that attains optimality for the seen cases. Scenario optimization is by now very well understood for convex problems, where a theory exists that rigorously certifies the generalization properties of the solution, that is, the ability of the solution to perform well in connection to new situations. This theory supports the scenario methodology and justifies its use. This paper considers nonconvex problems. While other contributions in the nonconvex setup already exist, we here take a major departure from previous approaches. We suggest that the generalization level is evaluated only after the solution is found and its complexity in terms of the length of a support subsample (a notion precisely introduced in this paper) is assessed. As a consequence, the generalization level is stochastic and adjusted case by case to the available scenarios. This fact is key to obtain tight results. The approach adopted in this paper applies not only to optimization, but also to generic decision problems where the solution is obtained according to a rule that is not necessarily the optimization of a cost function. Accordingly, in our presentation we adopt a general stance of which optimization is just seen as a particular case.

Journal ArticleDOI
TL;DR: In this paper, a two-stage stochastic mixed integer linear program is developed to co-optimize the distribution system operation and repair crew routing for outage restoration after extreme weather events.
Abstract: This paper proposes a novel method to co-optimize the distribution system operation and repair crew routing for outage restoration after extreme weather events. A two-stage stochastic mixed integer linear program is developed. The first stage is to dispatch the repair crews to the damaged components. The second stage is distribution system restoration using distributed generators, and reconfiguration. We consider demand uncertainty in terms of a truncated normal forecast error distribution, and model the uncertainty of the repair time using a lognormal distribution. A new decomposition approach, combined with the progressive hedging algorithm, is developed for solving large-scale outage management problems in an effective and timely manner. The proposed method is validated on modified IEEE 34- and 8500-bus distribution test systems.

Journal ArticleDOI
TL;DR: In this paper, a multi-period multi-objective mixed integer linear programming (MILP) is proposed to design and plan a network of reverse logistics under uncertainty for recycling C&D wastes in which the objectives are represented as profit and social impact maximization and environmental effect minimization.

Journal ArticleDOI
01 Oct 2018
TL;DR: The results show that the proposed hybrid metaheuristic algorithms outperform the best existing techniques on the majority of case studies.
Abstract: Nowadays, operation managers usually need efficient supply chain networks including important design factors such as economic and social considerations The recent decade has seen a rapid development of controlling the uncertainty in supply chain configurations along with proposing novel solution approaches By investigating the related studies, this paper shows that most of the current studies consider the economic aspects and just a few works present the two-stage stochastic programming as well as social considerations to design a closed-loop supply chain network This motivated our attempts to consider economic and social aspects simultaneously by using the mentioned suppositions among the first studies Another main contribution of this paper is the hybridization and tuning of a number of recent algorithms to address the problem The results show that the proposed hybrid metaheuristic algorithms outperform the best existing techniques on the majority of case studies

Journal ArticleDOI
TL;DR: This paper provides an in-depth review of systematic techniques that address uncertainties for ESOMs: Monte Carlo analysis, stochastic programming, robust optimization, and modelling to generate alternatives to provide extra policy insights.

Journal ArticleDOI
TL;DR: In this paper, a multi-objective mathematical programming model for use in the design of a sustainable supply chain network under uncertain conditions is presented, aimed at maximizing social benefits while minimizing economic costs and environmental impacts.

Journal ArticleDOI
Chen Yuwei1, Qinglai Guo1, Hongbin Sun1, Zhengshuo Li1, Wenchuan Wu1, Li Zihao1 
TL;DR: This paper proposes a new distance-based distributionally robust unit commitment model via Kullback–Leibler (KL) divergence, considering volatile wind power generation, and proposes a two-level decomposition method and an iterative algorithm to address the RDB-DRUC model.
Abstract: This paper proposes a new distance-based distributionally robust unit commitment (DB-DRUC) model via Kullback–Leibler (KL) divergence, considering volatile wind power generation. The objective function of the DB-DRUC model is to minimize the expected cost under the worst case wind distributions restricted in an ambiguity set. The ambiguity set is a family of distributions within a fixed distance from a nominal distribution. The distance between two distributions is measured by KL divergence. The DB-DRUC model is a “min-max-min” programming model; thus, it is intractable to solve. Applying reformulation methods and stochastic programming technologies, we reformulate this “min-max-min” DB-DRUC model into a one-level model, referred to as the reformulated DB-DRUC (RDB-DRUC) model. Using the generalized Benders decomposition, we then propose a two-level decomposition method and an iterative algorithm to address the RDB-DRUC model. The iterative algorithm for the RDB-DRUC model guarantees global convergence within finite iterations. Case studies are carried out to demonstrate the effectiveness, global optimality, and finite convergence of a proposed solution strategy.

Journal ArticleDOI
TL;DR: Computational results on a real-life case study demonstrate the proposed optimization tools’ applicability as well as the effect of disruption risk and sustainability dimensions on biofuel SC planning.
Abstract: We focus on design and planning of a biofuel supply chain (SC) network from biomass to demand centers where biomass supply is stochastic and seasonal, and facilities’ capacity varies randomly because of possible disruptions. We propose a cost-efficient multi-stage stochastic program in which the greenhouse gas emissions are mitigated and the social impact of the SC is considered. A rolling horizon procedure is presented to implement and evaluate the stochastic model solution. Computational results on a real-life case study demonstrate the proposed optimization tools’ applicability as well as the effect of disruption risk and sustainability dimensions on biofuel SC planning.

Journal ArticleDOI
15 Jul 2018-Energy
TL;DR: A two-stage stochastic optimization problem is formulated for the short-term operation planning of microgrids with multiple-energy carrier networks to determine the scheduled energy and reserve capacity and the effectiveness of demand response programs to reduce the operation costs and improve the security measures is investigated.

Journal ArticleDOI
01 Oct 2018-Energy
TL;DR: Results indicate that the proposed energy management strategy can greatly improve the fuel economy and be employed in real-time when compared with the stochastic dynamic programming and conventional RL approaches.

Journal ArticleDOI
TL;DR: Results show that the DRX market participation can improve the VPP's energy management, and can be solved efficiently by the scenario-based optimization approach.
Abstract: This paper presents a mathematical model for the energy bidding problem of a virtual power plant (VPP) that participates in the regular electricity market and the intraday demand response exchange (DRX) market. Different system uncertainties due to the intermittent renewable energy sources, retail customers’ demand, and electricity prices are considered in the model. The DRX market enables a VPP to purchase demand response services, which can be treated as “virtual energy resources,” from several demand response providers to reduce the penalty cost on the deviation between the day-head bidding and the real-time dispatch. This could increase the expected profit and the renewable energy utilization of the VPP. The overall energy bidding problem is modeled as a three-stage stochastic program, which can be solved efficiently by the scenario-based optimization approach. Extensive numerical results show that the DRX market participation can improve the VPP's energy management.

Journal ArticleDOI
TL;DR: In this paper, the minimization of stochastic functionals that are compositions of a nonsmooth convex function and a smooth function was studied, where the convex functions are composed of a convex and a stochastically weakly convex functal.
Abstract: We consider minimization of stochastic functionals that are compositions of a (potentially) nonsmooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly convex funct...

Journal ArticleDOI
TL;DR: A novel data-driven stochastic robust optimization (DDSRO) framework is proposed for optimization under uncertainty leveraging labeled multi-class uncertainty data to solve the resulting multi-level optimization problem efficiently.

Journal ArticleDOI
TL;DR: A novel two-stage scenario-based mixed fuzzy-stochastic programming model for integrated relief pre-positioning and procurement planning based on a quantity flexibility (QF) contract under a mixture of uncertain data is proposed.
Abstract: Humanitarian organizations typically pre-position relief items in strategic locations whose optimum levels are affected by the amounts of pre-disaster contractual agreements and post-disaster procurements. To account for these interrelationships, this paper proposes a novel two-stage scenario-based mixed fuzzy-stochastic programming model for integrated relief pre-positioning and procurement planning based on a quantity flexibility (QF) contract under a mixture of uncertain data. An effective multi-step solution method is also devised to solve the problem in real-sized instances. Applicability of the proposed model is examined through a real case study. Finally, a number of sensitivity analyses are conducted to provide helpful managerial insights.

Journal ArticleDOI
TL;DR: In this paper, a new model based on mixed-integer linear programming is proposed to properly model and evaluate the resiliency of smart distribution systems, where the optimal formation of dynamic microgrids, their service areas, and the optimal management of different technologies such as energy storage (ES) units, demand side management programs and distributed generations (DGs) units are investigated.

Journal ArticleDOI
TL;DR: This study establishes a mathematical model for the optimisation of logistics processes in modular construction covering three tiers of operation: manufacturing, storage and assembly and shows that the model is effective and can serve as decision support to optimise modular construction logistics.

Journal ArticleDOI
TL;DR: In this article, a multi-objective mixed integer linear programming model for the design of an integrated blood supply chain network for disaster relief is proposed, and a hybrid framework based on the two-stage stochastic programming and possibilistic programming approaches is devised to deal with a mixture of random and epistemic uncertainties.
Abstract: This paper proposes a multi-objective mixed integer linear programming model for the design of an integrated blood supply chain network for disaster relief. The developed model accounts for all the special aspects of blood supply chains involving uncertain demand of blood products and their irregular supply, perishability of blood products and shortage avoidance. It also provides a trade-off analysis between the cost efficiency (via minimizing the total costs), responsiveness (through minimizing the maximum unsatisfied demand) and effectiveness of the designed network (by minimizing the time span between blood production in regional blood centers and consumption in demand zones so that their freshness is preserved). A hybrid framework based on the two-stage stochastic programming and possibilistic programming approaches is devised to deal with a mixture of random and epistemic uncertainties. Some numerical experiments are conducted to validate the proposed model and its solution approach. Also, a real case study is presented to demonstrate the practicality of the proposed model. Helpful managerial insights are also provided through conducting a number of sensitivity analyses.

Journal ArticleDOI
TL;DR: A chance-constrained two-stage mean-risk stochastic programming model, where the conditional value-at-risk (CVaR) is specified as the risk measure, and enforces a joint probabilistic constraint on the feasibility of the second-stage problem concerned with distributing the relief supplies to the affected areas in case of a disaster.
Abstract: We consider a stochastic pre-disaster relief network design problem, which mainly determines the capacities and locations of the response facilities and their inventory levels of the relief supplies in the presence of uncertainty in post-disaster demands and transportation network conditions. In contrast to the traditional humanitarian logistics literature, we develop a chance-constrained two-stage mean-risk stochastic programming model. This risk-averse model features a mean-risk objective, where the conditional value-at-risk (CVaR) is specified as the risk measure, and enforces a joint probabilistic constraint on the feasibility of the second-stage problem concerned with distributing the relief supplies to the affected areas in case of a disaster. To solve this computationally challenging stochastic optimization model, we employ an exact Benders decomposition-based branch-and-cut algorithm. We develop three variants of the proposed algorithm by using alternative representations of CVaR. We illustrate the application of our model and solution methods on a case study concerning the threat of hurricanes in the Southeastern part of the United States. An extensive computational study provides practical insights about the proposed modeling approach and demonstrates the computational effectiveness of the solution framework.

Journal ArticleDOI
15 Apr 2018-Energy
TL;DR: This paper proposes a methodology for optimal bidding for a flexibility aggregator participating in three sequential markets, formulate the decision models as multi-stage stochastic programs and generate scenarios for the possible realizations of prices.

Journal ArticleDOI
TL;DR: A two-stage chance-constrained stochastic programming model that captures the uncertainties due to feedstock seasonality in a bio-fuel supply chain network performance and uses the state of Mississippi as a testing ground to visualize and validate the modeling results.