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This paper delves into the impacts of an ongoing global crisis on the resilience of supply chains. Furthermore, it proposes measures to address and mitigate the disruptions caused by the prevailing uncertainties. For example, while the economy has started to recover after the pandemic and demand has increased, companies have not fully returned to their pre-pandemic levels. To enhance their supply chain resilience and effectively manage disruptions, one viable strategy is the implementation of flexible/hybrid manufacturing systems. This research is motivated by the specific requirements of Vestel Electronics, a household appliances company, which seeks a flexible/hybrid manufacturing production setup involving dedicated machinery to meet regular demand and the utilisation of flexible manufacturing system (FMS) to handle surges in demand. We employ a scenario-based approach to model demand uncertainty, enabling the company to make immediate and adaptive decisions that take advantage of the cost-effectiveness of standard production and the responsiveness of FMS. To solve the problem, we propose a heuristic algorithm based on column generation. The numerical results demonstrate that our optimisation model provides solutions with an average optimality gap of less than 6% while also reducing the average cost of standard production schemes without FMS by over 12%. [ABSTRACT FROM AUTHOR]

As telehealth utilization for ambulatory and home-based care skyrockets, there has been a paradigm shift to a decentralized and hybrid care delivery modality integrating both in-person and telehealth services provided at different layers of the care delivery network, i.e., central hospitals, satellite clinics, and patient homes. The operations of such care delivery systems need to take into consideration patients' mobility and care needs, and rely on multiple types of nurses who can support and facilitate telehealth (with hospital physicians) in clinics and patient homes. We formulate an optimization problem, aiming at operationalizing the proposed care delivery network. Decisions regarding the type of care delivered, the location of care delivered, and the scheduling of all kinds of nurses are determined jointly to minimize operating costs while simultaneously satisfying patients' care needs. We propose a bi-level approximation that exploits the structure of the hybrid telehealth system, and develop column generation-based heuristic algorithms to identify the joint decision rules for clinic selection, patient assignment, and visiting nurse routing problems. Numerical experiment results demonstrate our algorithm's capability to achieve high-quality solutions in reasonable computation time, and is capable of solving instances with large patient sizes and time windows. Our work supports the efficient and effective operation of the proposed hybrid telehealth systems to improve patient access to care. [ABSTRACT FROM AUTHOR]

Given the increasing importance of cascading trip prevention, this study presents the pumped storage characteristics to cooperate with thermal units and further ensure the safety of grid operation. The proposed model comprises two phases: the first phase is the day-ahead decision-making phase, which synergistically optimizes thermal units and pumped storage to improve the flexibility of grid operation; the second phase is the intra-day adjustment phase considering the uncertainty of the wind-photovoltaic and transmission line failure outage to enhance the robustness. Furthermore, this model employs a column and constraint generation algorithm to solve the two-phase, three-layer optimization problem, thereby minimizing the adjustment cost under the riskiest scenarios. The experimental results show that adding pumped storage reduces the total system operating cost by 3.99%, the renewable energy abandonment rate to 0.65%, and the thermal power unit output standard deviation to 74.13 MW. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Shanghai Jiao Tong University (1006-2467) is the property of Journal of Shanghai Jiao Tong University Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of South China University of Technology (Natural Science Edition) is the property of South China University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of South China University of Technology (Natural Science Edition) is the property of South China University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In recent years, the ever-rising penetration of distributed photovoltaics (PV) power has presented substantial challenges in power system dispatch due to its inherent randomness and unpredictability. To bridge this gap, this paper proposes a two-stage robust optimization method for power system security dispatch considering traditional generators as well as flexible resources, such as load demand response and energy storage systems. Specifically, a price-based demand response model is established to optimize the system's load curve during a day. On this basis, a two-stage optimization problem for day-ahead and intraday power system dispatch model is proposed. The dispatch objective is to minimize the overall cost in worst-case scenarios through properly scheduling unit commitment (UC) as well as flexible resources in each dispatch interval. Column and constraint generation (C&CG) algorithm is adopted for problem solving. The effectiveness of the proposed method is validated by case studies based on a modified 6-node system and a 24-node system. Simulation results indicate that through appropriately scheduling the energy storage system and load demand response, the proposed dispatch method can significantly reduce the total operation cost of a PV rich power system, which in turn facilitates the integration of PV power. [ABSTRACT FROM AUTHOR]

The raw material purchasing (RMP) problem is to determine the purchasing quantities of raw materials in given periods or cycles. Raw material purchasing optimization is crucial for large-scale steel plants because it is closely related to the supply of raw materials and cost savings. The raw material purchasing of large-scale steel enterprises is characterized by many varieties, large quantities, and high costs. The RMP objective is to minimize the total purchasing cost, consisting of the price of raw materials, purchasing set-up costs, and inventory costs, and meet product demand. We present a mixed integer linear programming (MILP) model and a column generation (CG) solution for the resulting optimization problem. The column generation algorithm is the generalization of the branch and bound algorithm while solving the linear programming (LP) relaxation of MILP using column generation (CG), and its advantage is to handle large-sized MILPs. Experimental results show the effectiveness and efficiency of the solution. [ABSTRACT FROM AUTHOR]

In recent years, frequent occurrence of extreme weather events has caused great losses to the power system. Meanwhile, the high penetration of renewable energy has brought new challenges to the safe operation of the system. Coordination of various measures against different stages of disaster can effectively reduce the overall loss and enhance system's resilience. This paper proposed a methodology to coordinate preventive and emergency dispatch stages based on the defender–attacker–defender model, in which various dispatching measures are modelled as defenders, whereas the extreme weather event and wind power's uncertainty are modelled as attackers. Specifically, a two‐stage three‐layer robust optimal dispatching model is established, in which conventional generator's output, wind farm's grid‐connected planning, and load shedding are taken as the main dispatching measures. To solve this model, the column and constraint generation algorithm is used to transform the three‐layer optimization model into a mixed integer linear problem. The effectiveness of the proposed model is verified in the modified IEEE RTS‐79 test system, and the results show that the coordination of preventive and emergency dispatch can effectively reduce the load outage cost under extreme weather, thus enhancing the ability of power system to cope with extreme scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we address the electric vehicle routing problem with time windows and propose two branch-and-price-and-cut methods based on a column generation algorithm. One is an exact algorithm whereas the other is a heuristic method. The pricing sub-problem of the column generation method is solved using a label correcting algorithm. The algorithms are strengthened with the state-of-the-art acceleration techniques and a set of valid inequalities. The acceleration techniques include: (i) an intermediate column pool to prevent solving the pricing sub-problem at each iteration, (ii) a label correcting method employing the ng-route algorithm adopted to our problem, (iii) a bidirectional search mechanism in which both forward and backward labels are created, (iv) a procedure for dynamically eliminating arcs that connect customers to remote stations from the network during the path generation, (v) a bounding procedure providing early elimination of sub-optimal routes, and (vi) an integer programming model that generates upper bounds. Numerical experiments are conducted using a benchmark data set to compare the performances of the algorithms. The results favour the heuristic algorithm in terms of both the computational time and the number of instances solved. Moreover, the heuristic algorithm is shown to be specifically effective for larger instances. Both algorithms introduce a number of new solutions to the literature. [ABSTRACT FROM AUTHOR]

The integration of power grids and communication networks in smart grids enhances system safety and reliability but also exposes vulnerabilities to network attacks, such as Denial-of-Service (DoS) attacks targeting communication networks. A multi-index evaluation approach is proposed to optimize routing modes in integrated energy cyber-physical systems (IECPS) considering potential failures from attacks. Security and economic service evaluation indexes are incorporated to quantify the significance of information flow routing. An optimization model for electric, heat, and gas routing in worst-case scenarios is formulated and solved using a column and constraint generation algorithm. The optimized routing method effectively circumvents specified attack areas, reducing the correlation degree of communication links within the attack area. Comparison with single-service optimization methods demonstrates the superiority of the proposed approach in mitigating the impact of network attacks on IECPS. The study highlights the importance of considering security and economic factors in optimizing routing modes to enhance the resilience of integrated energy cyber-physical systems against network attacks, particularly DoS attacks on communication networks. The evaluation index approach presented in this study provides a comprehensive method for assessing the importance of communication links in IECPS and optimizing routing modes to improve system robustness and reliability in the face of network attacks. [ABSTRACT FROM AUTHOR]

Customized bus systems can improve service quality and efficiency by taking advantage of the speed regulation and capacity variation of autonomous bus systems. To address the challenges of customized bus systems design, this study proposes a collaborative optimization model of vehicle scheduling and speed regulation for the autonomous customized bus system. This model minimizes enterprise operation and passenger travel costs by considering mileage constraints, the time window of passenger travel constraints, and demand pairs coverage constraints. Based on the theoretical properties discovered in the joint design model, the problem is decomposed into a set partitioning master problem and route-selection subproblem. An algorithm combining column generation approach and genetic algorithm is proposed to solve the joint design model. To accelerate the calculation in searching for the shortest route for subproblems, hierarchical filtering strategy is used to reduce the cost of finding feasible routes and improve computational efficiency. The case study reveals that the proposed algorithm exhibits better convergence and stability according to the Wilcoxon test. In a numerical experiment with 100 demand pairs, the joint model can be solved by the algorithm proposed in the study optimally with 19% of the computation time required by the exact algorithms. The departure frequency was reduced by 22%, and the operating cost was reduced by 42% compared with those of customized bus lines serviced separately by human-driven buses. Sensitivity analyses were performed on various operating parameters, such as modular bus capacity and speed boundary, across three different scale cases. The results demonstrate that reasonable parameter settings are beneficial for reducing operating costs and vacant seats. • A collaborative optimization model of bus scheduling and speed regulation is proposed. • An algorithm combining column generation and genetic algorithm is proposed. • Hierarchical filtering strategy is used in the subproblem of the proposed algorithm. • An autonomous customized bus system can reduce corporate costs compared to human-driven buses. [ABSTRACT FROM AUTHOR]

With the aggravation of the shortage of staffing hospital beds, elective surgeries have to be postponed or even cancelled, which directly affects hospital income and patient health. Therefore, we propose a fuzzy scheduling model based on a patient transfer strategy in the hierarchical diagnosis and treatment system to ensure timely surgery. We propose a risk estimation method based on health failure mode and effect analysis to reduce the transfer risk and represent the surgery duration and the length of stay as fuzzy numbers to deal with the uncertainty. Given that solving the fuzzy model is challenging, we propose an equivalent formulation to transform the fuzzy model into a two-stage mixed integer linear programming (TMIP) model, which can reduce the loss of decision-making information. Finally, the column and constraint generation algorithm is used to solve the TMIP model that is suited for the structure of the main problem and subproblem. The experiment shows that the patient transfer strategy can effectively relieve the hospital bed shortage, and its potential can be further released if the transfer risk can be properly assessed. The proposed method for solving the fuzzy model can reduce the information loss comparing traditional methods. [ABSTRACT FROM AUTHOR]

This paper studies the berth allocation and quay crane assignment problem (denoted by BACAP) under uncertainty. We assume that the ships' arrival and operation time is uncertain in this problem. We merge the proactive and reactive strategies to address the two‐stage robust optimization (denoted by RO) model for the BACAP to obtain a complete schedule with robustness. We obtain the berth allocation and quay crane assignment with a proactive strategy in the first stage. In the second stage, we formulate a rescheduling model with a reactive strategy considering the sensitivity towards the change in the complete schedule. The second stage model is based on the prospect theory, a quantitative way to describe the stakeholders' perception, including the port managers and shipowners, of the deviation from the baseline plan. The two stages are iterated until a favorable schedule with high robustness is found. To illustrate the superiority of the two‐stage robust optimization model with the prospect theory for the complete schedule, we give an intuitive example to compare the performance among the related models. The two‐stage RO model with the prospect theory for the complete schedule can generate a lower cost and higher robustness schedule. As for the solution methods, the column and constraint generation (denoted by C&CG) algorithm is applied to obtain the exact solution for the two‐stage RO model. Moreover, we propose the scenario‐constrained C&CG (denoted by SC) algorithm, which can reduce constraints and variables for the master problem to accelerate the solving process of the two‐stage RO model. In addition, the optimality of the SC algorithm is verified by analyzing the pattern of the occurrence of the worst‐case scenarios. Besides, to tackle the large‐scale instances, we propose the schedule‐fixed (denoted by SF) algorithm, in which the results of the previous iterations are treated as fixed. The SF algorithm can increase computing efficiency with a small gap compared to the optimal solution value. Furthermore, extensive numerical experiments are conducted on both real‐life instances and randomly generated instances to verify the superiority and generality of our model and algorithms. [ABSTRACT FROM AUTHOR]

With the continuous expansion of grid-connected wind, photovoltaic, and other renewable energy sources, their volatility and uncertainty pose significant challenges to system peak regulation. To enhance the system's peak-load management and the integration of wind (WD) and photovoltaic (PV) power, this paper introduces a distributionally robust optimization scheduling strategy for a WD–PV thermal storage power system incorporating deep peak shaving. Firstly, a detailed peak shaving process model is developed for thermal power units, alongside a multi-energy coupling model for WD–PV thermal storage that accounts for carbon emissions. Secondly, to address the variability and uncertainty of WD–PV outputs, a data-driven, distributionally robust optimization scheduling model is formulated utilizing 1-norm and ∞-norm constrained scenario probability distribution fuzzy sets. Lastly, the model is solved iteratively through the column and constraint generation algorithm (C&CG). The outcomes demonstrate that the proposed strategy not only enhances the system's peak-load handling and WD–PV integration but also boosts its economic efficiency and reduces the carbon emissions of the system, achieving a balance between model economy and system robustness. [ABSTRACT FROM AUTHOR]

In the era of e-commerce, a new business mode—e-grocery platform has become popular in recent years. An e-grocery platform need not own and operate shops. The platform assigns the orders that customers release on the platform to the part-time couriers; then the couriers go to some nearby shops, buy the commodities required by orders, and deliver them to the orders' shipping address. This study proposes a mathematical model on selecting and accepting customer orders, assigning the accepted orders to couriers, selecting shops for buying each order's required commodities, and routing each courier among her/his visited shops and assigned order's shipping address. Moreover, the uncertain arrivals of future orders is taken into account by the proposed model. For solving the proposed two-stage stochastic integer programming model with the integer recourse function, this study also designs a novel algorithm based on column generation. Based on the real data from platform operators in Shanghai and Hangzhou, numerical experiments are conducted to validate the efficiency of the proposed algorithm. Sensitivity analysis based on the real data are also conducted to derive potentially useful managerial implications for practitioners who operate third-party e-grocery platforms. [ABSTRACT FROM AUTHOR]

Transshipment yards are not usually considered in optimization approaches proposed for solving the log transportation problem. However, they may provide substantive advantages with respect to the usual logistics practice of direct delivering from supply forests to mills. Therefore, this paper evaluates, at the operational level, different supply chain topologies with the purpose of assessing potential costs savings associated to the use of intermediate storage facilities. The researched problem is defined by stated sets of log-suppliers, storage and transshipment yards, and facilities demanding several types of logs over a known planning horizon. The optimal transportation and inventory plan must be found. An optimization algorithm based on Column Generation + GRASP pricing metaheuristic was developed to compute minimal operation costs associated to different supply-chain topologies over a bank of instances generated from realistic information of the forestry activity in the Argentinean province of Misiones. [ABSTRACT FROM AUTHOR]

Decision making problems are typically concerned with maximizing efficiency. In contrast, we address problems where there are multiple stakeholders and a centralized decision maker who is obliged to decide in a fair manner. Different decisions give different utility to each stakeholder. In cases where these decisions are made repeatedly, we provide efficient mathematical programming formulations to identify both the maximum fairness possible and the decisions that improve fairness over time, for reasonable metrics of fairness. We apply this framework to the problem of ambulance allocation, where decisions in consecutive rounds are constrained. With this additional complexity, we prove structural results on identifying fair feasible allocation policies and provide a hybrid algorithm with column generation and constraint programming-based solution techniques for this class of problems. Computational experiments show that our method can solve these problems orders of magnitude faster than a naive approach. [ABSTRACT FROM AUTHOR]

At present, the number of electric vehicles is increasing day by day. The full integration of electric vehicles and multi-energy coupled integrated energy systems is the future development trend. This paper introduces a novel form of flexible energy storage in the integrated energy system ;(IES): electric vehicle (EV). And It proposes that mixed natural gas hydrogen be used as the primary energy source for IES, which replaces traditional natural gas. Combined with the above, the IES is scheduled to meet the system’s multiload for heating, cooling, and electricity demands. Based on the integrated energy system’s structure and energy conversion principles, a robust twostage optimization model for the IES is proposed to minimize the daily operation scheduling costs. The proposed model considers the uncertainty of distributed renewable generation and flexible energy storage. Uncertain adjustment parameters are introduced into the model, which can flexibly adjust the conservatism of the scheme. Using the column and constraint generation algorithm (C&CG) and the strong duality theory, the model presented in this paper is solved and the optimal scheduling scheme is obtained. The final simulation results validate the effectiveness of the model and algorithm. The addition of flexible energy storage and mixed natural gas hydrogen effectively improves the economy and flexibility of the system while reducing carbon emissions costs. Consideration of uncertainty improves system robustness and safety. In addition, sensitivity analyses of the influence of the proportion of hydrogen mixed with natural gas, the setting of uncertain adjustment parameters, electricity prices, weather, and load fluctuations on system operation. The results show that compared to existing research, electric vehicles as a flexible energy storage device and mixed natural gas hydrogen supply, increase the economic benefits of IES by 19.8% and 23%, respectively. [ABSTRACT FROM AUTHOR]

Faced with the uncertainty of wind and photovoltaic power output and load fluctuation caused by the increase of new energy penetration in active distribution network, the demand for operational flexibility and the construction demand for flexible resources of distribution network are gradually increasing. The flexible operation of active distribution network can be realized by coordinated planning of the soft open point integrated with energy storage system (ESOP) and flexible resources. Firstly, the flexibility resource adjustability evaluation and margin indicators are proposed for the response model of typical flexibility resources. Secondly, a two‐stage distributionally robust coordinated planning model considering the coordination planning scheme of distributed generation, flexibility resource, and ESOP as well as the comprehensive norm uncertainty of wind power and photovoltaic outputs multi‐operation scenarios is established with the distribution network construction cost, annual operation cost, and annual power sales revenue as the objective functions meanwhile the investment and flexibility resource operation as constraints. Finally, the column constraint generation algorithm is used to solve the problem, and the effectiveness of the proposed model is verified by the modified IEEE33 node system. [ABSTRACT FROM AUTHOR]

This study investigates a variant of the Vehicle Routing Problem (VRP) for customized on-demand bus service platforms. In this problem, the platform plans customized bus routes upon receiving a batch of orders released by passengers and informs the passengers of the planned pick-up and drop-off locations. The related decision process takes into account some passenger-side time window-related requirements, walking limits, the availability and capacities of various types of buses. A mixed-integer linear programming model of this new VRP variant with floating targets (passengers) is formulated. To solve the model efficiently, a solution method is developed that combines the branch-and-bound and column generation algorithms and also includes embedded acceleration techniques such as the multi-labeling algorithm. Experiments based on real data from Dalian, China are conducted to validate the effectiveness of the proposed model and efficiency of the algorithm; the small-scale experimental results demonstrate our algorithm can obtain optimal results in the majority of instances. Additionally, sensitivity analysis is conducted, and model extensions are investigated, to provide customized bus service platform operators with potentially useful managerial insights; for example, a platform need not establish as many candidate stops as possible, a wide range of walking distance may not bring early arrival at destinations for customers, more mini-buses should be deployed than large buses in our real-world case. Moreover, the rolling horizon-based context and zoning strategies are also investigated by extending our proposed methodology. [ABSTRACT FROM AUTHOR]

Owing to their flexibility and rapid response, grid-connected distributed energy resources (DERs) are wielding growing influence in frequency regulation markets (FRMs). Nevertheless, compared with conventional large-scale generators, small-scale DERs are usually weakly shielded by cyber security measures. This offers attackers the opportunity of disrupting the clearing and settlement of FRMs by manipulating the bid information of DERs. In this paper, the frequency regulation market equilibrium is studied considering the dynamic gaming between attackers and defenders, both of which need the knowledge of FRMs for their interventions. Specifically, a tri-level programming model characterizing the attacker–defender–operator (ADO) interdiction problem in FRMs is developed and then analyzed using a column and constraint generation algorithm, thereby achieving market equilibrium representing the defender's best response to the attacker. The defense strategy in the market equilibrium can attenuate the negative influence of cyber attacks upon the FRMs to the maximum extent. Finally, based on the operating rules of the California Independent System Operator, the FRM process considering the ADO interdiction is simulated and the numerical equilibrium results are presented. [ABSTRACT FROM AUTHOR]

Background: Mixed electron‐photon beam radiation therapy (MBRT) is an emerging technique in which external electron and photon beams are simultaneously optimized into a single treatment plan. MBRT exploits the steep dose falloff and high surface dose of electrons while maintaining target conformity by leveraging the sharp penumbra of photons. Purpose: This study investigates the dosimetric benefits of MBRT for soft tissue sarcoma (STS) patients. Material and methods: A retrospective cohort of 22 STS of the lower extremity treated with conventional photon‐based Volumetric Modulated Arc Therapy (VMAT) were replanned with MBRT. Both VMAT and MBRT treatments were planned on the Varian TrueBeam linac using the Millenium multi‐leaf collimator. No electron applicator, cutout or additional collimating devices were used for electron beams of MBRT plans. MBRT plans were optimized to use a combination of 6 MV photons and five electron energies (6, 9, 12, 16, 20 MeV) by a robust column generation algorithm. Electron beams in this study were planned at standard 100 cm source‐axis distance (SAD). The dose to the clinical target volume (CTV), bone, normal tissue strip and other organs‐at‐risk (OARs) were compared using a Wilcoxon signed‐rank test. Results: As part of the original VMAT treatment, tissue‐equivalent bolus was required in 10 of the 22 patients. MBRT plans did not require bolus by virtue of the higher electron entrance dose. CTV coverage by the prescription dose was found to be clinically equivalent between plans of either modality: V50Gy$V_{\text{50Gy}}$(MBRT) = 97.9 ± 0.2% versus V50Gy$V_{\text{50Gy}}$(VMAT) = 98.1 ± 0.6% (p=0.34). Evaluating the absolute paired difference between doses to OARs in MBRT and VMAT plans, we observed lower V20Gy$V_{\text{20Gy}}$ to normal tissue in MBRT plans by 14.9 ± 3.2% (p<10−6$p<10^{-6}$). Similarly, V50Gy$V_{\text{50Gy}}$ to bone was found to be decreased by 8.2 ± 4.0% (p<10−3$p<10^{-3}$) of the bone volume. Conclusion: For STS with subcutaneous involvement, MBRT offers statistically significant sparing of OARs without sacrificing target coverage when compared to VMAT. MBRT plans are deliverable on conventional linacs without the use of electron applicators, shortened source‐to‐surface distance (SSD) or bolus. This study shows that MBRT is a logistically feasible technique with clear dosimetric benefits. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Although railway systems have been widely used in public transportation for several years, crew scheduling research focuses on airline operations. Since the crew costs constitute the critical part of the operational costs in railway public transportation, the crew scheduling problem gains more importance. Crew scheduling aims to assign all trips to duty packages in a timeline while satisfying several labour working rules, company requirements, and operational restrictions. Because of the complexity of real-world conditions, crew scheduling problems are NP-complete. In this study, the crew scheduling problem was addressed, and a constraint programming based column generation algorithm was proposed as a solution approach. A column generation algorithm was employed to solve problems having a considerable number of variables. In this study, the master problem was designed as a set partitioning problem that aimed to assign all trips to duty while minimizing the cost. In the subproblem, new column(s) satisfying all constraints were generated and added to the master problem to reduce the cost. To analyse the performance of the proposed approach, an integer programming model of the problem was developed. An extensive computational study is presented to compare the results of these two modelling approaches via different real-life problem instances. [ABSTRACT FROM AUTHOR]

The dial-a-ride problem (DARP) is that of satisfying a number of pickup and drop-off customer requests, using a fleet of vehicles. In real life, traffic conditions can affect expected travel times, and hence the satisfaction of rigid pickup/drop-off time windows and scheduled ride times. This article considers the DARP with customer-adaptive ride times under different service conditions and strategies. The problem is formulated as a mixed integer linear programming model that minimizes service cost and customer inconvenience. A hybrid genetic–variable neighbourhood search algorithm (GAVNS) is proposed to solve the problem. Experiments are conducted to compare the performance of GAVNS with that of an approximate column generation algorithm, and to evaluate the application of different strategies on service efficiency and customer satisfaction. The results demonstrate the efficiency of GAVNS, and that limited violations of time-window and ride-time constraints can improve the service efficiency while preserving customer satisfaction levels. [ABSTRACT FROM AUTHOR]

By shifting towards renewable energy sources, manufacturing facilities can significantly reduce their carbon footprint. This environmental issue can be addressed by developing sustainable production through on-site renewable electricity generation and demand-side management policies. In this study, the energy required to power the manufacturing system is obtained from different energy sources: the conventional grid, on-site renewable energy, and an energy storage system. The main objective is to generate a production schedule for a flexible multi-process and multi-product manufacturing system that optimizes the utilization and procurement of electricity without affecting the final demand. A mathematical programming model is proposed to minimize both the total production costs and energy costs, considering a time-of-use pricing policy and an incentive-based program. The uncertainty in renewable energy generation, specifically under the worst-case scenario, is taken into account and the model is transformed into a robust two-stage optimization model. To solve this model, a decomposition approach based on a genetic algorithm is applied. The effectiveness of the proposed model and algorithm is tested on a real industry case involving feed-animal products. A sensitivity analysis is conducted by modifying problem parameters. Finally, a comparison with the nested Column and Constraint Generation algorithm is performed. The obtained results from these analyses validated the proposed model and algorithm. [ABSTRACT FROM AUTHOR]

We consider a robust optimization problem with continuous decision-dependent uncertainty (RO-CDDU), which has two significant features: an uncertainty set linearly dependent on continuous decision variables, and a convex piecewise-linear objective function. We prove that ROCDDU is strongly NP-hard in general and reformulate it into an equivalent mixed-integer nonlinear program (MINLP) with a decomposable structure to address the computational challenges. Such an MINLP model can be further transformed into a mixed-integer linear program (MILP) using extreme points of the dual polyhedron of the uncertainty set. We propose an alternating direction algorithm and a column generation algorithm for RO-CDDU. We model a robust demand response (DR) management problem in electricity markets as RO-CDDU, where electricity demand reduction from users is uncertain and depends on the DR planning decision. Extensive computational results demonstrate the promising performance of the proposed algorithms in both speed and solution quality. The results also shed light on how different magnitudes of decision-dependent uncertainty affect the DR decision. [ABSTRACT FROM AUTHOR]

Dockless bike-sharing systems have grown rapidly in China in recent years. A large number of shared bikes have been put into use, which results in a serious problem of uncollected faulty bikes. However, since the exact number of faulty shared bikes cannot be known a priori, a reverse logistic network must be designed strategically to reduce the total costs of the collection process. This paper studies a robust reverse logistic network design problem of shared bikes that integrates the locations of recycling centres and the planning of collection routes in uncertain collection demand situations. A two-stage robust location routing model is presented to capture the uncertainty of collection demands, and then a set-partition reformulation is presented to address the computationally intractable model. We develop a column-and-constraint-generation-based algorithm combining a tailored column generation algorithm to efficiently solve the proposed model. Numerical experiments and parameter analyses, which are based on real data from bike-sharing companies, are conducted to evaluate the performance of the proposed algorithm. A case study is presented to further analyse the spatial features of the reverse logistic network of shared bikes. Benefits of applying robust optimization are demonstrated experimentally in terms of total cost under uncertain collection demand. • A robust reverse logistic network design problem in bike sharing is studied. • A column-and-constraint-generation based algorithm is presented. • A case study demonstrates the benefits of applying robust optimization. [ABSTRACT FROM AUTHOR]

Recently, many firms have adopted joint production and distribution decisions for perishable products to achieve timely delivery at minimum costs and meet the requirements for high customisation more effectively. This study addresses a two-stage integrated production and distribution problem, explicitly considering that customised orders of perishable products are processed in parallel servers by scheduling in the first stage and delivered through vehicle routing in the second stage. The firm needs to assign orders to servers and vehicles, schedule the production and decide the routes for distribution to minimise the firm's total costs and total weighted waiting costs for customers. We exploit a novel mixed-integer program to make a trade-off between cost and service for the studied problem. We first transform the program into a set-partitioning formulation. Then, we illustrate some structural properties and propose an exact algorithm using the column generation and branch and bound algorithm. We further develop some acceleration techniques and an arc-based fix and price heuristic for practical application. The experimental results show that the algorithms are efficient. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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Demand-side energy storage is an important foundation for enhancing load flexibility to accommodate renewable energy. With the widespread adoption of renewable energy, demand-side energy storage planning, and its incentive mechanism have also attracted the attention of a large number of scholars. However, there are still few studies on incentives from a carbon perspective. To fill the gap, a dynamic carbon incentive mechanism is proposed in this study. In addition, a hierarchical two-stage robust planning model for demand-side energy storage that incorporates the proposed carbon incentive mechanism is developed. At the first level, the economic dispatch is performed, and bus carbon intensities are calculated based on the carbon emission flow theory. The second level is a two-stage robust planning model to obtain the optimal capacities of demand-side energy storage, which is solved based on the nested column and constraint generation algorithm. The proposed model is implemented and evaluated on the MATLAB/YALMIP platform using IEEE 24-bus power systems. The results validate the efficacy of the model in promoting carbon-oriented demand-side energy storage planning, leading to a substantial reduction of carbon emissions by 8.44%. Notably, when compared to existing incentive mechanisms, the proposed carbon incentive mechanism exhibits distinct advantages in achieving carbon reduction with less both subsidy costs and fixed investments. [ABSTRACT FROM AUTHOR]

Urban last-mile delivery providers are facing more and more challenges with the explosive development of e-commerce. The advancement of smart mobile and communication technology in recent years has stimulated the development of a new business model of city logistics, referred to as crowdsourced delivery or crowd-shipping. In this paper, we investigate a form of crowdsourced last-mile delivery that utilizes the journeys of commuters/travelers (crowd-couriers) to deliver parcels from intermediate stations to customers. We consider a logistics service provider that jointly optimizes parcel allocation to intermediate stations and the delivery routing of the crowd-couriers. The joint optimization model gives rise to a new variant of the last-mile delivery problem. We propose a data-driven column generation algorithm to solve the problem based on a set-partitioning formulation. Additionally, a rolling-horizon approach is proposed to address large-scale instances. Extensive numerical experiments are conducted to verify the efficiency of our model and solution approach, as well as the significance of the joint optimization of parcel allocation and the delivery route of the crowdsourced last-mile delivery. The results show that our data-driven column generation algorithm can obtain (near-)optimal solutions for up to 200 parcels in significantly less time than the exact algorithm. For larger instances, the combination of the data-driven column generation algorithm and the rolling-horizon approach can obtain good-quality solutions for up to 1000 parcels in 15 min. Moreover, compared with crowd-courier route optimization only, the joint optimization of parcel allocation and crowd-routing reduces the total cost by 32%. • A joint optimization problem of parcel allocation and crowd routing is proposed. • A route-based set partitioning model is formulated. • An efficient data-driven column generation method is developed to solve the model. • Extensive numerical experiments are conducted. [ABSTRACT FROM AUTHOR]

We study a two‐stage resource pooling problem with multiple resources and customers. The central decision‐maker decides the capacity level of the resources within a total budget before the realization of uncertain demand. Then, the fulfillment policy is determined by individual service‐level requirements. We use a robust satisficing framework to formulate the problem and allow ambiguity in the distribution of demand. Moreover, we introduce a new utility‐based probability distance allowing the model to be solved exactly using a column and constraint generation algorithm. We also provide a more efficient solution method for some special cases. Finally, we conduct experiments for a process flexibility problem, which is an example of the resource pooling problem. We show the advantage of our model over some benchmark approaches, and show the impact of the flexibility structure and correlation between demands. [ABSTRACT FROM AUTHOR]

In this article, the Resource Constrained Clustered Shortest Path Tree Problem is defined. It generalizes the classic Resource Constrained Shortest Path Tree Problem since it is defined on an undirected, complete and weighted graph whose set of nodes is partitioned into clusters. The aim is then to find a shortest path tree respecting some resource consumption constraints and inducing a connected subgraph within each cluster. The main support and motivation for studying this problem are related, among the others, to the design of telecommunication networks, and to Disaster Operations Management. In this work, we present a path‐based formulation for the problem, addressing the case of local resource constraints, that is, resource constraints on single paths. For its resolution, a Branch&Price algorithm featuring a Column Generation approach with Multiple Pricing Scheme is devised. A comprehensive computational study is conducted, comparing the proposed method with the results achieved by the CPLEX solver, adopted to solve the mathematical model. The numerical results underline that the Branch&Price algorithm outperforms CPLEX, both in terms of solution cost and time. [ABSTRACT FROM AUTHOR]

At an airport, the flights should be attached to the gates to embark or disembark the passengers. The airport gate assignment problem concerns the efficient utilization of gates by assigning flights to the gates according to the flights' planned schedules. However, due to ever-increasing air traffic demands and unpredictable weather conditions, it is hard to expect that the flights strictly follow the planned schedules. Therefore, establishing a robust gate assignment plan against uncertain flight schedule deviations is crucial for airport operators. However, ensuring the robustness of the plan by imposing too long idle times of gates may deteriorate the efficiency of gate usage. To address the trade-off between two goals, we introduce an overlap chance-constrained airport gate assignment problem that limits the probability of an overlap occurrence of flight schedules for each gate to given thresholds while maximizing the sum of preference values of flights for gates. We propose a network-based integer programming model for this problem, estimating the probability distribution using the historical flight arrival/departure deviation data. Then, we strengthen the model using the concept of gate assignment patterns, and a branch-and-price algorithm is devised to solve the model. A labeling algorithm-based efficient column generation algorithm is developed, further accelerated by clustering gates with similar characteristics. Through computational experiments, we demonstrate the efficiency of the proposed algorithm, and the trade-off between the overlap occurrence probability and the preference is analyzed using real-life instances. • Studies the airport gate assignment problem under uncertain flight schedules. • Proposes a chance-constrained MIP model to establish a robust assignment plan. • Proposes an estimation method for the probability of overlap of flight schedules. • Devises an efficient branch-and-price algorithm to solve the MIP model. • Demonstrates the effectiveness and efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

In 2005 Avella and Vasil'Ev [2] presented an efficient cutting plane algorithm for solving an integer binary programming formulation of the university course timetabling problem (UCTP). Here, we present a new and efficient adjustment of the branch and price algorithm for solving the same formulation of UCTP. In every iteration of the branch and price algorithm, the column generation algorithm is used for solving the linear programming relaxation. For the first time, in this paper the set packing constraints of the UCTP formulation are chosen as the specially structured constraints of the column generation algorithm. Then, a new efficient two phase heuristic method is presented for solving the set packing problem. The resulting adjusted column generation is used within a branch and price algorithm and a comparison is performed with the cutting plane algorithm presented by Avella and Vasil'Ev. The numerical results show that the computing time of the presented branch and price algorithm is always less than that of branch and cut algorithm. Moreover, the number of subproblems and master problems of the presented branch and price algorithm depends on the structure of the problem. Finally, for all test instances the number of variables is very large that justifies the use of the branch and price algorithm for solving the problem. [ABSTRACT FROM AUTHOR]

Green container terminals have gained much attention to satisfy the demand for sustainable and environmentally friendly transport. As one of the major polluters in container terminals, rubber-tyred gantry cranes have already been widely replaced by electric rubber-tyred gantry cranes (ERTGs). This article exploits the features of ERTGs and studies the ERTG scheduling problem in container terminal yards considering the carbon dioxide emissions and task delays simultaneously. The problem is converted into a selective vehicle routing problem with soft time windows (SVRPSTW) and formulated as a mixed integer linear programming model. A column generation algorithm embedded in a branch-and-bound framework is employed to solve the problem. A hybrid acceleration strategy combining the label-setting algorithm with a tabu search algorithm is proposed. Finally, the proposed method is validated via computational experiments. The proposed method provides an efficient tool for carbon-efficient scheduling of ERTGs and thus contributes to the development of green ports. [ABSTRACT FROM AUTHOR]

To solve the mismatch between the supply and demand of shared electric vehicles (SEVs) caused by the uneven distribution of SEVs in space and time, an SEV relocating optimization model is designed based on a reward mechanism. The aim of the model is to achieve a cost-minimized rebalancing of the SEV system. Users are guided to attend the relocating SEVs by a reward mechanism, and employees can continuously relocate multiple SEVs before returning to the supply site. The optimization problem is solved by a heuristic column generation algorithm, in which the driving routes of employees are added into a pool by column generation iteratively. In the pricing subproblem of column generation, the Shuffled Complex Evolution–University of Arizona (SCE–UA) is designed to generate a driving route. The proposed model is verified with the actual data of the Dalian city. The results show that our model can reduce the total cost of relocating and improve the service efficiency. [ABSTRACT FROM AUTHOR]

—To copy with the peak valley difference and peak load problem of power distribution network (PDN), this paper proposes a distributionally robust planning model for PDN considering the flexible management via the multi-energy station (MES) based integrated demand response (IDR). The planning covers reinforcement of the existing substation and feeders as well as the investment of MES and IDR. The IDR involves the incentive interruptible load response (ILR), transferable load response (TLR) and price-based power-gas substitution (PGS) which is implemented on MES. The MES integrates multiple energy storages and energy coupling devices, which is served as a platform for PDN operator to centrally track the final demand and improve the response potential of IDR. The proposed planning method aims at minimizing the present value of PDN investment cost and operation cost during the planning period. To handle the uncertainty of PDN end-use loads, a two-stage Kullback–Leibler divergence (KLD)-based distributionally robust optimization (DRO) planning model is formulated. Finally, the columns and constraints generation algorithm is utilized to solve the KLD-DRO planning model. Case studies are carried out on a practical 152-bus urban distribution system to validate the effectiveness of the proposed methodology and quantitatively analyze the key influence factors of PDN investment. • The multi-energy station based integrated demand response is carried out. • The incentive interruptible load, transferable load and price-based power-gas substitution are all considered. • A KL divergence-based distributionally robust planning model is formulated. [ABSTRACT FROM AUTHOR]

This paper proposes a bi-level robust planning model to address the rational configuration of a hydrogen energy system, accounting for the impact of wind power uncertainty in an integrated electricity–heat–hydrogen energy system (IEHHES) with the increasing wind power penetration. The upper-level problem aims to determine the capacity of the hydrogen energy system in this system, whereas the lower-level problem is formulated as a two-stage robust optimization model to simulate the typical daily operational scheme of the system, considering uncertain wind turbine output and the on/off switching of devices. This model considers multiple hydrogen utilization modes and the physical characteristics of various hydrogen storage tanks. The complex bi-level robust model is intractable directly. Therefore, this bi-level robust planning model is initially decomposed into planning and operation subproblems. These subproblems are then can be solved in parallel using the alternating direction method of multipliers (ADMM) algorithm; the planning subproblem, a quadratic programming model, is solved using a commercial solver; the operating subproblem, a two-stage robust optimization model, is solved using the column and constraint generation algorithm. Finally, case studies validate the advantages and effectiveness of the developed model and algorithm. • A novel bi-level robust model is proposed to plan the hydrogen energy system for IEHHES. • A method for solving a bi-level robust model based on ADMM and C&CG algorithm is proposed. • A two-stage robust lower-level model considering wind power uncertainty is proposed. • Multimode utilization of hydrogen and hydrogen physical characteristics is considered. • Test results validate the advantages and effectiveness of the developed model and method. [ABSTRACT FROM AUTHOR]

• A flexible uncertainty subset for high-correlation and multi-peaked distribution uncertainty is established. • A two-stage robust optimization model based on scenario clustering for the PVC production is proposed. • The effectiveness of proposed method is demonstrated with a PVC case study. In this paper, a data-driven robust optimization method based on scenario clustering is proposed for addressing energy consumption uncertainty characterized by correlation and multi-peaked distribution within the PVC production process. Firstly, principal component analysis (PCA) and kernel density estimation (KDE) methods are used to capture the correlation and distribution information effectively across multidimensional uncertain parameters; then a modified K-means clustering method based on density peaks is applied to cluster energy consumption scenarios and the flexible uncertainty subsets is established. A two-stage robust optimization model for the vinyl chloride production section is then proposed, and the column and constraint generation algorithm is applied to solved. Finally, the effectiveness of the proposed method is validated through a PVC production case study. Comparative results demonstrate that the proposed model reduces energy consumption under uncertainty and improves the robustness of PVC production scheduling. [ABSTRACT FROM AUTHOR]

• A public transit accessibility under heat exposure model is studied with time-dependent consideration. • A column generation method to urban rail-bus-walk service network integration is devised. • Experiments in Beijing show the impact of heat exposure on public transit accessibility. The evolution of urban transportation systems is increasingly driven by the integration of rail, bus, and walking pathways, forming a cohesive service network. This urban rail-bus-walk service network integration is pivotal in addressing urban challenges and ensuring seamless mobility. Nevertheless, the effectiveness of such integrated systems depends on their accessibility and the willingness of individuals to take them as their primary transportation mode. In the context of climate change, extreme heat events pose an increasing threat to passenger comfort and health, which in turn, affects individuals' decisions to use public transit. Additionally, walking to transit stops or waiting for transportation becomes more challenging during such extreme heat conditions. This paper tackles the challenge of comprehensively addressing the evolving issues related to public transit accessibility in response to rising temperatures, an area of research that has received limited attention until now. This paper introduced an approach aimed at optimizing the urban rail-bus-walk service network with a focus on both accessibility and heat exposure considerations. By calculating the transportation accessibility level under varying temperature conditions and identifying its vulnerability to high temperatures, this paper presents a methodology to enhance the transit service. Such improvement involves not only adjustments to the integration network but also considering of cooling facilities, such as shaded routes and shelters. Column generation is applied to solve this problem and the optimization result demonstrates improvement of accessibility under the extreme heat condition. [ABSTRACT FROM AUTHOR]

Hydrogen is called to be one of the most important energy vectors in future energy systems. Nowadays, its use in the industry sector is prominent, finding multiple applications in fertilizer production or oil refining. In this sense, some industry sectors demand a considerable amount of hydrogen for their processes. In many cases, hydrogen must be purchased externally, which supposes a challenge due to hydrogen transportation is costly and few efficient. In this context, local hydrogen production through mature electrolysis technology may suppose an attractive alternative in industrial parks. This paper focuses on this topic, in particular, a risk-averse electrolyser sizing methodology is developed. The new approach accounts for uncertainties in electricity prices as well as local renewable generation and demand through an original hybrid stochastic-robust model. The developed uncertainty modelling is integrated into a novel four-level optimization framework, whose main result is the optimal electrolyser rated power. To efficiently attain the solution, an original hybridization of the Benders' decomposition and the Column and Constraint Generation Algorithm is proposed. The developed methodology results efficient in an illustrative three-industry park, showing that installing local hydrogen generation may reduce the amount of hydrogen purchased externally (by 38%) and project costs by 2.5%. Furthermore, increasing the robustness level leads to increase the project cost by 8%, while assuming unfavourable realization of uncertainties. Moreover, the developed tool is further validated in larger parks, involving an increasing number of industries, showing that the proposed methodology scales well with the size of the park. • A novel risk-averse methodology for electrolyser sizing is developed. • The new tool is conceived for industrial parks but adaptable to other systems. • Project costs can be reduced by 2.5% when local hydrogen production is enabled. • The robustness level impacts incrementing the total expenditures by 8%. • The developed methodology scales well with the size of the system. [ABSTRACT FROM AUTHOR]

As traditional fossil energy sources such as coal cause serious environmental pollution, it is a major trend to promote the construction of a 'clean' power system with new energy sources as the mainstay. However, the uncertainty of intermittent energy output and its high proportion of grid connection bring challenges to the scheduling operation of the power system. In this paper, the authors propose a two‐stage robust dispatching strategy for the combined wind‐photovoltaic‐fired‐pumped storage system to improve the capacity of renewable energy (RER). The outer layer of the model is based on minimizing the start‐stop cost of thermal power units to obtain the start‐stop scheme of thermal power units, and the inner layer of the model integrates the system operation cost, pollutant emission cost, deviation penalty, and other constraints of wind power and PV output to obtain the dispatching scheme with the lowest overall operation cost under the worst scenario of wind power and PV fluctuation. The model is solved alternatively by column constraint generation algorithm (C&CG) and strong pairwise theory. The feasibility and effectiveness of the proposed method was verified based on the improved 30‐machine test system as an example. [ABSTRACT FROM AUTHOR]

To solve the mismatch between the supply and demand of shared electric vehicles (SEVs) caused by the uneven distribution of SEVs in space and time, an SEV relocating optimization model is designed based on a reward mechanism. The aim of the model is to achieve a cost-minimized rebalancing of the SEV system. Users are guided to attend the relocating SEVs by a reward mechanism, and employees can continuously relocate multiple SEVs before returning to the supply site. The optimization problem is solved by a heuristic column generation algorithm, in which the driving routes of employees are added into a pool by column generation iteratively. In the pricing subproblem of column generation, the Shuffled Complex Evolution--University of Arizona (SCE-UA) is designed to generate a driving route. The proposed model is verified with the actual data of the Dalian city. The results show that our model can reduce the total cost of relocating and improve the service efficiency. [ABSTRACT FROM AUTHOR]

With the rise of smart cities, relevant passenger data can be collected to improve the quality of transport services. In this article, a demand‐responsive feeder service is presented. A feeder service transports passengers from a low‐demand area, like a suburban area, to a transportation hub, like a city center. The feeder service modeled in this article considers two sets of bus stops: mandatory stops and optional stops. Mandatory stops are always visited by a bus, while optional stops are only visited when a client nearby makes a request for transportation. This gives the service both flexibility and some predictability. To optimize the performance of the service, mathematical modeling techniques to improve the model's runtime are developed. It is concluded that a combination of column generation and the separation of sub‐tour elimination constraints decreases the computing time of small and midsize instances significantly. [ABSTRACT FROM AUTHOR]

Convex hull pricing is a well-documented method for coping with the non-existence of uniform clearing prices in electricity markets with non-convex costs and constraints. We revisit primal and dual methods for computing convex hull prices, and discuss the positioning of existing approximation methods in this taxonomy. We propose a dual decomposition algorithm known as the Level Method and we adapt the basic algorithm to the specificities of convex hull pricing. We benchmark its performance against a column generation algorithm that has recently been proposed in the literature. We provide empirical evidence about the favorable performance of our algorithm on large test instances based on PJM and Central Europe. [ABSTRACT FROM AUTHOR]

Nowadays, with the rapid development of hydrogen powered vehicles, the demand for hydrogen refueling stations (HRSs) in the transportation field is growing. The renewable energy, e.g., wind energy, is used to produce and store hydrogen on site for HRSs, which may be a relatively cheap and clean solution. Considering the wind farm (WF) and HRSs belong to different entities, a new cooperative operation model of the WF-HRSs combined system is proposed. Specifically, the robust optimization methods are implemented to characterize the uncertainties of wind power and market electricity price, respectively, to alleviate risk. To ensure the fairness of profit allocation, the bargaining power is measured by various contribution levels of each stakeholder based on the Nash–Harsanyi bargaining game theory. Furthermore, the model is transformed into two sequential subproblems: energy trading problem (SP1) and the payment bargaining problem (SP2). Accordingly, a solving technique adopting column and constraint generation algorithm is provided to solve the SP1. In addition, for the sake of privacy protection, a distributed approach based on data-centric mode is developed to solve SP2. Finally, the numerical results can validate the effectiveness and scalability for the proposed scheme and algorithms. [ABSTRACT FROM AUTHOR]