Scenario-based Stochastic Programming Research Articles

A robust fuzzy stochastic programming for sustainable procurement and logistics under hybrid uncertainty using big data

Today, in many organizations, the debate about the difference in core capabilities has become an important factor for market competition. Companies, based on the field of activity, decide to strengthen some of their capabilities, capacities, and expertise. Therefore, the focus of an organization on the strengths and efforts to develop its sustainability will lead to a competitive advantage in the marketplace. Due to changes in environmental factors, organizations have focused on carbon emissions in procurement and transportation that have the highest carbon footprint. This paper proposes a multi-objective, eco-sustainability model for a supply chain. The objectives are to minimize overall costs, maximize the efficiency of transportation vehicles and minimize information fraud in the process of information sharing within supply chain elements. Big data is considered in the amount of information exchanged between customers and other elements of the proposed supply chain; since there are frauds in information sharing then using big data 5Vs the model is adapted to control the cost of information loss leading to customer dissatisfaction. Since uncertainty is inevitable in the real environments, in this research hybrid uncertainty is considered. Because two sources of uncertainty are considered in most of the parameters, thus it is necessary to robustify the decision-making process. The model is a mixed integer nonlinear program including big data for an optimal sustainable procurement and transportation decision. A heuristic method is used to solve the big data problem that makes use of a robust fuzzy stochastic programming approach. The proposed model can prevent disturbances by using a scenario-based stochastic programming approach. An effective hybrid robust fuzzy stochastic method is also employed for controlling uncertainty in parameters and risk taking out of outbound decisions. To solve the multi-objective model, augmented ε-constraint method is utilized. The model performance is investigated in a comprehensive computational study.

Optimization of Empty Container Repositioning in Liner Shipping

Empty container repositioning (ECR), which arises due to imbalances in world trade, causes extra costs for the container liner carrier companies. Therefore, one of the main objectives of all liner carriers is to reduce ECR costs. Since ECR decisions involve too many parameters, constraints and variables, the plans based on real-life experiences cannot be effective and are very costly. For this purpose, this study introduces two mathematical programming models in order to make ECR plans faster, more efficient and at the lowest cost. The first mathematical programming model developed in this study is a mixed-integer linear programming (MILP) model and the second mathematical programming model is a scenario-based stochastic programming (SP) model, which minimize the total ECR costs. Unlike the deterministic model, the SP model takes into account the uncertainty in container demand. Both models have been tested with real data taken from a liner carrier company. The numerical results showed that, in a reasonable computational time, both models provide better results than real-life applications of the liner carrier company.

Risk averse energy management strategy in the presence of distributed energy resources considering distribution network reconfiguration: an information gap decision theory approach

Distributed energy resources (DERs) and distribution network reconfiguration have considerable effects on both the economic and operational performance of distribution networks. However, the uncertain nature of renewable energy sources (RESs), wind energy, for instance, can bring about serious challenges to the distribution system operators and distribution companies (DisCos). Therefore, a suitable methodology is a matter of the utmost importance to handle the uncertainty of RESs. In addition, DisCos can benefit from the utilisation of energy storage technologies to increase the penetration of RESs into the system. In this regard, this study proposes a risk-averse energy management strategy (RA-EMS) in the presence of DERs, while the impact of uncertainties of RESs on the optimal configuration of the network is investigated. The uncertainty of RESs is modelled through the information gap decision theory, which has significant advantages such as low computational burden, no need for probability density function, and exact results compared to other methodologies for uncertainty handling. The proposed RA-EMS model is implemented on the IEEE 33-bus distribution system, and its superiority over the scenario-based stochastic programming is demonstrated. The robust configuration of the system against RESs' uncertainty is obtained for different levels of uncertainty radius.

Risk and Uncertainty Analysis of Cooling Demand in Multi-Chiller System Using Downside Risk Constraints Method

The optimal performance of a multi-chiller system (MCS) is the crucial factor in managing the expected power consumption (EPC). Also, the uncertainty of cooling demand in the industrial or residential sector plays a crucial role, which should be modeled and managed. So, the stochastic risk-constrained performance of the optimal chiller loading is studied in an uncertain environment in this paper. Scenario-based stochastic programming is applied to the provided case study to model the cooling demand uncertainty (CDU), and the downside risk constraints (DRC) are implemented to model the associated risks. The risk-averse performance of the MCS is compared with the risk-neutral one to show the positive effects of the DRC. The proposed model is implemented under the DICOPT solver in GAMS software. The comparison results show that the expected power consumption of MCS is increased slowly, while the expected risk-in-power consumption (ERIPC) is decreased promptly.

A scenario-based stochastic programming approach for designing and planning wheat supply chain (A case study)

A scenario-based stochastic programming approach for designing and planning wheat supply chain (A case study)

Co-optimized trading of hybrid wind power plant with retired EV batteries in energy and reserve markets under uncertainties

To be competitive in the electricity markets, various technologies have been reported to increase profits of wind farm owners. Combining battery storage system, wind farms can be operated as conventional power plants which promotes the integration of wind power into the power grid. However, high expenses on batteries keep investors away. Retired EV batteries, fortunately, still have enough capacity to be reused and could be obtained at a low price. In this work, a two-stage optimization of a wind energy retired EV battery-storage system is proposed. The economic performance of the proposed system is examined concerning its participation in the frequency containment normal operation reserve (FCR-N) market and the spot market simultaneously. To account uncertainties in the wind farm output, various electricity market prices, and up/down regulation status, a scenario-based stochastic programming method is used. The sizing of the equipment is optimized on top of daily operations of the hybrid system which formulates a mixed-integer linear programming (MILP) problem. Scenarios are generated with the Monte Carlo simulation (MCS) and Roulette Wheel Mechanism (RWM), which are further reduced with the simultaneous backward method (SBM) to increase computational efficiency. A 21 MW wind farm is selected as a case study. The optimization results show that by integrating with a retired EV battery-storage system (RESS) and a bi-directional inverter, the wind farm can increase its profits significantly when forwarding bids in both of the aforementioned electricity markets.

A multi-objective and multi-scenario optimization model for operation control of CO2-flooding pipeline network system

Abstract Countries with high carbon emissions are actively exploring carbon capture, utilization and storage (CCUS) system. CCUS-based CO2 enhanced oil recovery (CO2-EOR) technology is favored for sustainable oilfield development and its contribution to mitigating global warming. In this paper, under the crafts constraints of injection stations and CO2-flooding wells, as well as the flow rate and pressure constraints along pipeline network, a multi-objective mixed integer nonlinear programming (MOMINLP) model is proposed for the optimal operation control of oilfield surface CO2-flooding pipeline network system. The minimum operating costs of pumps, the maximum CO2 injection volume and the minimum demand-injection volume deviation are set as objective functions. The uncertainty of demand CO2 injection volume caused by geological uncertainty is settled by scenario-based stochastic programming method. In addition, the piecewise linearization method and the augmented e-constraint method (AUGMECON) are introduced to deal with the nonlinear constraints and get the Pareto optimal solutions, respectively. Finally, the proposed model is successfully applied to a large-scale looped and branched CO2-flooding pipeline network system in Sinkiang, China with three cases for comparison to verify its applicability and superiority.

Two-stage hybrid stochastic/robust optimal coordination of distributed battery storage planning and flexible energy management in smart distribution network

Abstract This paper presents a two-stage formwork for the coordinated distributed battery energy storage systems (DBESSs) planning and the flexible energy management (FEM) in a smart distribution network (SDN) in the presence of electric vehicles’ (EVs’) parking lot and variable renewable energy sources (VRESs). In the first stage, from distribution system operator's (DSO's) viewpoint, the linear DBESSs planning problem minimizes the difference between summation of its investment, degradation and charging costs and its revenue due to injecting power into the network at the discharging mode, where this problem subjects to the linear SDN optimal power flow equations and VRES, DBESS and EVs’ parking lot constraints. Noted that the bounded uncertainty–based robust model (BURM) is used to model the uncertainty of load, charging/discharging price, VRES power and EV parameters according to the uncertainty levels. In addition, the FEM strategy is applied to the SDN to obtain the suitable flexibility, security and operational indices based on the second stage problem formulation. This strategy minimizes the difference between energy cost paid to the upstream network and flexibility benefit from DSO and flexibility operator (FO) viewpoints while it considers linear AC optimal power flow and renewable and flexible sources equations as problem constraints. Moreover, in order to achieve the robust flexibility capability of EVs’ parking lot in the SDN, the uncertainty of the FEM strategy is modelled in the proposed hybrid stochastic/robust optimization. Hence, the scenario-based stochastic programming (SBSP) is used for the uncertain parameters of load, energy price and VRES power, but, BURM models the EVs uncertainty. Finally, the proposed two-stage formwork is simulated on the 19-bus LV CIGRE benchmark grid using GAMS software to investigate the capability and efficiency of the model. According to numerical results, the proposed strategy calculates the optimal location and size for DBESSs depending on the energy price, consumers and EVs demand and VRESs size in the SDN, and thus, it can obtain flexible, secure and efficient operation indices in this network based on the lowest possible cost for the investment of DBESSs.

Robust Aircraft Maintenance Routing Problem Using a Turn-Around Time Reduction Approach

This article discusses the problem of how to efficiently build aircraft routes that better withstand potential disruptions, such as bad weather, technical problems, and passenger delays. This optimization problem is called robust aircraft maintenance routing problem (RAMRP). There are three approaches in the literature to deal with the RAMRP, such as the buffer time allocation approach (BT), the departure retiming approach (DR), and the scenario-based stochastic programming approach (SSP). Most of the previous approaches have some shortcomings in terms of fleet productivity and delay absorption. In addition, the majority of the RAMRP models overlook maintenance regulations, which result in the generation of infeasible routes. In this article, RAMRP is investigated with two main objectives. First, a novel robustness approach, called the turn-around time reduction approach (TRTR), that avoids the shortcomings of the existing approaches, is incorporated into RAMRP. The second objective is to develop an RAMRP model that simultaneously considers all maintenance regulations. The effectiveness of the proposed RAMRP model along with the TRTR is demonstrated using real data from a major Middle Eastern airline. The results reveal an improved performance of the TRTR over the BT by about 3.43%–12.20% and 2.5%–13.58%, while handling the expected propagated delay costs and fleet productivity, respectively. In addition, the results show that the TRTR is better than the SSP by about 2.07%–18.82%, while minimizing the propagated delay costs. Therefore, the TRTR has a great potential to be implemented in the actual industry.

A New Clustering Approach for Scenario Reduction in Multi-Stochastic Variable Programming

In the scenario-based stochastic programming problem, the solving complexity and computational burden increases as the number of scenarios increase, which involves necessary scenario reduction operations. For the scenario reduction problem with multiple random variables, we present a comprehensive optimal scenario reduction method based on a new optimization framework to eliminate redundant initial scenarios. In this framework, we propose the concept of correlation loss, to solve the problem of serious deviation of correlation in the reduced scenarios. The method uses a corrloss weight to balance the two objectives of the proposed scenario reduction framework. One is to minimize the correlation loss before and after scenario reduction, and the other is to maximize the similarity between the original scenario set and the reduced scenario set. In particular, it has strong universality. Numerical comparative experiments are carried out to evaluate the performance of the method. Application studies to microgrid economic operation optimization are also made to prove the effectiveness of the proposed method.

A Multi-objective Optimization Model for Robust Skip-Stop Scheduling with Earliness and Tardiness Penalties

Inefficient transport systems impose extra travel time for travelers, cause dissatisfaction and reduce service levels. In this study, the demand-oriented train scheduling problem is addressed using a robust skip-stop method under uncertain arrival rates during peak hours. This paper presents alternative mathematical models, including a two-stage scenario-based stochastic programming model and two robust optimization models, to minimize the total travel time of passengers and their waiting time at stations. The modeling framework accounts for the design and implementation of robust skip-stop schedules with earliness and tardiness penalties. As a case study, each of the developed models is implemented on line No. 5 of the Tehran metro, and the results are compared. To validate the skip-stop schedules, the values of the stochastic solution and the expected value of perfect information are calculated. In addition, a sensitivity analysis is conducted to test the performance of the model under different scenarios. According to the obtained results, having perfect information can reduce up to 16% of the value of the weighted objective function. The proposed skip-stop method has been shown to save about 5% in total travel time and 49% in weighted objective function, which is a summation of travel times and waiting times as against regular all-stop service. The value of stochastic solutions is about 21% of the value of the weighted objective function, which shows that the stochastic model demonstrates better performance than the deterministic model.

Scenario-based Co-Optimization of neighboring multi carrier smart buildings under demand response exchange

Abstract Nowadays energy management of smart buildings with environmentally oriented intentions has become as one of the most critical challenges in human societies. To address this issue, this paper proposes an unprecedented cost-emission based scheme for energy management of interconnected multi energy hubs (MEH) aimed at minimizing the procurement costs as well as reducing carbon emission. These two incompatible objectives are optimized by means of e -constraint technique and max–min fuzzy decision making to create an impartial compromise between cost saving and environmental obligations. The proposed MEH consists of three networked energy hubs with different distributed renewable and dispatch-able energy resources along with electrical/thermal energy storages and plug-in electric vehicles, which are connected to each other and exchange electricity and heat between themselves in such a way that minimize the operating costs of whole system. Meanwhile, an impressive price-based demand response program is included in the scheme to optimize the operating costs of MEH. The demands of MEH include electrical and thermal loads that have priced in time-of-use tariff to investigate the impact of energy carrier prices on the operation costs of MEH. Furthermore, an efficient scenario-based stochastic programming has been employed to tackle the uncertainty induced by renewable productions. Finally, the problem is solved by CPLEX solver under GAMS software and comparison numerical results are duly depicted to acknowledge sufficiency of the proposed approach. The results evidenced that the proposed MEH structure not only reduces the procurement costs of whole system, but also increases system independence from upstream network by exchanging power and heat between networked energy hubs.

Stochastic programming model for scheduling demand response aggregators considering uncertain market prices and demands

This paper proposes a stochastic decision making model for a demand response (DR) aggregator as an interface between the market and customers in a competitive environment. The DR aggregator participates in day-ahead (DA) energy and balancing markets as well as offers selling price to the customers to maximize its expected profit, considering the reaction of customers to the rivals’ offering prices. Moreover, the effect of load reduction due to implementing DR contracts on the decision making process of the DR aggregator is assessed. However, the main focus is on the operation of both shiftable and sheddable loads in price-based DR programs with detail. In order to investigate the behavior of different DR actions from the DR aggregator viewpoint, the restrictions imposed by the preferences of customers to the decisions made by the DR aggregators are modeled via a bi-level stochastic programming approach. The upper level represents the decisions made by the DR aggregator, while the lower level models the customers’ behavior. To deal with various uncertainties, a risk-constrained scenario-based stochastic programming framework is presented where the DR aggregator’s risk aversion is modeled using conditional value at risk (CVaR) method. Finally, a detailed illustrative case study based on the Nordic energy market data is provided and the effects of different DR actions and risk aversion factor on the profit of the aggregator are analyzed.

RETRACTED: Risk-based stochastic scheduling of energy hub system in the presence of heating network and thermal energy management

Energy hub as the future’s energy technology has discussed a new point of view in the energy consumption optimization field. The heating market as a new energy market, which is recently in some countries, presents a new venue for an energy hub operation. Heat demand side management is another control variable that makes the hub’s management more active and flexible. Providing heat from the heating market and utilization heat demand response features can influence the hub’s operational cost because of adding new degrees of freedom to the problem. In this paper, risk-based stochastic scheduling of energy hub is formulated via scenario-based stochastic programming by considering a wind turbine, electricity market, electrical and heat storage systems, electrical and heat demand response programs (DRP), and the heating market as the new found energy market. The downside risk constraints (DRC) are proposed to minimize the risk associated with uncertainties in order to obtain the risk-based scheduling of energy hub. Simulation results have been presented in different cases to show the impact of DRC implementation which the expected cost is increased while the risk-in-cost (RIC) is decreased. Finally, the effect of the DRP on the problem is investigated and the results show that the expected cost and RIC are decreased.

Day‐ahead electric vehicle aggregator bidding strategy using stochastic programming in an uncertain reserve market

Electric vehicle (EV) as dynamic energy storage systems could provide ancillary services to the grids. The aggregator could coordinate the charging/discharging of EV fleets to attend the electricity market to get profits. However, the aggregator profits are threatened by the uncertainty of the electricity market. In this study, an EV aggregator bidding strategy in the day-ahead market (DAM) is proposed, both reserve capacity and reserve deployment are considered. The novelty of this study is that: (i) The uncertainty of the reserve developments is addressed in terms of both time and amount. (ii) Scenario-based stochastic programming method is used to maximise the average aggregator profits based on one-year data. The proposed method, jointly considers the reserve capacity in the DAM and the reserve deployment requirements in the real-time market (RTM). (iii) The risk of the deployed reserve shortage is addressed by introducing a penalty factor in the model. (iv) An owner-aggregator contract is designed, which is used to mitigate the economic inconsistency issue between the EV owners and the aggregator. Results verify the performance of the proposed strategy, that is the average aggregator profits are guaranteed by maximising reserve deployment payments and mitigating the penalties in RTM and thus the reserve deployment requirements uncertainty is well managed.

Trading Small Prosumers Flexibility in the Energy and Tertiary Reserve Markets

This paper addresses the participation of an aggregator of small prosumers in the energy and tertiary reserve markets. A two-stage stochastic optimization model is proposed to exploit the load and generation flexibility of the prosumers. The aim is to define energy and tertiary reserve bids to minimize the net cost of the aggregator buying and selling energy in the day-ahead and real-time markets, as well as to maximize the revenue of selling tertiary reserve during the real-time stage. Scenario-based stochastic programming is used to deal with the uncertainties of photovoltaic power generation, electricity demand, outdoor temperature, end-users’ behavior, and preferences. A case study of 1000 small prosumers from MIBEL is used to compare the proposed strategy to two other strategies. The numerical results show that the proposed strategy reduces the bidding net cost of the aggregator by 48% when compared to an inflexible strategy typically used by retailers.

Dynamic Coordinated Active–Reactive Power Optimization for Active Distribution Network with Energy Storage Systems

This paper proposes a coordinated active–reactive power optimization model for an active distribution network with energy storage systems, where the active and reactive resources are handled simultaneously. The model aims to minimize the power losses, the operation cost, and the voltage deviation of the distribution network. In particular, the reactive power capabilities of distributed generators and energy storage systems are fully utilized to minimize power losses and improve voltage profiles. The uncertainties pertaining to the forecasted values of renewable energy sources are modelled by scenario-based stochastic programming. The second-order cone programming relaxation method is used to deal with the nonlinear power flow constraints and transform the original mixed integer nonlinear programming problem into a tractable mixed integer second-order cone programming model, thus the difficulty of problem solving is significantly reduced. The 33-bus and 69-bus distribution networks are used to demonstrate the effectiveness of the proposed approach. Simulation results show that the proposed coordinated optimization approach helps improve the economic operation for active distribution network while improving the system security significantly.

A modified particle swarm optimization algorithm for scheduling renewable generation in a micro-grid under load uncertainty

Renewable Energy Sources (RESs) have many benefits especially when integrated in micro-grids. In this paper, the particle swarm optimization (PSO) algorithm is modified for the optimal power sharing among several RESs such as wind (WT), photovoltaic (PV), and a combined heat and power (CHP) plants within a micro-grid framework. To evaluate the proposed method, first it is utilized to optimally schedule RESs in a micro-grid with the aim of cost minimization without uncertainty. Then, it is implemented under the load uncertainty and the random nature of demand is modeled by the scenario-based stochastic programming. Finally, the proposed algorithm is verified using some benchmark functions. The proposed method is compared with some different Meta-heuristic algorithms and it presents encouraging results in the RESs scheduling and solving benchmark functions.

Risk‐averse energy management system for isolated microgrids considering generation and demand uncertainties based on information gap decision theory

There are many technical challenges for integration of renewable energy sources (RESs) in the context of microgrids. Among these challenges, spinning reserve energy management should be accurately considered in the microgrid scheduling system for a better system operation. This study presents a methodology to model and analyse a novel scheme to integrate RESs, particularly photovoltaic (PV) systems, in diesel generation-based isolated microgrids. The proposed approach considers the uncertainties of PV power generation and demand, simultaneously, by solving a bi-level multi-objective optimisation problem using information gap decision theory (IGDT). The proposed energy management system is formulated considering spinning reserve constraints and the uncertainties associated with PV power generation and load, by solving a unit commitment problem. This method, a non-probabilistic approach, does not require the probability density function of uncertain parameters and provides a robust framework to better understand the potential savings due to the PV integration. In order to test and perform the analysis, realistic data from a 20 MW hybrid PV project is used as a case study. Furthermore, the proposed method is compared with probabilistic techniques, such as Monte Carlo simulations and scenario-based stochastic programming technique. The presented studies demonstrate applicability of the proposed model for real microgrids.

Integrated dynamic models for hedging international portfolio risks

We develop scenario-based stochastic programming models for hedging the risks of international portfolios using options. The models provide increasing level of integration in managing market and foreign exchange (FX) risks. We start with a single-stage model with currency options for selective hedging of FX risks, while market risk is addressed through diversification, we add stock options to hedge market risks, and add quantos and currency options to develop an integrated model, using an innovative method to price quantos on the scenario tree underpinning the stochastic program. The models are extended to multi-stage settings.Backtesting on market data over a 14-year period that includes the global financial crisis of 2008, we demonstrate the effectiveness of taking increasingly integrated views of risk management. Simultaneous hedging of market and FX risks using stock and currency options has the best ex post performance. The differences are economically significant, and statistical significance is established through rigorous hypothesis testing. The models are particularly effective during the crisis. Test results show that two-stage models outperform their single-stage counterparts, regardless of the hedging strategy.