Robust Scheduling Research Articles

Network-based two-stage robust scheduling strategy for the aircraft assembly system with uncertain duration

Improving the flexibility and robustness of scheduling strategies is crucial for timely delivery of aircraft in dynamic environments. However, with the large scale and frequent disturbances of aircraft assembly operations, conventional dynamic scheduling methods face more difficulty in solving the aircraft assembly scheduling problem with duration uncertainty, especially in analyzing the job duration error transfer characteristics and achieving inverse scheduling optimization. Therefore, this paper proposes an efficient network-based two-stage robust scheduling strategy. Firstly, with the help of network theory, we study the heuristic information about global propagation characteristics of job duration fluctuation and identify the key jobs with high influence of duration error diffusion. Secondly, the dynamic scheduling of aircraft assembly is transformed into a two-stage scheduling with resource-constrained project scheduling and inverse scheduling with resource reallocation for flexible durations. The network-based two-stage robust scheduling strategy achieves scheduling jobs to comply with precedence and resource constraints based on an improved genetic algorithm in the first stage, and the inverse optimization of resource reallocation based on network-based hybrid non-dominated sorting genetic algorithm-II after disturbances in the second stage. Finally, the effectiveness of the strategy is verified on the benchmark from the project scheduling problem library and aircraft assembly data. The experiments show a significant improvement in the performance of key job identification and scheduling in aircraft assembly. Our study provides an efficient scheduling solution for implementing complex aircraft assembly systems with uncertain durations.

Robust Scheduling of Multi-Skilled Workforce Allocation: Job Rotation Approach

This paper addresses scheduling challenges in software development organizations, specifically focusing on a novel version of the software project scheduling problem (SPSP). This enhanced model incorporates the dynamics of learning and forgetting phenomena, crucial in maintaining employee competencies, particularly when unexpected events such as absenteeism or shifts in project priorities occur. The paper introduces a new declarative reference model for SPSP, aimed at proactively managing the assignment of versatile programmers to tasks within an portfolio of IT projects, while considering the effects of forgetting. Implemented within a constraints programming environment, this model facilitates decision making in project management for software companies. It serves to find feasible solutions and identify conditions necessary to meet specified expectations. The effectiveness of the proposed SPSP model is demonstrated through numerical examples.

Proactive scheduling for steel plants with unrelated parallel machines and time uncertainty

This paper deals with the steel plant proactive scheduling problem with unrelated parallel machines and time uncertainty to enhance the rationality of machine assignment and processing path, improve the schedule robustness and guarantee capability of energy. First, a scheduling model is formulated with the objectives of average process time, matching degree and oxygen consumption fluctuation. Then, an improved preference-based NSGA-II is designed to solve the problem. The algorithm introduces the preference information into the optimization process and designs an individual sorting method based on the technique for order preference by similarity to ideal solution (TOPSIS) to guide the evolution direction. Besides, to improve the local search ability, variable neighborhood search is incorporated to generate new solutions with high quality. Computational experiments prove that the algorithm can effectively address the proactive scheduling problem. The sensitivity analysis and results of different scheduling models verify the robustness and superiority in machine matching and energy synergy of the model.

A novel demand response-based distributed multi-energy system optimal operation framework for data centers

To address the increasing energy demands in data centers, distributed multi-energy system (DMES) can provide an efficient solution. This study proposes a DMES coupled by photovoltaics, wind turbines, ground source heat pump, internal combustion engines, electric chillers, absorption chillers, and energy storage device. The optimal scheduling of DMES with source-load interaction plays a crucial role in improving the performance of data centers. To achieve this, an integrated demand response (IDR) strategy is established, considering time-of-use pricing and renewable energy peak subsidies. Then, a clean and economical optimal operation model for DMES based on proposed IDR strategy and carbon trading mechanisms is established. Furthermore, to enhance the robustness of scheduling, this study analyzes the impacts of uncertainties in renewable energy output and demand response on DMES operation using the Monte Carlo method and interval method. Case study results demonstrate that the proposed IDR strategy increases electricity and cooling loads while reducing heat loads during the peak period of renewable energy generation, compared to the traditional IDR strategy. The proposed scheduling model, which incorporates the proposed IDR strategy and carbon trading mechanism, improves data center performance by reducing total costs by 1.85%, carbon emissions by 0.56%, electricity purchases by 2.93%, while increasing renewable energy utilization by 0.77%. The results also highlight the critical role of energy storage devices, with an optimal initial charge state is 0.5. Additionally, optimization considering multiple uncertainties, results in higher total costs and broader interval widths compared to single-factor uncertainty optimization, but reduces system operational risk.

Reliable and robust scheduling of airport operation resources by simulation optimization feedback and conflict resolution

Reliable and robust airport flight ground service resources collaborative scheduling has emerged as an issue of major concern at congested airports, which has great significance on airport service quality and operation efficiency. Due to the uncertainty of the service process of multiple vehicles in airport ground operations, the combination of simulation and optimization (sim-opt) techniques has been proven to be an effective means to solve the collaborative scheduling problem. However, existing models still have limitations on the reliability of feasible solutions and the robustness of evaluations. In this work, we developed a conflict resolution based sim-opt framework that combines the search capability of mathematical optimization models with the ability of simulation models to describe uncertainty. The dynamic window is introduced to divide the flight zone into multiple sub-intervals, which allows for iterative search and evaluation of the optimal schedule solution while reducing model calculation time. Additionally, a matching algorithm based on slack and tight constraints is proposed to optimize the possible resource requirements of each vehicle, thereby improving the initial schedule solution’s search depth and reliability. Furthermore, a conflict resolution feedback mechanism between adjacent windows is constructed to optimize the scheduling plan, reducing misjudgment and omission of the optimal solution and enhancing the sim-opt framework’s robustness. Finally, experiments on real airport datasets of three different scales demonstrate that our proposed method efficiently allocates resources with a smaller flight delay time as well as reducing total vehicle cost time during the flight ground service process.

An Analytical Feasibility Condition for The Multi-stage Robust Scheduling of Energy Storage Systems with Application on SCUC

An Analytical Feasibility Condition for The Multi-stage Robust Scheduling of Energy Storage Systems with Application on SCUC

Robust Scheduling of a Hybrid Hydro/Photovoltaic/Pumped-Storage System for Multiple Grids Peak-Shaving and Congestion Management

Robust Scheduling of a Hybrid Hydro/Photovoltaic/Pumped-Storage System for Multiple Grids Peak-Shaving and Congestion Management

Robust scheduling of virtual power plant with power-to-hydrogen considering a flexible carbon emission mechanism

Robust scheduling of virtual power plant with power-to-hydrogen considering a flexible carbon emission mechanism

Integration of mobile power-hydrogen storage systems in distribution-level networks: A fuzzy information gap optimization framework

In recent years, renewable energy sources (RESs) have had unquestionably significant benefits. However, maximum penetration of RESs has always been challenging due to their intermittent nature. To address this challenge, this study advances a framework for the flexibility of the distribution network (DN) by employing transportable electrical storages (TESs) and transportable hydrogen storages (THSs). To do so, the TESs are considered to transfer electrical energy among high-penetrated and high-demand points. In addition, curtailed renewable power can be converted to green hydrogen and transferred to hydrogen refueling stations (HRSs) using the THSs. To further flexibility, this work considers an incentive-based demand response (DR) program and vehicle-to-parking lot (V2PL) capable plug-in electric vehicles (PEVs). Moreover, a binary-based method is developed to carry out the trajectory planning of the TESs and THSs and the Floyd algorithm is exploited to minimize traveling and simulation time. Furthermore, the fuzzy information gap decision theory (IGDT) is proposed to enhance the scheduling robustness against the uncertainty of RESs. The obtained results corroborated the positive impact of the TESs and THSs by declining the operation cost by about 4.8 %. Moreover, the proposed uncertainty management model is quite robust against RESs’ uncertainty by achieving about 37.5 % less operation cost.

Robust job shop scheduling with machine unavailability due to random breakdowns and condition-based maintenance

This paper presents a novel solution approach for a variant of the job shop scheduling problem with machine unavailability due to both condition-based preventive maintenance and corrective maintenance following random breakdowns. We first provide an exact mathematical formulation of the problem under simplifying assumptions, namely that the number of breakdowns for each job position on each machine is known, the degradation rates are fixed, and the preventive and corrective maintenance durations are deterministic parameters. Moreover, to handle the more realistic case of stochastic machine degradation, random breakdowns, and uncertain maintenance durations, a simulation-optimisation algorithm is proposed. The real makespan function is first approximated using multiple surrogate measures, which are optimised through independent genetic algorithms. Then, the fittest solutions obtained from these surrogate measures are simulated, and the best among them is added to an elite list, which is included in the genetic algorithms' populations for the next iteration. Schedule robustness is ensured by using an objective function that consists of the weighted average of the expected makespan and its 90th percentile. Furthermore, to reduce the likelihood of falling into a local optimum, a stopping criterion based on simulated annealing is implemented. Numerical experimentation on extended benchmark instances confirmed the validity of the mathematical formulation and the favourable performance of the proposed simulation-optimisation algorithm in terms of computational time and solution quality.

Robust multi-equipment scheduling for U-shaped container terminals concerning double-cycling mode and uncertain operation time with cascade effects

The integrated scheduling of quay cranes, internal vehicles, and yard cranes in container terminals aims to improve port operations and often requires scheduling robustness under uncertainty with cascade effects. In container terminal operations, uncertainty in equipment operating time poses challenges to effective scheduling, as even small fluctuations can create cascade effects throughout the operations, rendering the original schedule ineffective. This research aims to develop a new method that enables a balance between optimization and robustness in container terminal scheduling. Additionally, the double-cycling operation mode and U-shaped port layout, known for their improved efficiency in container terminals, are gaining increasing attention and hence are incorporated into this study. It creates a three-stage hybrid flow shop scheduling problem with bi-directional flows, waiting time, and uncertain operation time. To address the complex problem, a mixed integer programming model is proposed to characterize the integrated scheduling problem, and an index based on complex network structure entropy is designed to evaluate the anti-cascade effect as well as the robustness of the schedule. The index and makespan serve as the bi-objectives, transforming the original problem into a bi-objective optimization one. The non-dominated sorting genetic algorithm-Ⅱ with appropriate coding and decoding rules is utilized to solve the model and obtain a set of Pareto frontier solutions. The feasibility of the new method is verified through a real case analysis. Specifically, comparative analysis with basic stochastic programming, basic robust optimization, triangular fuzzy programming, and maximum gap method are used to demonstrate the effectiveness of the new method. The paper also provides insightful practical implications for port managers, and the genericity of the method could also contribute to its practical values spreading to a wider scope of beneficiaries, such as manufacturing warehousing and distribution management.

Strategies for electric vehicle bidding in the German frequency containment and restoration reserves market

Germany's transition to renewable energy sources for a sustainable future has introduced variability and instability in the national power grid, thus necessitating innovative solutions to ensure grid stability and reliable energy supply. The integration of electric vehicles (EVs) in the German balancing market, notably within the frequency containment reserve and automatic frequency restoration reserve sectors, is a potential stabilizing force. However, the complexity of this integration, governed by specific rules in the German energy sector, has not been fully explored. To bridge this gap, a robust schedule that maximizes the economic viability and reliability of EV integration by considering critical elements such as uniform product size, alignment with local market product duration, and customer baseline load is proposed in this study. Mixed-integer linear programming is used for the effective integration of EVs in the German balancing market. This framework emphasizes computational efficiency, providing market participants with precise insights into EV behavior and strategies for energy storage optimization. The effectiveness and reliability of the proposed method are substantiated through case studies. The proposed method consistently achieved maximum profit and a significant reduction in the number of failed cases, which underscores its applicability in real-world scenarios.

Two-stage robust scheduling and real-time load control of community microgrid with multiple uncertainties

With the increasing popularity of wind and solar generation, the stable and economic operation of the community microgrid system become more challenging. This paper is concerned with the robust scheduling and real-time control of demand response (DR) air conditioning (AC) loads for community microgrid. Firstly, a two-stage robust scheduling model coupled by the day-ahead dispatch and real-time dispatch is established by considering the uncertainties of wind/photovoltaic power generation and loads. Moreover, the incorporation of multiple interval uncertain sets is introduced to characterize the uncertainties related to wind power, photovoltaics, and load, thereby reducing the conservativeness of the model. Secondly, the real-time control of AC loads by adjusting the on/off actions and temperature setpoints with limited impact on user comfort so as to track the optimized electricity consumption curve. Finally, the simulation results show the effectiveness and robustness of the proposed optimization dispatch and real-time control algorithm.

Graph-Based Deadlock Analysis and Prevention for Robust Intelligent Intersection Management

Intersection management systems, with the assistance of vehicular networks and autonomous vehicles, have potential to perform traffic control more precisely than contemporary signalized intersections. However, as infrastructural intersection management controllers do not directly activate motions of vehicles, it is possible that the vehicles fail to follow the instructions from controllers, undermining system properties such as deadlock-freeness and traffic performance. In this paper, we consider a class of robustness issues, the time violations, which stem from possible discrepancies between scheduled orders and real executions. We refine a graph-based intersection model to build our theoretical foundations and analyze potential deadlocks and their resolvability. We develop solutions that mitigate negative effects of time violations. Particularly, we propose a Robustness-Aware Greedy Scheduling (RGS) algorithm for robust scheduling and evaluate the deadlock-free robustness of different intersection models and scheduling algorithms. Experimental results show that the RGS algorithm is able to significantly improve robustness and keep a good balance with traffic performance.

Robust scheduling in a two-machine re-entrant flow shop to minimise the value-at-risk of the makespan: branch-and-bound and heuristic algorithms based on Markovian activity networks and phase-type distributions

Robust scheduling in a two-machine re-entrant flow shop to minimise the value-at-risk of the makespan: branch-and-bound and heuristic algorithms based on Markovian activity networks and phase-type distributions

A bi-objective optimization for finance-based and resource-constrained robust project scheduling

Numerous finance-based projects encounter disturbances from a variety of uncertain factors during their execution, under which both the original baseline schedule and financing alternative become infeasible. However, many previous studies on the finance-based project scheduling problem (FBSP) neglected a potential feature of stochastic activity durations. In this paper, we address the issue of generating a robust project schedule that not only satisfies financing credit and renewable resource limits, but also tackles disruptions due to activity uncertainty. A bi-objective model for finance-based and resource-constrained robust project scheduling problem (FBRCRPSP) is constructed, where the trade-off between profit and robustness is considered. Based on the transformed integer programming model, an exact procedure of ε- constraints is proposed to obtain Pareto-optimal solutions for small-sized instances. For large-scale projects, a non-dominated sorting genetic algorithm with local search (NSGA-II-LS) that deeply explores the neighboring solution space is developed, in which a generic procedure with two new recursion policies is proposed to determine the robustness of schedules. Benchmarking is conducted to evaluate the efficiency of the algorithms via some performance criteria. The results show that all developed approaches have good performance in small-sized instances, and the NSGA-II-LS outperforms the non-dominated sorting genetic algorithm without local search (NSGA-II) in terms of the spread, convergence, and diversity of Pareto-optimal solutions significantly. In addition, some managerial insights are summarized to enlighten project managers.

Capacity Value Assessment for a Combined Power Plant System of New Energy and Energy Storage Based on Robust Scheduling Rules

With the rapid increase in new energy penetration, the uncertainty of the power system increases sharply. We can smooth out fluctuations and promote the more grid-friendly integration of new energy by combining it with energy storage. This paper proposes an evaluation method for assessing the value of a combined power plant system of new energy and energy storage using robust scheduling rules. Firstly, the k-means clustering algorithm is improved by using the elbow method in order to generate typical scenarios that can be used for the operation optimization of the combined power plant system of new energy and energy storage. Then, a two-stage robust optimization model of the combined power plant system of new energy and energy storage with a min–max–min structure is constructed according to the uncertainty of new energy. In this model, the operation constraints and coordinated control of wind–solar–thermal–storage units are considered. By constructing the uncertainty set of the new energy output, the overall operating cost of the system is minimized and uncertainty adjustment parameters are introduced to flexibly adjust the conservatism of the scheduling rules. Furthermore, based on the column and constraint generation algorithm and strong duality theory, the original problem can be decomposed into a master problem and subproblems with mixed integer linear characteristics for an alternating solution, so as to obtain the optimal solution of the original problem, and finally obtain the robust scheduling rule with the lowest operating cost under the worst scenario. Finally, based on the wind and solar power output curves and the output of each unit under the robust scheduling rules, combined with the value estimation method of the combined power plant system of new energy and energy storage, the value of the combined power plant system of new energy and energy storage is evaluated. Through the establishment of models and example analysis, it is proven that raising the quantity of the grid-connected power generated with new energy will cause an increase in the volatility of the power system; it will also bring considerable benefits to new energy plants, and the energy storage can improve the stability of the system. The above can provide references for the subsequent energy storage configuration in the planning of a combined power plant system of new energy and energy storage.

An advanced hyperheuristic approach for the home health care scheduling problem with time window in deterministic and uncertain environments

In the last two decades, Home Health Care (HHC) services have garnered substantial attention from global researchers and practitioners. These services face significant challenges related to strategic, tactical, and operational decisions that must be solved for enhancing their efficiency and quality. Notably, researchers have focused significantly on the scheduling and routing aspects, recognizing their potential to enhance patient satisfaction, safety, and cost-effectiveness for both patients and HHC companies. Recent studies have highlighted the stochastic nature of these services, including random service and travel times, that may affect the scheduling and routing components. Nonetheless, a significant portion of recent research predominantly focuses on the deterministic version of the problem, disregarding its fundamental stochastic nature as emphasized by feedback from HHC companies. Within this context, we propose a two-stage mixed integer mathematical formulation to address the Home Health Care Scheduling and Routing Problem (HHCSRP), encompassing stochastic demand, service, and travel times. Given the inherent Nondeterministic Polynomial (NP)-hardness of these scheduling and routing problems, we introduce a hyperheuristic approach based on a TS metaheuristic and Variable Neighborhood Search (VNS) heuristic. Extensive experiments validate the effectiveness of our proposed modeling and solving approaches, outperforming similar methods across various metrics. Notably, our stochastic model exhibits superior performance in terms of parameters like the number of patients served within time windows and computational time required to achieve optimal solutions. This study thus contributes a valuable decision support system for Home Health Care companies, empowering them to make informed decisions and construct robust schedules for their caregivers.

Adaptively optimal energy management for integrated hydrogen energy systems

AbstractIntegrated hydrogen energy systems (IHESs) have become attractive alternatives to cope with the depletion of fossil fuels and increasingly severe climate change problems. This paper proposes an adaptively optimal energy scheduling method based on deep deterministic policy gradient (DDPG) to improve the operational efficiency of IHES. The optimal scheduling problem is formulated as a Markov decision process problem with action space, environmental states, and action‐value function. The DDPG‐based optimal energy management algorithm with actor‐critic structure is proposed based on policy gradients and neural networks. Through actor‐critic network training and policy iteration, the energy management scheme can be adaptively optimized according to the dynamic responses of IHES. The benefits of the proposed algorithm are analysed through time‐domain simulations, and the scheduling robustness under different uncertain conditions is verified.

Medium- and long-term interval optimal scheduling of cascade hydropower-photovoltaic complementary systems considering multiple uncertainties

An effective way to promote the consumption of renewable energy resource generation is by forming a joint power supply system between photovoltaic (PV) power plants widely distributed along a river basin and large-scale cascade hydropower plants, using shared transmission lines to transmit power to the power grid system. However, renewable energy resource generation has significant prediction uncertainty and can flood into the power grid, which is detrimental to its safe and stable operation. To solve the above issues, this paper proposes an improved interval optimization method to model the uncertainties of the inflow runoff of a cascade hydropower plant and the photovoltaic power output. On this basis, a medium- and long-term interval optimization scheduling model is established for a cascade hydro-PV complementary system based on extreme scenarios. This model does not need to obtain an accurate probability density distribution for renewable energy, and can realize the overall optimization of runoff-PV uncertainty scenarios within a certain range, taking into account the economy and robustness of system operation. In order to ensure the solution efficiency, the original model is transformed into a mixed integer linear programming (MILP) model by a variety of deterministic transformation methods and linearization techniques. The case study shows that: 1) Under the premise that the system power output is relatively stable, the power curtailment of the interval optimized scheduling scheme proposed in this paper is reduced by 47.5% compared with the robust scheduling scheme. The ability to cope with extreme scenarios is also significantly improved compared with the deterministic scheduling scheme. 2) There is a game relationship between the robustness and economy of the obtained scheduling scheme. When the fluctuation interval width of random variables increases from 20% to 30% and 40%, the corresponding total power generation decreases by 2.4% and 4.7%, respectively. 3) A large penalty factor is conducive to reducing the amount of abandoned hydropower, but in general, the penalty factor and ecological flow level have no obvious influence on the dispatching results, and the values of both can be reasonably determined according to the actual operation requirements.