Search

This paper addresses the problem of optimal Construction Supply Chain (CSC) design and integration in deterministic and stochastic environments by providing a family of models for the optimization of a dynamic, multi-product, multi-site contractor-led CSC. With the objective of minimizing the total CSC cost, optimal decisions are made on network design, production, inventory holding and transportation, while also considering discounts for bulk purchases, logistics centers, on-site shortages and an inventory-preparation phase. The models integrate the operations of temporal and project-based supply chains into a sustainable network with repetitive flows, large scope contracts and economies of scale to provide the main contractor with a versatile optimization framework which can account for different levels of uncertainty. The novelty of this paper lies in providing a flexible integrative optimization CSC tool that accounts for multiple CSC actors (suppliers and/or logistics centers), projects, products, time periods, operations, and different decision-making environments depending on the nature of the problem and the risk-attitude of the decision maker. This paper contributes to the fast-growing research field of stochastic CSC optimization showcasing stochastic transitions of a mixed-integer linear programming model to chance-constrained programming and two-stage programming and incorporating uncertainties with different types of probability distributions or scenarios, and even interdependent uncertainties—approaches that have not been explored extensively in the CSC context. The results reveal that the stochastic approaches sacrifice the minimum cost of deterministic solutions having average settings to obtain robust well-hedged solutions over the possible parameter variations and that the selection of a suitable method for modeling uncertainty is context-dependent. [ABSTRACT FROM AUTHOR]

To address uncertainty as well as transient stability constraints simultaneously in the preventive control of wind farm systems, a novel three-stage optimization strategy is established in this paper. In the first stage, the probabilistic multi-objective particle swarm optimization based on the point estimate method is employed to cope with the stochastic factors. The transient security region of the system is accurately ensured by the interior point method in the second stage. Finally, the verification of the final optimal objectives and satisfied constraints are enforced in the last stage. Furthermore, the proposed strategy is a general framework that can combine other optimization algorithms. The proposed methodology is tested on the modified WSCC 9-bus system and the New England 39-bus system. The results verify the feasibility of the method. [ABSTRACT FROM AUTHOR]

In order to promote the efficient and intelligent construction of container ports, we focus on the optimization of berth-and-quay-crane (QC) allocation in tidal terminal operations. This paper investigates the quay-crane-profile-(QC-profile)-based assignment problem, and considers the uncertainty in QC profiles regarding QC efficiency for the first time. A mixed-integer programming (MIP) model is established for a discrete berth allocation with a crane-assignment problem (BACAP), considering the tide time window. We aim to minimize the total time loss caused by anchorage and the delay of vessels. Leveraging the theory of uncertainty optimization, the proposed deterministic model is extended into a stochastic programming (SP) model and a distributionally robust optimization (DRO) model, via the consideration of the random QC efficiency. To solve the proposed models, a column generation (CG) algorithm is employed, utilizing the mathematical method and subproblem-solving approach. The numerical experiments with different instances demonstrate that the DRO model yields a smaller variation in the objective function values, and the effectiveness of the CG method. The experimental results verify the robustness of the constructed models, and the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Providing new models or designing sustainable networks in recent studies represents a growing trend. However, there is still a gap in the simultaneous modeling of the three dimensions of sustainability in the electronic medical device supply chain (SC). In this paper, a novel hybrid chance-constrained programming and cost function model is presented for a green and sustainable closed-loop medical ventilator SC network design. To bring the problem closer to reality, a wide range of parameters including all cost parameters, demands, the upper bound of the released c o 2 , and the minimum percentage of the units of product to be disposed and collected from a customer and to be dismantled and shipped from DCs are modeled as uncertain along with the normal probability distribution. The problem was first formulated into the framework of a bi-objective stochastic mixed-integer linear programming (MILP) model; then, it was reformulated into a tri-objective deterministic mixed-integer nonlinear programming (MINLP) one. In order to model the environmental sustainability dimension, in addition to handling the total greenhouse gas emissions, the total waste products were also controlled. The efficiency and applicability of the proposed model were tested in an Iranian medical ventilator production and distribution network. For sensitivity analyses, the effect of some critical parameters on the values of the objective functions was carefully examined. Finally, valuable managerial insights into the challenges of companies during the COVID-19 pandemic were presented. Numerical results showed that with the increase in the number of customers in the COVID-19 crisis, social responsibility could improve cost mean by up to 8%. [ABSTRACT FROM AUTHOR]

In this paper, we develop an exact reformulation and a deterministic approximation for distributionally robust joint chance-constrained programmings $ ({\rm DRCCPs}) $ (DRCCPs) with a general class of convex uncertain constraints under data-driven Wasserstein ambiguity sets. It is known that robust chance constraints can be conservatively approximated by worst-case conditional value-at-risk (CVaR) constraints. It is shown that the proposed worst-case CVaR approximation model can be reformulated as an optimization problem involving biconvex constraints for joint DRCCP. This approximation is essentially exact under certain conditions. We derive a convex relaxation of this approximation model by constructing new decision variables which allows us to eliminate biconvex terms. Specifically, when the constraint function is affine in both the decision variable and the uncertainty, the resulting approximation model is equivalent to a tractable mixed-integer convex reformulation for joint binary DRCCP. Numerical results illustrate the computational effectiveness and superiority of the proposed formulations. [ABSTRACT FROM AUTHOR]

Due to the high randomness and volatility of renewable energy sources such as wind energy, the traditional thermal unit commitment (UC) model is no longer applicable. In this paper, in order to reduce the possible negative effects of an inaccurate wind energy forecast, the chance-constrained programming (CCP) method is used to study the UC problem with uncertainty wind power generation, and chance constraints such as power balance and spinning reserve are satisfied with a predetermined probability. In order to effectively solve the CCP problem, first, we used the sample average approximation (SAA) method to transform the chance constraints into deterministic constraints and to obtain a mixed-integer quadratic programming (MIQP) model. Then, the quadratic terms were incorporated into the constraints by introducing some auxiliary variables, and some second-order cone constraints were formed by combining them with the output characteristics of thermal unit; therefore, a tighter mixed-integer second-order cone programming (MISOCP) formulation was obtained. Finally, we applied this method to some systems including 10 to 100 thermal units and 1 to 2 wind units, and we invoked MOSEK in MATLAB to solve the MISOCP formulation. The numerical results obtained within 24 h confirm that not only is the MISOCP formulation a successful reformulation that can achieve better suboptimal solutions, but it is also a suitable method for solving the large-scale uncertain UC problem. In addition, for systems of up to 40 units within 24 h that do not consider wind power and pollution emissions, the numerical results were compared with those of previously published methods, showing that the MISOCP formulation is very promising, given its excellent performance. [ABSTRACT FROM AUTHOR]

Process integration, which started its development in the early 1970s, is an emerging branch of study for conserving various resources. Process integration studies the interdependencies among various process units at the system level and the development and use of tools for holistically designing process networks with generic optimization of resources and sustainable development. The problems addressed in process integration are often referred to as resource conservation or source–sink allocation problems. Most of these problems are solved with precise input parameters. However, due to a wide range of known and unknown factors, these input parameters are uncertain in practical applications. To make the designed network more reliable, these uncertainties should be incorporated at the targeting stage of the problem. Over the years, researchers have used various approaches for managing resource conservation networks under uncertainty. This review examines the different mathematical optimization approaches adopted for handling uncertainties associated with the resource conservation networks along with their practical applications in recent years. The paper primarily examines the four most common approaches used to address uncertainties in process integration: sensitivity analysis, chance-constrained programming, fuzzy optimization, and interval programming. Recent advances in handling uncertainties within the framework of process integration, covering both mathematical programming and Pinch analysis, are also discussed. The review ends with a discussion on the significance and contributions of recent approaches. Some of the important future research directions are also identified to be addressed using process integration and Pinch analysis. [ABSTRACT FROM AUTHOR]

Heating, ventilation, and air-conditioning (HVAC) systems are ideal demand-side flexible resources to provide regulation services. However, finding the best hourly regulation capacity offers for HVAC systems in a power market ahead of time is challenging because they are affected by non-Gaussian uncertainties from regulation signals. Moreover, since HVAC systems need to frequently regulate their power according to regulation signals, numerous thermodynamic constraints are introduced, leading to a huge computational burden. This paper proposes a tractable chance-constrained model to address these challenges. It first develops a temporal compression approach, in which the extreme indoor temperatures in the operating hour are estimated and restricted in the comfortable range so that the numerous thermodynamic constraints can be compressed into only a few ones. Then, a novel convexification method is proposed to handle the non-Gaussian uncertainties. This method leverages the Gaussian mixture model to reformulate the chance constraints with non-Gaussian uncertainties on the left-hand side into deterministic non-convex forms. We further prove that these non-convex forms can be approximated by mixed-integer second-order cone constraints that can be efficiently solved by off-the-shelf solvers. The optimality gap because of this approximation is marginal under mild conditions. Numerical experiments are conducted to validate the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, an integer programming model is offered for capacitated multi-allocation median hub location problems applicable to both cooperative and competitive environments among airlines. We divided the hubs into six independent categories by comparing the parameters of ticket price, travel time, and service quality for both the follower and leader airlines. The degrees of importance for the parameters of time and cost were determined by a multivariate Lagrange interpolation method, which could be of significant help in allocating travelers to the follower airline hubs. Then, with regard to the seasonal demand of travelers, travel demand was considered as an uncertain parameter. To identify the deterministic equivalent forms for the considered categories of hub location models, the robust optimization method and the chance-constrained programming model were employed. Finally, the developed model was tested for a case study. The results indicated that the coalition of follower airlines could absorb nearly 2% of the leader airline travelers with relatively lower travel cost and time. [ABSTRACT FROM AUTHOR]

The U-shaped assembly lines help to have more flexibility than the straight assembly lines, where the operators can perform tasks in both sides of the line, the entrance and the exit sides. Having more than one operator in any station of the line can reduce the line length and thereby affects the number of produced products. This paper combines the U-shaped assembly line balancing problem with the multi-manned assembly line balancing problem in one problem. In addition, the processing times of the tasks are considered as stochastic, where they are represented as random variables with known means and variances. The problem is formulated as a mixed-integer linear programming and the cycle time constraints are formulated as chance-constraints. The proposed algorithm for solving the problem is a differential evolution algorithm. The parameter of the algorithm is optimized using experimental design and the computational results are done on 71 adapted problems selected from well-known benchmarks. [ABSTRACT FROM AUTHOR]

Chance-constrained economic dispatch (CCED) is widely used to cope with uncertainties brought by renewable energy sources. In CCED, security of power system is guaranteed by restricting risks under permitted level. As the penetration rate of renewable energy increases rapidly, the CCED model may be infeasible because of inadequate system reserve and/or transmission congestion under certain circumstances. Therefore, the curtailment of renewable energy is indispensable to guarantee security in some scenarios for power systems with high penetration of renewable energy. To address this crucial issue, this paper proposes a novel CCED model, where generation of conventional units and curtailment strategies of renewable energy are co-optimized to minimize total operational cost and restrict operational risks. An efficient solution method is developed to schedule generation and curtailment sequentially, in which tractable optimization models are formulated for each step. Numerical tests demonstrate that the proposed model can significantly reduce the probability of emergency control of curtailment compared with conventional CCED models. Furthermore, this solution method also outperforms scenario-based method with significantly improved computational efficiency and higher-quality solution. [ABSTRACT FROM AUTHOR]

Uncertain parameters and factors substantially impact the operational performances of combined cooling, heating, and power (CCHP) systems. This paper constructs a chance-constrained programming model for system design and energy dispatch management of a hybrid solar CCHP system under the uncertainties of solar energy and building loads. The uncertain scenarios with probability distributions are generated in the Latin hypercube sampling and clustering methods. The chance-constrained model transforms stochastic optimization into deterministic optimization based on these scenarios. Then, the multi-objective optimization model of CCHP system considering the performances of economic, energy, emission, and flexibility is established, and the modified ε -constraint method is employed to obtain Pareto solutions. A case study validates the proposed model. The capacities and operational strategies of components in the hybrid CCHP system are optimized, and the impacts of the confidence level of probability distributions of uncertain factors on the optimization results are discussed. The results indicate that the photovoltaic capacity in the hybrid CCHP system declines by 87.5% when the confidence level increases from 0.50 to 0.99. But other components' capacities are raised, and the gas turbine capacity as the key component rises by 10.49%. The energetic and environmental performances of the CCHP system rise with the confidence level, and the operation safety is improved. [ABSTRACT FROM AUTHOR]

With the increasing share of variable and limitedly predictable renewable energy in power systems worldwide, ensuring reserve capacity to maintain the balance of supply and demand becomes more important. On the other hand, the development of the virtual power plant model (VPP) allows renewable sources and energy storage to participate in reserve service. This paper addresses the optimal reserve bidding strategy problem of a VPP comprising of renewable energy resources (RESs), energy storage systems (ESSs), and several customers. The VPP participates in balance capacity (BC), day-ahead (DA), and intra-day (ID) markets. The scheduling problem is formulated as a two-stage chance-constrained optimization model taking the uncertainty of RESs production, load consumption, and probability of reserve activation into account. The response of VPP after its reserve capacity is called and generated is also considered to increase the operational flexibility of VPP. The proposed model is implemented on a test VPP system, and the effects of RESs sizing, ESSs sizing, and the probability of reserve activation are analyzed. Results indicate that the proposed model can perform well under real-world conditions. [ABSTRACT FROM AUTHOR]

A multi-mode resource-constrained project scheduling problem (MRCPSP) with multiple skills is investigated in this paper. Unlike the traditional form of this problem, and considering the real-world project circumstances, project activities can be preempted. In this paper, a new multi-objective mixed-integer linear programming (MILP) model with three objective functions is extended. These objectives are: (1) minimizing the project makespan, (2) minimizing the total resource costs, and (3) minimizing the total project risk. Based on real-life projects, non-renewable resources are represented as an uncertain stochastic parameter. To cope with the uncertain environment, chance-constrained programming with a confidence level is considered. A real-world construction project of a sports center in Tehran is utilized to demonstrate the applicability of the presented formulation. A well-known lexicographic optimization method, namely AUGMECON2, is applied to solve the proposed formulation with three objectives. Ultimately, for the case study and two datasets J30 and MM50, the proposed lexicographic optimization algorithm is compared with an efficient multi-objective mathematical programming technique known as the AUGMECON method. The comparison is based on performance metrics (i.e., IGD and HV) commonly used in multi-objective optimization. The results show the relative dominance of the proposed lexicographic optimization algorithm over the AUGMECON method in all sizes of the problem instances. [Display omitted] • Considering a multi-skill multi-mode resource-constrained project scheduling problem with preemption. • Presenting a new multi-objective mixed-integer linear programming model for problem with a time lag between activities. • Minimizing three objectives: the total project risk, project makespan, and total project cost simultaneously. • Investigating the real project of building a sports center in a prominent engineering company to validate the model. • Proposing chance-constrained programming with the stochastic parameter and AUGMECON2 method for the first time. [ABSTRACT FROM AUTHOR]

Efficient vessel scheduling in port is critical for enhancing navigational efficiency. However, it faces substantial challenges due to unforeseeable events. In this context, this paper addresses the vessel scheduling problem with stochastic sailing times in port. The problem is formulated into a chance-constrained programming (CCP) model and then transformed into an equivalent deterministic programming problem. A novel approach utilizing a machine learning-based adaptive differential evolution algorithm (MLDE) is proposed to address this model. In MLDE, a K-means clustering method is employed to generate initial population, aiming to enhance the population's quality and diversity while mitigating the impact of random interference. Throughout the mutation and crossover stages, we introduce a parameter adaption strategy based on Q-learning, which is established as a Markov decision process (MDP) model. The model effectively defines the state, action, and reward functions to guide the population toward selecting the optimal scaling factor and crossover probability parameters. Numerical experiments based on different instance sizes are conducted at the Comprehensive port. The obtained results reveal the superior performance of the MLDE algorithm in comparison to existing metaheuristic algorithms and traditional differential evolution (DE) variants. A statistical analysis experiment is also conducted to further confirm the superiority of MLDE. [ABSTRACT FROM AUTHOR]

This paper proposes an uncertainty modeling method for the aggregated power flexibility of DERs. Basically, both outer and inner approximated power-energy boundary models are utilized to describe the aggregated flexibility of controllable DERs. These power and energy boundary parameters are uncertain because the availability of controllable devices, such as electric vehicles and thermostatically controlled loads, cannot be precisely predicted. The optimal operation problem of the aggregator is thus formulated as chance-constrained programming (CCP). Then, a flexibility envelope searching algorithm based on the ALSO-X+ method is proposed to solve the CCP, the result of which is a conservative approximation of the original CCP but not as conservative as the Conditional Value-at-Risk approximation. After optimizing the aggregated power of the group of DERs, the decision at the aggregator level is disaggregated into the flexibility regions of individual DERs. Finally, the numerical test demonstrates the effectiveness and robustness of the proposed method. • Uncertainty modeling of the aggregated flexibility of DERs. • Chance constraint approximation based on the ALSO-X+ approach. • Comparative analysis of costs, risk levels, and feasibility with Conditional Value at Risk. • Comparison between the outer and inner approximated flexibility aggregation models. [ABSTRACT FROM AUTHOR]

The integration of renewable energy sources may result in more severe active power disturbances, and requires more load shedding. The battery energy storage system (BESS) characterized with high flexibility can handle such uncertain disturbances and reduce load shedding amount. This paper proposes a chance-constrained optimal sizing scheme of the BESS to coordinate with the synchronous generator and emergency load shedding (ELS) for frequency stability. First, considering the role of the synchronous generator, BESS, and ELS in frequency stability control, an extended system frequency response model is established to calculate the amount of load shedding, and the required capability of frequency regulation. Then, a multi-objective and chance-constrained mixed integer nonlinear programming (MINLP) model is built for the BESS sizing to minimize investment cost and maximize operation profits, which considers the uncertainties of disturbances. With the utilization of the linear weighted method, max-affine function-based piecewise linearization method and Bernstein approximation, the model is reformulated into a tractable form, which is iteratively solved by the multi-cut Benders decomposition. Case studies were carried out to verify the effectiveness of the proposed scheme, showing superior performance in reducing load shedding amount and improving frequency nadir. • A hierarchical optimization framework for the BESS sizing to coordinate with synchronous generators and ELS. • An estimation method for the required frequency regulation capability of the BESS and the amount of ELS. • A chance-constrained and multi-objective MINLP model for the BESS sizing with coordinated frequency control and uncertain disturbances. • Reformulate the chance-constrained and multi-objective model into a tractable MILP form. [ABSTRACT FROM AUTHOR]

This paper develops a robust chance-constrained model for handling the uncertainties of generation and consumption in multi-carrier energy hubs. The proposed model incorporates corresponding loading factors for each type of electrical, heating, and cooling loads. This is done to assess the maximum loadability of the whole system. In this respect, the chance-constrained approach is implemented for the feasibility assessment of the operation problem with uncertainties. The uncertainties which are assumed here include the forecast errors of electrical, heating, and cooling load demands, and the volatile solar power generation. The overall problem formulation is developed in the mixed-integer linear programming (MILP) framework. The standard chance-constrained approach is converted to a deterministic optimization model by utilizing the Big M method. The main objective of the proposed model is to maximize the loadability index with uncertainties while addressing the permissible risk index of the decision-maker. The studied energy hub comprises electrical, heating, and cooling loads, and the energy flow technique is adopted in this paper to model the load balance equations. The simulation results are presented for different scenarios while addressing features of the proposed model for the summer and winter seasons. Furthermore, the developed model is evaluated for different scenarios and a comparison is made with the information-gap decision theory (IGDT) method.

An emphasis on sustainable growth helps decrease the initial capital and reduce the impact of industry on an ecologically sensitive environment through resource conservation. Pinch Analysis serves as a valuable tool to identify the potential for resource conservation, waste minimization, and resource costs. However, there are inherent uncertainties associated with these resource conservation networks. The concept of Pinch Analysis is broadened to multi-objective resource conservation problems incorporating parametric uncertainties in this paper. The objective functions are combined to form a single compound objective function using the weighted sum approach. For the compound objective function, prioritized sequences (or resource combinations) are generated through multi-objective prioritized costs to accommodate parametric uncertainties. The multi-objective prioritized cost vs. weights curve helps determine the unique prioritized sequences for different range of weights to achieve optimal solutions. An exact analytical expression for the maximum number of prioritized sequences is also derived. Furthermore, a method is presented to construct the complete Pareto-optimal front to represent all optimal solutions graphically. Two illustrative examples, the hydrogen conservation problem with two objectives (cost and emission) and the water conservation problem with three objectives (cost, land requirement, and emission), demonstrate the proposed method's utility and efficacy. A multi-objective resource conservation problem under normally distributed parametric uncertainties. [Display omitted] • Included parametric uncertainties in multi-objective resource conservation problems. • Stochastic Pinch Analysis minimizes multiple objectives with multiple resources. • Determined the maximum number of possible prioritized sequences of resources. • Proposed multi-objective prioritized cost to determine the optimal sequence. • Determined Pareto-optimal fronts to represent all the efficient solutions. [ABSTRACT FROM AUTHOR]

To explore the bidirectional interaction between renewable energy and buildings in multi-agent energy systems, this paper proposes a distributed cooperative operation strategy for multi-agent energy systems integrated with wind, solar, and buildings based on chance-constrained programming (CCP). First, the multi-agent energy system integrated with wind, solar, and buildings is comprehensively modeled with detailed electric and thermal characteristics for flexibility enhancement. Then for maximizing the profits of the cooperative energy system and each engaged agent, a Nash bargaining model is presented and is divided into two subproblems: the coalition income and the power payment. To preserve the privacy of agents, the adaptive alternating direction method of multipliers (ADMM) is exploited to solve both subproblems. Meanwhile, the CCP method is applied to address diverse uncertainties from wind and solar power generation as well as outdoor temperature. Finally, the effectiveness of the proposed strategy is validated. The simulation results show that, besides the privacy of information among all agents being well preserved, our strategy enhances the profits not only for the energy system but also for all engaged agents. • A distributed cooperative operation strategy for multi-agent energy systems integrated with wind, solar, and buildings is proposed. • Bidirectional interactions between wind/solar power plant and buildings are realized by the Nash bargaining-based incentive cooperative mechanism. • Indoor temperature comfort in buildings is ensured under diverse uncertainties by exploring the building flexibility through chance-constrained programming. • Power trading results and the economy of the energy system and the participating agents are analyzed. [ABSTRACT FROM AUTHOR]

The proliferation of charging stations entails multiple challenges for power systems. In this regard, the installation of photovoltaic-battery systems may help to mitigate the negative effects of charging points. However, such assets should be carefully planned, paying attention to economic aspects, principally. Most of existing works optimize the photovoltaic-battery system in charging infrastructures taking a representative-space of the involved variables (e.g. photovoltaic potential, charging demand or energy prices). However, this approach tends to ignore low-probable scenarios. Thus, the best-case scenario for charging demand (i.e. that for which the highest charging profit is accessible) may not be included in the analysis and therefore such demand could be not attended properly, thus losing this monetary opportunity. This paper focuses on this issue and questions if considering the best-case scenario into planning photovoltaic-battery systems for charging stations is worthwhile or not. To this end, a novel best-case-aware planning tool is developed, including the best-case scenario through a novel chance-constrained formulation. The overall problem is then decomposed into a master-slave structure by which the economy of the system is optimized together with the number of scenarios for which the best-case profile can be attended. A case study serves to validate the developed tool and shed light on the questions arisen in this work. In particular, it is checked that considering the best-case scenario into planning tools is questionable from a monetary point of view. Nevertheless, its inclusion unlocks some collateral advantages such as incrementing the users' satisfaction or reducing the grid-dependency. [ABSTRACT FROM AUTHOR]

[Display omitted] • Incorporating parametric uncertainties in resource conservation networks. • Stochastic optimization of resource conservation networks with multiple resources. • Generalized prioritized cost to determine appropriate resources to be used. • Comparing Pinch Analysis with numerical optimization. • Sensitivity diagram to represent optimal resource at different cost ratios. Process industries often utilize a large number of valuable resources. To minimize operating costs and to promote sustainability, it is essential to prevent the overuse of resources. In conjunction with the prioritized cost concept, Pinch Analysis helps in achieving cost-optimal multi-resource allocation networks. Previous works were restricted to optimizing resource allocation networks with deterministic parameters without considering uncertainties associated with them. Uncertainties in source and resource parameters are incorporated in this paper through chance-constrained programming and solved through Pinch-based and numerical optimization-based methods. The notion of prioritized cost is extended to include uncertainties in various network parameters. Based on specified reliability for the multi-resource allocation network, the proposed approach determines the optimal operating cost of the network, and the results are verified through Monte Carlo simulations. Two examples from the field of water conservation and material conservation are solved to establish the utility of the proposed method. Optimal combinations of resources are pictorially represented at different cost ratios through a novel sensitivity diagram. [ABSTRACT FROM AUTHOR]

This paper deals with multi-objective stochastic linear programming problem. The problem is considered by introducing the coefficients of the decision variables and the right-hand-side parameters in the constraints as normal random variables. A method for converting the problem into its deterministic problem is proposed and hence two-phase approach with equal weights is proposed for finding an efficient solution. The advantages of the approach are: as weights which is positive, not necessarily equal and generate an efficient solution. A numerical example is given to illustrate the suggested methodology. [ABSTRACT FROM AUTHOR]

In low-voltage distribution networks, distributed energy storage systems (DESSs) are widely used to manage load uncertainty and voltage stability. Accurate modeling and estimation of voltage fluctuations are crucial to informed DESS dispatch decisions. However, existing parametric probabilistic approaches have limitations in handling complex uncertainties, since they always rely on predefined distributions and complex inference processes. To address this, we integrate the patch time series Transformer model with the non-parametric Huberized composite quantile regression method to reliably predict voltage fluctuation without distribution assumptions. Comparative simulations on the IEEE 33-bus distribution network show that the proposed model reduces the DESS dispatch cost by 6.23% compared to state-of-the-art parametric models. [ABSTRACT FROM AUTHOR]

Managing uncertainties and risks is always a difficult but fascinating task in fresh fruit supply chains, especially when dealing with the strategy for the production and conveyance of fresh fruit in Vietnam. Following the COVID-19 outbreak, the confluence of economic recession and persistent adverse weather conditions has exacerbated challenges faced by dragon fruit cultivators. This research investigates a two-stage stochastic programming (TSSP) approach which is developed and served as a valuable tool for analyzing uncertainties, optimizing operations, and managing risks in the fresh fruit industry, ultimately contributing to the sustainability and resilience of supply chains in the agricultural sector. A prototype is provided to illustrate the complex and dynamic nature of dragon fruit cultivation and consumption in Vietnam. Data on the selling prices of dragon fruit were collected from several sources between 2013 and 2022 in Binh Thuan Province, Vietnam. The results were obtained from the model by using three different approaches in order of their versatility and efficacy: (1) Scenario tree generation; (2) Sample average approximation; (3) Chance-constrained programming. [ABSTRACT FROM AUTHOR]

• Integrated demand response mechanism (IDR) in the micro-energy grid can reduce the peak-valley difference of load, promote supply–demand balance and improve the economy of system operation. • Power to gas (P2G) and combined heat and power (CHP) devices can effectively improve the coupling relationship of electricity, gas, and heat in the micro-energy grid. • Through various devices in this paper, the inflexible operation strategy of the traditional micro-energy grid is decoupled, and the determining electricity by heat characteristic limitation of CHP units is relieved. • The simulation results show that the ladder-type carbon trading mechanism has a more potent binding force on carbon emissions and can effectively improve the environmental protection of the system. • In the process of solving, the sequence operation theory (SOT) methods can be used to solve the model quickly and accurately. The micro-energy grid can meet various load demands and realize the complementary advantages of different energy sources, which provides a new way to solve the problems of energy utilization efficiency and environmental pollution. However, how coordinating multiple energy sources and improving the flexibility of the micro-energy grid is an urgent problem to be solved. This paper proposes an optimal scheduling model based on chance-constrained programming (CCP), which considers electric vehicle (EV) charging characteristics, integrated electricity-heat demand response, and ladder-type carbon trading in the background of various renewable uncertainty. Firstly, this paper uses power to gas (P2G) technology and combined heat and power (CHP) technology to improve the flexibility of the system and realize the coupling between different energy sources. Secondly, integrated demand response (IDR) is used to explore potential interaction capabilities between electric-heat flexible load and micro-energy grid. Then, the ladder-type carbon trading mechanism is introduced in the optimization scheduling model to reduce the carbon emissions of the system. Finally, sequence operation theory (SOT) transforms the original CCP model into a conveniently solvable mixed-integer linear programming (MILP) model. The simulation results show that all subsystems are closely coupled due to the participation of P2G and CHP, which reduces the operation cost of the system by 3.9 %. The results also indicate that the IDR mechanism improves energy efficiency and reduces operating costs by 7.8 %. Finally, the results substantiate that the ladder-type carbon trading mechanism reduces the carbon emissions of the system by 18.1 % and improves the environmental benefits of the system. [ABSTRACT FROM AUTHOR]

A high level of electricity price volatility increases financial risks and safety issues in power system operations. Storage devices as an efficient solution to mitigating price volatility have attracted extensive attention. In this paper, the mechanism of how storage devices impact price volatility is investigated at first. Through analyzing the connection between an economic dispatch problem and its Lagrange dual, we reveal that the capacity and charge/discharge power of a storage device installed at a node have an aggregate impact on the range of the price changes of that node. A model to calculate the sensitivity of price volatility to storage device parameters is proposed. To determine the optimal nodes to place storage devices and the optimal storage capacities to constrain the price change levels, this paper develops a chance-constrained optimization model, and a scenario-based approach is adopted to solve the problem. The IEEE 24-bus system is employed in the case studies, associated with Gurobi and Julia. Simulation studies show that if there is one node with the highest price change all the time, the price volatility must have the highest sensitivity to the storage device on that node. However, in the case where there are multiple nodes having the highest price changes at different times, a node with high price change does not necessarily mean high sensitivity. The simulation studies verify that the chance-constrained optimization model is effective to suppress excess price changes. • The impact of energy storage devices on price volatility is revealed by Lagrange duality. • A model to calculate sensitivity of price volatility to storage parameters is established. • A chance-constrained optimization model is proposed to find the optimal nodes to place storage devices. [ABSTRACT FROM AUTHOR]

We propose a novel two-stage distributionally robust joint chance-constrained (DRJCC) model to design a resilient humanitarian relief network with uncertainties in demand and unit allocation cost of relief items in the post-disaster environment. This model determines the locations of the supply facilities with pre-positioning inventory levels and the transportation plans. We investigate the problem under two types of ambiguity sets: moment-based ambiguity and Wasserstein ambiguity. For moment-based ambiguity, we reformulate the problem into a mixed-integer conic program and solve it via a sequential optimization procedure by optimizing scaling parameters iteratively. For Wasserstein ambiguity, we reformulate the problem into a mixed-integer linear program. We conduct comprehensive numerical experiments to assess the computational efficiency of the proposed reformulation and algorithmic framework, and evaluate the reliability of the generated network by the proposed model. Through a case study in the Gulf Coast area, we demonstrate that the DRJCC model under Wasserstein ambiguity achieves a better trade-off between cost and network reliability in out-of-sample tests than the moment-based DRJCC model and the classical stochastic programming model. [ABSTRACT FROM AUTHOR]

• New comprehensive framework for a CCHP-based MG operation. • New CCP approach for guaranteeing confidence level of the whole system. • Proposing a comparative structure for participating in power and heat markets. • Utilizing multi-carrier storage, hybrid chiller, besides new mathematical for CHP. Microgrids (MGs) have a special role in developing several consumers' energy infrastructure and supply in more economical, safer, and sustainable ways. The interaction and mutual relationship between each energy carrier on the reliable performance of other carriers and the high growth of tri-generation technologies in the MG face the optimal performance of such networks with many challenges. Combined cooling, heating, and power (CCHP)-based MGs are a new generation of MGs that simultaneously provide electrical, thermal, and cooling loads. However, the interaction between these carriers is very influential in CCHP-based MG's operation, which is rarely analyzed. Hence, this paper focuses on the operation of CCHP-based MG coupled with hybrid chiller, multi-energy storage, solar and wind power, etc., under the chance-constrained programming (CCP) approach by considering the mutual relationship between carriers. While modeling consumption and wind and solar energies fluctuations, the proposed approach analyzes the violation of the balance constraint for each carrier and subject it to guarantee the corresponding confidence level. Therefore, the degree of dependence of the system on each carrier and the mutual relationship between carriers are analyzed in this work. This paper also presents a new incentive framework for participating in the electricity and heating markets for the system. The proposed model is implemented on the test system, and the results are discussed for different cases for several confidence levels. The results illustrate the importance of the electricity carrier confidence level on the safe performance of the whole system compared to other carriers. Only by increasing the operation cost of the electricity sector by 4.3%, the system's reliable performance is guaranteed with a probability of 98%. [ABSTRACT FROM AUTHOR]

Transportation activities, especially road transportation, have a great impact on economic growth. On the other hand, sustainability is a major concern for transportation planning. In this work, a data-oriented network is developed to evaluate the sustainability of vehicle types. Then, this network is integrated with a multi-objective optimization model in order to provide the planning of a three-stage transportation problem, according to traffic congestion. Some criteria including total profit, efficiency of different vehicle types, relationship among the customers supplied by a specified retailer, risk of underestimating unmet demand, and selling price are used to determine the objective functions. The Chance-Constrained Programming (CCP) and Chebyshev Goal Programming (CGP) approaches are applied to solve the proposed integrated model. To the best of the authors' knowledge, it is the first time that traffic congestion under the conditions of simultaneous fuzzy and stochastic uncertainty has been integrated into sustainable transportation planning. In addition, the applicability and validity of the developed model are assessed on a case study. The results are then analyzed and appraised by Data Envelopment Analysis (DEA) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) methods. The findings prove that the components of the proposed model have a very beneficial effect on the solution, and also perform much better than the competing approaches in the literature. Two important points from the results of this paper are that (a) traffic congestion is more effective in the initial levels of the supply chain, and (b) transportation planning using efficient vehicles may reduce the desirability of the objective function values. [ABSTRACT FROM AUTHOR]

With high renewable energy sources (RESs) penetration in distribution networks, handling the uncertainties of RESs outputs and multi-time coupling problems in the dynamic network reconfiguration (DNR) is a big challenge. Besides, the existing mathematical and artificial intelligence algorithms for network reconfiguration face the problem of falling into local optima and poor convergence. To address the above challenge and problem, this paper first establishes a chance-constrained programming model to handle the uncertainties. Then the Minty algorithm is applied for efficiency and accurate static network reconfiguration (SNR) in each time interval. Finally, a branch exchange-based method is proposed to eliminate violations for the operation times of switches. Numerical simulations on the IEEE 33 system and an actual 151-bus distribution network show the superiority of the proposed algorithm over existing methods.

To meet evacuation needs from carless populations who need personalized assistance to evacuate safely, in this article we propose a ridesharing-based evacuation program that recruits volunteer drivers before a disaster strikes, and then matches volunteer drivers with evacuees once demand is realized. We optimize resource planning and evacuation operations under uncertain spatiotemporal demand, and construct a two-stage stochastic mixed-integer program to ensure high demand fulfillment rates. We consider three formulations to improve the number of evacuees served, by minimizing an expected penalty cost, imposing a probabilistic constraint, and enforcing a constraint on the conditional value at risk of the total number of unserved evacuees, respectively. We discuss the benefits and disadvantages of the different risk measures used in the three formulations, given certain carless population sizes and the variety of evacuation modes available. We also develop a heuristic approach to provide quick, dynamic and conservative solutions. We demonstrate the performance of our approaches using five different networks of varying sizes based on regions of Charleston County, South Carolina, an area that experienced a mandatory evacuation order during Hurricane Florence, and utilize real demographic data and hourly traffic count data to estimate the demand distribution. [ABSTRACT FROM AUTHOR]

Water distribution networks (WDNs) are defined as the planning for the development, distribution, and utilization of water resources. The main challenge of WDNs is to preserve limited water resources while providing effective benefits from these resources in accordance with environmental considerations. Water distribution networks use hydraulic components to connect water resources to consumers. The diameter of each pipe, the layout of the pipe network, and the total length of pipes all contribute to the most effective layout for a water distribution system. This study considers the assurance that the flow (discharge) of water is in accordance with what is expected, with such aspects apt to be described as a particular form of reliability. As a result, this study proposes a stochastic optimization model with non-linear probability constraints for overcoming the challenges of water distribution networks while taking water flow reliability into account. The pressure drop equation causes the non-linear shape. The stochastic model of the opportunity constraint is changed to a deterministic multi-objective model using an approach based on integer programming and sample averaging to solve the resulting model. The direct search approach (neighbourhood search) is then applied to tackle the integer part. [ABSTRACT FROM AUTHOR]

This study explores a road–rail intermodal routing problem. To improve the carbon efficiency of transportation, reducing CO2 emissions is considered by the routing. Soft time windows are incorporated into the routing to optimize the timeliness of the first-mile pickup and last-mile delivery services in intermodal transportation. The routing is further modeled in a time-dependent and fuzzy environment where the average truck speeds of the road depend on the truck departure times and are simultaneously considered fuzzy along with rail capacities. The fuzzy truck speed leads to the fuzziness of three aspects, including speed-dependent CO2 emissions of the road, a timetable-constrained transfer process from road to rail, and delivery time window violation. This study formulates the routing problem under the above considerations and carbon tax regulation as a combination of transportation path planning problem and truck departure time and speed matching problem. A fuzzy nonlinear optimization model is then established for the proposed routing problem. Furthermore, chance-constrained programming with general fuzzy measure is used to conduct the defuzzification of the model to make the problem solvable, and linearization techniques are adopted to linearize the model to enhance the efficiency of problem-solving. Finally, this study presents an empirical case to demonstrate the effectiveness of the designed approach. This case study evaluates the performance of carbon tax regulation by comparing it with multi-objective optimization. It also focuses on sensitivity analysis to discuss the influence of the optimistic–pessimistic parameter and confidence level on the optimization results. Several managerial insights are revealed based on the case study. [ABSTRACT FROM AUTHOR]

The unit commitment problem (UCP) is one of the key and fundamental concerns in the operation, monitoring, and control of power systems. Uncertainty management in a UCP has been of great interest to both operators and researchers. The uncertainties that are considered in a UCP can be classified as technical (outages, forecast errors, and plugin electric vehicle (PEV) penetration), economic (electricity prices), and "epidemics, pandemics, and disasters" (techno-socio-economic). Various methods have been developed to model the uncertainties of these parameters, such as stochastic programming, probabilistic methods, chance-constrained programming (CCP), robust optimization, risk-based optimization, the hierarchical scheduling strategy, and information gap decision theory. This paper reviews methods of uncertainty management, parameter modeling, simulation tools, and test systems. [ABSTRACT FROM AUTHOR]

The high proportion of renewable energy connected to the power grid puts enormous pressure on the power system for peaking. To reduce the peak-to-valley load difference, reduce the abandoned wind and light rate, and improve the economy of power system peaking, this paper constructs a wind–light–fire-storage joint optimal dispatching model based on electricity price response and uncertainty of wind and photovoltaic power. First, the model adds electricity price response to guide customers to change their electricity consumption habits by adjusting electricity prices at different times, bringing economic benefits to customers while shifting part of the peak load to the trough to achieve the purpose of peak shaving and valley filling; Secondly, considering the impact of wind and photovoltaic output uncertainty on power grid peaking, chance-constrained programming is added to the model, which is based on the simulation method, using the Latin hypercube sampling method, eventually transformed into a mixed integer linear programming model for solution; Finally, simulation is carried out in the modified IEEE30 node system to verify the feasibility and effectiveness of the model.

The connection between various energy types in the integrated power and natural gas system has grown stronger in recent years, as has the penetration rate of clean energy. Wind power generation volatility offers a considerable barrier to power system operation. This research provides a multi-time scale economic dispatch model with flexibility limitations to address this issue. Through chance-constrained programming, the equipment flexibility is described by probability functions and predetermined confidence levels in this model, and the generating cost and wind power consumption are improved through day-ahead and intra-day optimal scheduling. Finally, the effectiveness of the proposed model is verified by two case studies of integrated energy systems, where the results show that about 68.0–72.1% wind power curtailment can be effectively reduced while satisfying all load and system safety requirements. [ABSTRACT FROM AUTHOR]

Due to the uncertain fluctuations of renewable energy and load power, the state variables such as bus voltages and pipeline mass flows in the combined cooling, heating, and power campus microgrid (CCHP-CMG) may exceed the secure operation limits. In this paper, an optimal energy flow (OEF) model for a CCHP-CMG using parameterized probability boxes (p-boxes) is proposed to describe the higher-order uncertainty of renewables and loads. In the model, chance constraints are used to describe the secure operation limits of the state variable p-boxes, and variance constraints are introduced to reduce their random fluctuation ranges. To solve this model, the chance and variance constraints are transformed into the constraints of interval cumulants (ICs) of state variables based on the p-efficient point theory and interval Cornish-Fisher expansion. With the relationship between the ICs of state variables and node power, and using the affine interval arithmetic method, the original optimization model is finally transformed into a deterministic nonlinear programming model. It can be solved by the CONOPT solver in GAMS software to obtain the optimal operation point of a CCHP-CMG that satisfies the secure operation requirements considering the higher-order uncertainty of renewables and loads. Case study on a CCHP-CMG demonstrates the correctness and effectiveness of the proposed OEF model.

Product reuse and recovery is an efficient tool that helps companies to simultaneously address economic and environmental dimensions of sustainability. This paper presents a novel problem for stock management of reusable products in a single-vendor, multi-product, multi-retailer network. Several constraints, such as the maximum budget, storage capacity, number of orders, etc., are considered in their stochastic form to establish a more realistic problem. The presented problem is formulated using a nonlinear programming mathematical model. The chance-constrained approach is suggested to deal with the constraints’ uncertainty. Regarding the nonlinearity of the model, grey wolf optimizer (GWO) and whale optimization algorithm (WOA) as two novel metaheuristics are presented as solution approaches, and the sequential quadratic programming (SQP) exact algorithm validates their performance. The parameters of algorithms are calibrated using the Taguchi method for the design of experiments. Extensive analysis is established by solving several numerical results in different sizes and utilizing several comparison measures. Also, the results are compared statistically using proper parametric and non-parametric tests. The analysis of the results shows a significant difference between the algorithms, and GWO has a better performance for solving the presented problem. In addition, both algorithms perform well in searching the solution space, where the GWO and WOA differences with the optimal solution of the SQP algorithm are negligible.

Battery energy storage systems (BESS) are regarded as a multi-functional power system participator, participating in the energy arbitrage strategy (EAS), the frequency regulation strategy (FRS) and so on. However, the existing BESS mainly make profit from the EAS instead of the FRS in many countries such as China. Because there is no appropriate control strategy for BESS, when the developing ancillary services market cannot price the contribution of BESS in FRS. Meanwhile, BESS do have redundant power and capacity, if only the EAS is applied. Therefore, it is significant that BESS are involved in the FRS, that the EAS has the priority in BESS utilization. In this paper, a frequency regulation strategy for the user-side BESS is proposed, on the constraints of the planned energy arbitrage. Specifically, the chance-constrained programming is applied to solve the randomness of frequency regulation requirement, ensuring the BESS profit from the EAS. Also, the exiting BESS are fully used with extra profit from FRS. At last, the promising results prove the advantages of the proposed FRS.

This study investigates the planning problem of fast-charging stations for electric vehicles with the consideration of uncertain charging demands. This research aims to determine where to build fast-charging stations and how many charging piles to be installed in each fast-charging station. Based on the multicommodity flow model, a chance-constrained programming model is established to address this planning problem. A scenario-based approach as well as a big-M coefficients generation algorithm are applied to reformulate the programming model into tractable one, then the Dantzig–Wolfe decomposition method is leveraged to find its optimal solution. Finally, a numerical experiment is conducted in a 25-node network to assess the efficiency of the proposed model and solution approach. [ABSTRACT FROM AUTHOR]

We study a chance-constrained optimization problem where the random variable appearing in the chance constraint follows a normal distribution whose mean and variance both depend linearly on the decision variables. Such structure may arise in many applications, including the normal approximation to the Poisson distribution. We present a polynomial-time algorithm to solve the resulting nonconvex optimization problem, and illustrate the efficacy of our method using a numerical experiment. [ABSTRACT FROM AUTHOR]