Robust Scheduling Research Articles

Optimal scheduling of virtual power plants with reversible solid oxide cells in the electricity market

Virtual power plants (VPP) can act as an independent entity to aggregate different distributed resources to participate in the electricity market, which is an inevitable trend in building green and low-carbon power systems. To investigate the beneficial effect of bi-directional electric-hydrogen conversion on market trading and optimal scheduling of VPP, this paper presents an optimal scheduling method for VPP with reversible solid oxide cells (RSOC) in the electricity market. Firstly, according to the Butler-Volmer equation and Faraday law, the relationship between the hydrogen flow rate and the electric power is established, and the equivalent physical models of the two RSOC working modes are developed based on the relationship. Then, the optimal scheduling model of the VPP participating in the energy and reserve joint market is proposed based on the two-stage robust optimization theory. The system operator reserve demand is used to describe the uncertainty of the transactions between VPP and reserve market. Finally, the column and constraint generation (C&CG) algorithm is used to solve the two-stage robust scheduling model. The simulation results show that RSOC can effectively promote renewable energy consumption and improve the VPP operating profit. Where, the operating profit can be increased by 46.5 % and the wind power consumption rate can be increased by 3.4 %, compared with the non-hydrogen VPP. Furthermore, compared with the traditional conversion equipment, RSOC can increase the VPP operating profit by 2.3 % and the wind power consumption rate by 1.85 %.

EXPRESS: Distributionally Robust Appointment Scheduling That Can Deal with Independent Service Times

Consider a single server that should serve a given number of customers during a fixed period. The Appointment Scheduling Problem (ASP) determines the schedule of planned appointments that minimizes some cost function that accounts for both the cost of idle times and the cost of waiting. When service time distributions are fully specified, the ASP presents a much investigated computationally challenging stochastic program. When service time distributions are only partially specified, one can apply distributionally robust optimization (DRO) to find the schedule that minimizes costs in worst-case circumstances. We assume that only the mean, mean absolute deviation and range of the service times are known, and develop a DRO method that finds the optimal (minimax) schedule. For independent service times, the minmax problem becomes nonlinear and difficult, if not impossible, to solve exactly. Existing DRO methods for ASP with partial information (such as mean and variance) therefore consider relaxations that allow correlations between service times. Such relaxations have major repercussions, as the worst-case scenario will then be highly correlated. Our method thus deals with independent service times and finds the robust schedule as the solution to a linear program. We identify several new structural features of optimal robust schedules. We also apply the method to model extensions including sequencing and alternative objective functions.

Trade-offs between optimal and robust scheduling in one-stage production

Given stochastic disturbances, such as variation in processing times, robust scheduling is recommended over optimal scheduling for production. Different from optimal scheduling that seeks an optimal solution to a key performance indicator (KPI), which relates to the average of a KPI, robust scheduling is to minimize the largest deviation from the optimum for the worst-case scenarios, which relates to the variance of a KPI. However, minimizing the variance does not necessarily optimize the average of a KPI. As one of the fundamental KPIs in production scheduling, total completion time (TCT) drives many other KPIs, such as average flow time, waiting time, due dates, and length of stay. Stochastic processing times and NP-hardness to minimize the variance of TCT, i.e., min(VTCT), are two challenges in production scheduling. To investigate the trade-offs between optimal and robust scheduling, we apply the differentiation method to analyze the first and second moments of TCT. In our approach, we use three statistical measures for processing times, which are the lower bound, the expected value, and the upper bound. We also use three terms for sequencing, which are x(1) the processing time of the initial job, x(i) the processing time of a job in the current position i of a sequence, and x′(i) the difference of processing times between two adjacent jobs. Applying the three measures for processing times to each of the three independent terms for sequencing, we generate 27=3·3·3 sequences to analyze the dynamics of VTCT. Through numerical analysis in our case studies, we show that our sequencing scheme can generate optimal solutions to min(TCT), and solid variation ranges of VTCT. Consequently, we can not only balance the trade-offs between min(TCT) and min(VTCT), but also analyze the trade-offs between optimal scheduling focusing on the first-moment of a KPI and robust scheduling focusing on the second moment. Moreover, our analysis approach using the differentiation method is unique for production scheduling, which enables us to develop analytical methods and heuristics for balancing trade-offs between optimal and robust scheduling.

Robust scheduling of a pulp and paper mill considering flexibility provision from steam power generation

The production scheduling and flexibility provision analysis are of great importance for industrial facilities to provide support for the main power grid. This study proposes a comprehensive scheduling model for an industrial pulp and paper (P&P) mill that considers the flexibility provision from steam power generation. In this model, the internal relationships between the production and consumption of electricity, steam, and pulp in the operational processes of the P&P mill are investigated. Meanwhile, the available flexibility of steam power generation is quantified and further enhanced for participation in the manual frequency restoration reserve (MFRR) market. Furthermore, a robust scheduling model that uses support vector clustering (SVC) technology is proposed to assess the impact of uncertainties in steam temperature and pressure on the available flexibility of steam power generation, thereby reducing the probability of failing to provide the contracted flexibility for MFRR. Simulation results demonstrate that the comprehensive scheduling model significantly increases the available flexibility of steam power generation for MFRR, resulting in a daily revenue increase of $1839.8. Moreover, a balance between the revenue obtained from the MFRR market and the probability of economic penalties incurred for failing to meet the contracted flexibility is achieved by comparing different levels of conservatism in the robust scheduling model.

Two-Stage Distributed Robust Optimization Scheduling Considering Demand Response and Direct Purchase of Electricity by Large Consumers

The integration of large-scale wind power into power systems has exacerbated the challenges associated with peak load regulation. Concurrently, the ongoing advancement of electricity marketization reforms highlights the need to assess the impact of direct electricity procurement by large consumers on enhancing the flexibility of power systems. In this context, this paper introduces a Distributed Robust Optimal Scheduling (DROS) model, which addresses the uncertainties of wind power generation and direct electricity purchases by large consumers. Firstly, to mitigate the effects of wind power uncertainty on the power system, a first-order Markov chain model with interval characteristics is introduced. This approach effectively captures the temporal and variability aspects of wind power prediction errors. Secondly, building upon the day-ahead scenarios generated by the Markov chain, the model then formulates a data-driven optimization framework that spans from day-ahead to intra-day scheduling. In the day-ahead phase, the model leverages the price elasticity of the demand matrix to guide consumer behavior, with the primary objective of maximizing the total revenue of the wind farm. A robust scheduling strategy is developed, yielding an hourly scheduling plan for the day-ahead phase. This plan dynamically adjusts tariffs in the intra-day phase based on deviations in wind power output, thereby encouraging flexible user responses to the inherent uncertainty in wind power generation. Ultimately, the efficacy of the proposed DROS method is validated through extensive numerical simulations, demonstrating its potential to enhance the robustness and flexibility of power systems in the presence of significant wind power integration and market-driven direct electricity purchases.

Computing the worst-case due dates violations with budget uncertainty

We study the problem of maximizing the violation of due dates when considering either the total violation, or the number of jobs that are tardy. We consider classical completion times and a variant useful in heuristics. The four problems arise when solving (exactly or heuristically) robust scheduling problems with release and due dates/deadlines and processing time uncertainty, and also routing problems with (soft) time windows and travel time uncertainty. We provide polynomial dynamic programming algorithms for the four problems.

Impact of effective schedule management on high-rise building projects

Effective schedule management is a critical factor in the successful execution of high-rise building projects. This paper explores the impact of robust schedule management practices on project performance, highlighting the benefits, challenges, and strategies for optimizing timelines. High-rise construction presents unique complexities, including coordination of multiple trades, strict safety regulations, and logistical challenges related to vertical construction. Utilizing advanced scheduling methodologies such as Critical Chain Project Management (CCPM) and Building Information Modeling (BIM), combined with traditional techniques like the Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT), can significantly enhance project efficiency. The integration of these methodologies facilitates better resource allocation, reduces delays, and improves overall project outcomes. The study also addresses the role of technology, including project management software like Primavera P6, in enhancing schedule accuracy and reliability. Additionally, it examines the critical role of project managers in orchestrating these activities and emphasizes the importance of effective communication and risk management. This comprehensive review provides insights into the key factors that contribute to successful schedule management, offering recommendations for future research and practice to further advance the field. Keywords: Building Information Modeling (BIM), Critical Chain Project Management (CCPM), High-Rise Building Projects, Project Performance Optimization, Schedule Management.

Multi-strategy cooperative scheduling for airport specialized vehicles based on digital twins

Efficient specialized vehicle cooperative scheduling is significant for airport operations, particularly during times of high traffic, which reduces the risk of flight delays and increases customer satisfaction. In this paper,we construct a multi-type vehicles collaborative scheduling model with the objectives of minimizing vehicle travel distance and vehicle waiting time. Additionally, a three-layer genetic algorithm is designed, and the crossover and mutation operations are enhanced to address the scheduling model. Due to the numerous uncertainties and stochastic interferences in airport operations, conventional scheduling methods unable to effectively address these challenges, this paper combines improved genetic algorithm, simulation algorithm, and digital twins technology, proposing a multi-strategy scheduling framework for specialized vehicles based on digital twins. The scheduling framework utilises digital twins to capture dynamic data from the airport and continuously adjusts the scheduling plan through the scheduling strategy to ensure robust scheduling for specialized vehicles. In the event of severe delays at the airport, fast and efficient re-scheduling can be achieved. Finally, the effectiveness of the proposed scheduling framework is validated using domestic flight data, and extensive experiments and analyses are conducted in different scenarios. This research contributes to addressing the optimization problem of cooperative scheduling for multi-type vehicles at airports.

Multi-Agent Deep Reinforcement Learning-Based Inference Task Scheduling and Offloading for Maximum Inference Accuracy under Time and Energy Constraints

The journey towards realizing real-time AI-driven IoT applications is facing a significant hurdle caused by the limited resources of IoT devices. Particularly for battery-powered edge devices, the decision between performing task inference locally or by offloading to edge servers, all while ensuring timely results and conserving energy, is a critical issue. This problem is further complicated when an edge device houses multiple local inference models. The challenge of effectively allocating inference models to tasks between local models and edge server models under strict time and energy constraints while maximizing overall accuracy is recognized as a strongly NP-hard problem and has not been addressed in the literature. Therefore, in this work we propose MASITO, a novel multi-agent deep reinforcement learning framework designed to address this intricate problem. By dividing the problem into two sub-problems namely task scheduling and edge server selection we propose a cooperative multi-agent system for addressing each sub-problem. MASITO’s design allows for faster training and more robust schedules using cooperative behavior where agents compensate for each other’s sub-optimal actions. Moreover, MASITO dynamically adapts to different network configurations which allows for high-mobility edge computing applications. Experiments on the ImageNet-mini dataset demonstrate the framework’s efficacy, outperforming genetic algorithms (GAs), simulated annealing (SA), and particle swarm optimization (PSO) in scheduling times by providing lower times ranging from 60% up to 90% while maintaining comparable average accuracy in worst-case scenarios and superior accuracy in best-case scenarios.

A Hybrid Approach for the Multi-Criteria-Based Optimization of Sequence-Dependent Setup-Based Flow Shop Scheduling

A key challenge in production management and operational research is the flow shop scheduling problem, characterized by its complexity in manufacturing processes. Traditional models often assume deterministic conditions, overlooking real-world uncertainties like fluctuating demand, variable processing times, and equipment failures, significantly impacting productivity and efficiency. The increasing demand for more adaptive and robust scheduling frameworks that can handle these uncertainties effectively drives the need for research in this area. Existing methods do not adequately capture modern manufacturing environments’ dynamic and unpredictable nature, resulting in inefficiencies and higher operational costs; they do not employ a fuzzy approach to benefit from human intuition. This study successfully demonstrates the application of Hexagonal Type-2 Fuzzy Sets (HT2FS) for the accurate modeling of the importance of jobs, thereby advancing fuzzy logic applications in scheduling problems. Additionally, it employs a novel Multi-Criteria Decision-Making (MCDM) approach employing Proportional Picture Fuzzy AHP (PPF-AHP) for group decision-making in a flow shop scheduling context. The research outlines the methodology involving three stages: group weight assessment through a PPF-AHP for the objectives, weight determination using HT2FS for the jobs, and optimization via Genetic Algorithm (GA), a method that gave us the optimal solution. This study contributes significantly to operational research and production scheduling by proposing a sophisticated, hybrid model that adeptly navigates the complexities of flow shop scheduling. The integration of HT2FS and MCDM techniques, particularly PPF-AHP, offers a novel approach that enhances decision-making accuracy and paves the way for future advancements in manufacturing optimization.

Multi-objective stochastic scheduling of inpatient and outpatient surgeries

AbstractWith the advancement of surgery and anesthesiology in recent years, surgical clinical pathways have changed significantly, with an increase in outpatient surgeries. However, the surgical scheduling problem is particularly challenging when inpatients and outpatients share the same operating room blocks, due to their different characteristics in terms of variability and preferences. In this paper, we present a two-phase stochastic optimization approach that takes into account such characteristics, considering multiple objectives and dealing with uncertainty in surgery duration, arrival of emergency patients, and no-shows. Chance Constrained Integer Programming and Stochastic Mixed Integer Programming are used to deal with the advance scheduling and the allocation scheduling, respectively. Since Monte Carlo sampling is inefficient for solving the allocation scheduling problem for large size instances, a genetic algorithm is proposed for sequencing and timing procedures. Finally, a quantitative analysis is performed to analyze the trade-off between schedule robustness and average performance under the selection of different patient mixes, providing general insights for operating room scheduling when dealing with inpatients, outpatient, and emergencies.

A data-driven robust optimization method based on scenario clustering for PVC production scheduling under uncertainty

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.

Deep reinforcement learning based energy management of a hybrid electricity-heat-hydrogen energy system with demand response

Hybrid electricity-heat-hydrogen energy system with demand response (DR) is promising in enhancing flexibility and energy efficiency. However, the multi-energy coupling and source-load uncertainties makes it challenging to efficiently schedule energy flows of electricity generation, storage and DR. To this end, this paper proposes a continues deep reinforcement learning algorithm, specifically the deep deterministic policy gradient (DDPG), for the energy management optimization. Different Markov decision processes are firstly employed to analyze and compare two kinds of incentive-based electro-thermal DR contracts, i.e., load curtailment and load shifting. Simulation results exemplify the superiority of the proposed DDPG-based scheduling incorporating electro-thermal DR in terms of economy and sustainability, leading to a 16.02 % reduction in scheduling costs for contract load curtailment and an 8.52 % reduction for contract load shifting when compared to that without DR consideration. Furthermore, the robustness of DDPG-based scheduling is verified under 60 random source-load scenarios compared with different algorithms. Compared to results obtained by DDPG, DDPG-LC and DDPG-LS reduce the mean cost by 22.15 % and 12.84 %, while their error from the theoretical optimum is only around 5 %. The results demonstrate that the approximate optimality and rapid decision-making illustrate DDPG's efficient real-time scheduling capability, thereby enhancing the system's adaptability to uncertain environments.

A robust optimization method for new distribution systems based on adaptive data-driven polyhedral sets

In order to better describe the uncertainty of renewable energy output, this paper proposed a novel robust optimization method for new distribution systems based on adaptive data-driven polyhedral sets. First, an ellipsoidal uncertainty set was established using historical data on renewable energy output, and a data-driven convex hull polyhedral set was established by connecting high-dimensional ellipsoidal vertices; on this basis, an adaptive data-driven polyhedral set model was established to address the problem of high conservatism in the scaling process of convex hull polyhedral sets. Furthermore, a novel adaptive data-driven robust scheduling model for new distribution systems was established, and a column-and-constraint generation (C&CG) algorithm was used to solve the robust scheduling model. Finally, the improved IEEE-33 bus system simulation verification shows that the robust scheduling model for new distribution systems based on adaptive data-driven polyhedral sets can reduce conservatism and improve the robustness of optimization results.

Day-Ahead scheduling of rural integrated energy systems based on distributionally robust optimization theory

The integration of diverse industries in rural areas is an important step in building a smart countryside and achieving rural revitalization. Aiming at the problem of high energy consumption and pollution in agricultural production parks under the traditional energy structure, a new rural comprehensive energy park distribution robust scheduling model for water containing product breeding greenhouses is proposed in this paper. Firstly, a greenhouse model for aquaculture based on the principle of thermal flow is established. Secondly, considering energy production, consumption and storage, a rural integrated energy system model is established. In response to the uncertainty of residential electricity load, solar radiation, and environmental temperature within the park, a distributed robust optimization model is established using Kullback Leibler divergence. Finally, a numerical simulation is conducted using energy data from a real rural aquaculture park. The results show that compared to agricultural production parks under traditional energy models, the new rural comprehensive energy system model proposed in this paper fully integrates rural resources, reduces daily operating costs by 74.832 %, and reduces total carbon emissions by 33.75 %, providing theoretical support for rural industrial structure adjustment and energy transformation.

Fast Algorithm for High-Throughput Screening Scheduling Based on the PERT/CPM Project Management Technique

High-throughput screening systems are robotic cells that automatically scan and analyze thousands of biochemical samples and reagents in real time. The problem under consideration is to find an optimal cyclic schedule of robot moves that ensures maximum cell performance. To address this issue, we proposed a new efficient version of the parametric PERT/CPM project management method that works in conjunction with a combinatorial subalgorithm capable of rejecting unfeasible schedules. The main result obtained is that the new fast PERT/CPM method finds optimal robust schedules for solving large size problems in strongly polynomial time, which cannot be achieved using existing algorithms.

The Impact of Cruise Controllability on the Decision Making of Schedule Construction

Nowadays, challenged by diverse uncertainties and disruptions (e.g., bad weather), as well as the strict environmental regulations imposed by authorities (e.g., on carbon emissions), airlines are struggling. How to improve their operational efficiency in such a volatile and adverse market becomes a top agenda of airlines. Among various operations, crew scheduling is fundamentally important as staffing cost is a big part of the total operational expenses. It is known that in crew scheduling, “robust crew pairing” is crucial to make the produced pairings less vulnerable in real operations. Existing studies generally construct robustness assuming that the aircraft cruise speed is fixed. However, prior studies have found that flight times exhibit significant variations due to reasons like cruise speed adjustment, and aircraft can control cruise speed for purposes like reducing delays. For crew, cruise speed controllability is also useful in hedging disruptions. For example, one flight can speed up to meet its on-time arrival even if it departs late due to crew disruptions. However, the impacts of cruise speed controllability on crew pairing robustness and the related environmental costs are under-explored. We thus propose this preliminary study to explore the possibility to use cruise speed controllability to enhance schedule robustness for crews.

Distributed robust scheduling optimization for energy system of steel industry considering prediction uncertainties

Predictive scheduling is commonly deployed for the energy systems in the steel industry, while the uncertainties caused by the predictions can lead to under-optimization or over-adjustment. In order to solve this problem, a novel distributed robust optimization framework is proposed in this study. A Robust Optimization (RO) model is established at first to mathematically address the prediction uncertainties, where the gas, steam, and electricity networks are considered as distributed participants, with their operating costs and CO2 emissions costs as the objectives for minimization. Then the vanilla 2-block Alternating Direction Multiplier Method (ADMM) is extended to a 3-block structure in this study for solving the established RO model in a distributed manner. Considering the superiority on efficiency, the Column-and-Constraint Generation (C&CG) algorithm is deployed for each block. To ensure convergence considering the extensive interaction between the updated dual and coupling variables in each iteration of the overall ADMM and each C&CG, an adaptive bridging method is developed in this study. Finally, experiments using real data from a steel plant in China demonstrate that the proposed framework has a deviation of less than 1.33 % while with higher efficiency and better robustness compared to other algorithms.

The Multi-Skilled Resource-Constrained Project Scheduling Problem: A Systematic Review and an Exploration of Future Landscapes

Abstract The Multi-skilled Resource Constrained Project Scheduling Problem (MS-RCPSP) is a complex and multi-faceted problem that involves scheduling activities whilst considering various resource constraints. These constraints include limited availability of workers, equipment, and materials, with each activity requiring a minimal set of skills to be executed. Furthermore, for a better resemblance to reality, workers/machines are assumed to be multi-skilled/multi-purpose posing another dimension of complexity to the problem. The objective is to minimize project duration, cost, or other relevant criteria while accounting for the inherent resources flexibility. This paper provides a systematic review of the literature pertaining to MS-RCPSP, and an in-depth analysis of 171 papers published between 2000 and 2021 inclusive. The conducted bibliometric analysis identifies the top contributing authors, most influential papers, existing research tendencies, and thematic research topics within the field. In addition, this review highlights different aspects of the MS-RCPSP, spanning the significance of performance measures, solution approaches, application areas, and the incorporation of time constraints. While project completion time, cost, and tardiness are common performance indicators, other measures such as multi-skilled staff assignment and schedule robustness are also deemed important. Although various methods have been employed to solve the MS-RCPSP including exact and approximate approaches, the selection of the most-suited approach depends on the problem’s scale, complexity, and constraints, necessitating careful consideration of each method’s strengths and weaknesses. Interestingly, several studies have jointly addressed resource and time constraints in the context of MS-RCPSP, often considering tardiness, and have proposed different algorithms, models, and metaheuristics to tackle these challenges. This paper clearly highlights research gaps and promising avenues for future research. This work provides valuable insights for project managers to effectively schedule tasks in the presence of multiple flexible resources.

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.