Stochastic Scheduling Research Articles

A stochastic bi-objective project scheduling model under failure of activities

A stochastic bi-objective project scheduling model under failure of activities

Optimal job scheduling to minimize total tardiness by dispatching rules and community evaluation chromosomes

In traditional scheduling, job processing times are assumed to be fixed. However, this assumption may not be applicable in many realistic industrial processes. Using the job processing time of real industrial processes instead of a fixed value converts the deterministic model to a stochastic one. This study provides three approaches to solving the problem of stochastic scheduling: stochastic linguistic, stochastic scenarios, and stochastic probabilistic. A combinatorial algorithm, dispatching rules and community evaluation chromosomes (DRCEC) is developed to generate an optimal sequence to minimize the tardiness performance measure in the scheduling problem. Thirty-five datasets of scheduling problems are generated and tested with the model. The DRCEC is compared to the Genetic Algorithm (GA) in terms of total tardiness, the tendency of convergence, execution time, and accuracy. The DRCEC has been discovered to outperform the GA. The computational results show that the DRCEC approach gives the optimal response in 63 per cent of cases and the near-optimal solution in the remaining 37 per cent of cases. Finally, a manufacturing company case study demonstrates DRCEC's acceptable performance.

Stochastic scheduling of autonomous mobile robots at hospitals.

This paper studies the scheduling of autonomous mobile robots (AMRs) at hospitals where the stochastic travel times and service times of AMRs are affected by the surrounding environment. The routes of AMRs are planned to minimize the daily cost of the hospital (including the AMR fixed cost, penalty cost of violating the time window, and transportation cost). To efficiently generate high-quality solutions, some properties are identified and incorporated into an improved tabu search (I-TS) algorithm for problem-solving. Experimental evaluations demonstrate that the I-TS algorithm outperforms existing methods by producing high-quality solutions. Based on the characteristics of healthcare requests and the AMR working environment, scheduling AMRs reasonably can effectively provide medical services, improve the utilization of medical resources, and reduce hospital costs.

Minimizing the expected maximum lateness for a job shop subject to stochastic machine breakdowns

This paper addresses a stochastic job shop scheduling problem with sequence-dependent setup times, aiming to minimize the expected maximum lateness. The stochastic nature is modeled by considering uncertain times between failures (TBF) and uncertain times to repair (TTR). To tackle this problem, a simheuristic approach is proposed, which combines a tabu search (TS) algorithm with Monte Carlo simulation. A total of 320 instances were used to conduct multiple experiments. Instances were generated with two distributions to study the behavior of stochastic TTR and TBF under log-normal and exponential distributions. Firstly, the performance of the simheuristic was evaluated for small instances by comparing it with the simulation of optimal solutions obtained with a mixed-integer linear programming (MILP) model. The simheuristic approach demonstrated an average improvement of around 7% compared to the simulation of MILP model solutions. Secondly, the simheuristic performance was evaluated for medium and large-size instances by comparing it with the simulation of the solutions obtained by the earliest due date (EDD) and process time plus work in the next queue plus negative slack (PT + WINQ + SL) dispatching rules. The results showed an average improvement of around 11% compared to EDD and 14% compared to PT + WINQ + SL. Furthermore, the results highlight that even when the two distributions have the same expected value and coefficient of variation, they can yield different expected maximum lateness values. This emphasizes the importance of precise distribution fitting when solving real cases to achieve effective scheduling performance.

Dynamic Scheduling Stochastic Multiworkflows With Deadline Constraints in Clouds

Nowadays, more and more workflows with different computing requirements are migrated to clouds and executed with cloud resources. In this work, we study the problem of stochastic multi-workflows scheduling in clouds and formalize this problem as an optimization problem that is NP-hard. To solve this problem, an efficient stochastic multi-workflows dynamic scheduling algorithm called SMWDSA is designed to schedule multi-workflows with deadline constraints for optimizing multi-workflows scheduling cost. The proposed SMWDSA consists of three stages including multi-workflows preprocessing, multi-workflow scheduling and scheduling feedback. In SMWDSA, a novel task sub-deadlines assignment stretagy is design to assign the task sub-deadlines to each task of multi-workflows for meeting workflow deadline constraints. Then, we propose a task scheduling method based on the minimal time slot availability to execution task for minimizing workflow scheduling cost while meetingt workflow deadlines. Finally, a scheduling feedback strategy is adopted to update the priorities and sub-deadlines of unscheduled tasks, for further minimizing workflow scheduling cost. We conduct the experiments using both synthetic data and real-world data to evaluate SMWDSA. The results demonstrate the superiority of SMWDSA as compared with the state-of-the-art algorithms. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Workflow scheduling in clouds is significantly challenging due to not only the large scale of workflows but also the elasticity and heterogeneity of cloud resources. Moreover, minimizing workflow scheduling cost and satisfying workflow deadlines are two critical issues in scheduling with cloud resources, especially the uncertainty of workflow arrive time and task execution time are considered. To meet workflow deadlines, it is an effective strategy to decompose workflow deadline constraints into task sub-deadline constraints. To minimize the workflow scheduling cost, each task in a workflow needs to be assigned to their most suitable VMs for execution. This article presents a novel workflow scheduling algorithm to schedule stochastic multi-workflows in clouds for optimizing multi-workflows scheduling cost and meeting workflows deadlines. This algorithm obtains the task sub-deadline constraints based on the characteristics of workflows for meeting the worklfow deadline constraint. Under the premise of meeting task deadlines, it schedules tasks to a VM with minimum the slot time, for minimizing the cost. Case studies based on well-known real-world workflows data sets suggest that it outperforms traditional ones in terms of success and cost of multi-workflows scheduling. It can thus aid the design and optimization of multi-workflows scheduling in a cloud environment. It can help practitioners better manage the scheduling cost and performance of real-world applications built upon cloud services.

Bi-Objective Modeling and Optimization for Stochastic Two-Stage Open Shop Scheduling Problems in the Sharing Economy

Nowadays, many manufacturing and service industries prefer to share resources such as facilities and workers to cooperatively perform tasks, which can efficiently improve resource utilization and customer satisfaction. Generally, the decision-makers need to pay more for resource usage, leading to an urgent demand to decrease operational costs. This article proposes a stochastic bi-objective two-stage open shop scheduling problem that models a vehicle maintenance process where tasks are appointed to be completed by multiple third-party companies with professional equipment. We formulate this optimization problem by minimizing the total tardiness and processing cost subject to various resource constraints. A hybrid multiobjective migrating birds optimization combined with a genetic operation and a discrete event system is designed by considering problem characteristics to solve the problem. In this method, the migrating birds optimization with some particular strategies aims at searching candidate solutions from the entire solution domain. Simultaneously, the discrete event system, by using stochastic simulation and discrete event-based simulation approaches, focuses on evaluating the performance of searched solutions. Simulation experiments are performed, and state-of-the-art algorithms are used as competitive approaches. The results confirm that this approach has an excellent performance in handling our considered problem.

An optimal multi-objective demand side management of a smart Microgrid consists of various building loads, considering relativity index and uncertainty

This paper addresses microgrid energy management in the presence of distributed generation and active loads while accounting for operational, economic, environmental, and reliability factors. The objective is to minimize the cost of shutdown during N-1 contingencies, projected emission-related expenses, and the overall operational cost of microgrids integrated with distributed generations. A stochastic scheduling technique that optimizes short-term microgrid operation, reducing costs and pollution through renewable resources is introduced. Utilizing demand response programs among residential, commercial, and industrial participants is proposed to counter the uncertainty of renewable resource-generated power. The demand response program implementation suggests considering financial incentives as bid prices, along with energy packages managed by demand response providers. Simulation results demonstrate three strategies to decrease operating costs and pollutants, contrasting scenarios with and without responsive load engagement. Equations governing AC power flow, microgrid operations, reliability, distributed generation, and, demand response programs and batteries, form the analytical core. Stochastic programming addresses uncertainties tied to demand, energy prices, renewable distributed generation production, and microgrid equipment availability. To attain dependable, optimal solutions with dynamic responsiveness, the combined ant lion optimization and crow search algorithm are employed. The proposed method is tested on a sample smart microgrid for validation. Numerical findings unequivocally underscore demand-side management potency in reducing power generation uncertainties from wind turbines and photovoltaics. This paper offers insights into microgrid energy management complexities, paving the way for resilient, cost-effective, and environmentally conscious energy distribution paradigms.

Typical academic building energy model development and energy saving evaluation using occupant-based control

Studies on occupant-based controls focused on office buildings have been increasing over the past decade because of the significant energy saving potential they can offer in buildings. However, there are very few studies that focus on academic buildings at colleges and universities, which represent a significant number of buildings in the U.S. This paper aims to develop typical academic building models and use these models to evaluate the energy savings potential of implementing occupant-based control (OBC) using EnergyPlus. Four types of typical university-level academic building models were determined based on cluster analysis, including Office-dominated, Laboratory-dominated, Study Room-dominated, and Mixed-use. The occupancy schedules were updated to include stochastic occupancy schedules to represent academic building use. Next, the baseline and proposed models were built. The proposed model uses OBC, resetting the temperature schedule and minimum outdoor air flow schedule based on occupancy, following the current recommendations of ASHRAE 90.1, and 62.1. To demonstrate the use of this developed model, it was run using ASHRAE Climate Zone 5A climate conditions. Results show that there is significant energy saving potential for academic buildings with the implementation of OBC, including an HVAC energy savings of 35%–51% using occupancy presence data for HVAC controls, and a further energy saving increase (3–9%) using occupancy counts for HVAC controls. The results of this work can be used to evaluate other energy saving measures, and aid building designers and operators in making informed decisions in applying appropriate control strategies to optimize building energy systems, as well as predict energy use and demand.

Nonparametric probabilistic forecasting based stochastic optimal scheduling of integrated electricity and gas systems

The volatility and sporadic availability of renewable energy create significant challenges to the optimal scheduling of integrated electricity and gas systems (IEGS). This paper develops a nonparametric probabilistic forecasting based stochastic scheduling approach of IEGS. The quantile at a series of quantile levels can be generated by direct quantile regression method. Given the set of predicted quantiles, a set of representative scenarios for wind power uncertainty can be obtained by using Monte Carlo simulation method and scenario reduction approach. Based on the implicit finite difference scheme, the original partial differential equations of the gas network are discretized to establish an algebraic model, which provide possibility for efficient solution. Then, the nonconvexity caused by the momentum equation is eliminated by the second-order core relaxation. Finally, the stochastic optimal scheduling model is reformulated as a second-order core programming problem. Numerical simulations are performed to showcase the superiority of the established stochastic optimal scheduling model.

Stochastic Multi-Objective Scheduling of a Hybrid System in a Distribution Network Using a Mathematical Optimization Algorithm Considering Generation and Demand Uncertainties

In this paper, stochastic scheduling of a hybrid system (HS) composed of a photovoltaic (PV) array and wind turbines incorporated with a battery storage (HPV/WT/Batt) system in the distribution network was proposed to minimize energy losses, the voltage profile, and the HS cost, and to improve reliability in shape of the energy-not-supplied (ENS) index, considering energy-source generation and network demand uncertainties through the unscented transformation (UT). An improved escaping-bird search algorithm (IEBSA), based on the escape operator from the local optimal, was employed to identify the optimal location of the HS in the network in addition to the optimal quantity of PV panels, wind turbines, and batteries. The deterministic results for three configurations of HPV/WT/Batt, PV/Batt, and WT/Batt were presented, and the results indicate that the HPV/WT/Batt system is the optimal configuration with lower energy losses, voltage deviation, energy not supplied, and a lower HS energy cost than the other configurations. Deterministic scheduling according to the optimal configuration reduced energy losses, ENS, and voltage fluctuation by 33.09%, 53.56%, and 63.02%, respectively, compared to the base network. In addition, the results demonstrated that the integration of battery storage into the HPV/WT enhanced the various objectives. In addition, the superiority of IEBSA over several well-known algorithms was proved in terms of obtaining a faster convergence, better objective value, and lower HS costs. In addition, the stochastic scheduling results based on the UT revealed that the uncertainties increase the power losses, voltage deviations, ENS, and HPV/WT/Batt cost by 2.23%, 5.03%, 2.20%, and 1.91%, respectively, when compared to the deterministic scheduling.

Optimal stochastic scheduling of a multi-carrier multi-microgrid system considering storages, demand responses, and thermal comfort

This paper focuses on the day-ahead scheduling of a multi-carrier multi-microgrid that delivers electricity, heat, and hydrogen to its customers. The microgrids are equipped with renewable sources, combined heat and power, gas boiler, electric boiler, multi-energy storage, and power-to-hydrogen facilities, and aim at minimizing their operational and environmental costs. Demand response for electrical and hydrogen loads as well as thermal comfort for heat demand have been considered to increase flexibility. The distribution company, which aims at maximizing its profit, imports electricity and natural gas from the main grid. Stochastic optimization is proposed, and the generated scenarios were reduced using the mixed-integer linear programming method. Considering that the problem possesses two conflicting objective functions, the problem was two-level with nonlinear terms. The Karush–Kuhn–Tucker conditions, duality theory, and Fortuny–Amat transformation were implemented to transfer the problem into a single-level mixed-integer linear programming problem. The effectiveness of the proposed framework in four cases has been tested on a hypothetical multi-carrier multi-microgrid. Energy storage, demand response, and thermal comfort resulted in a microgrid cost reduction of 12.31 % and a distribution company profit reduction of 17.25 %. According to the results, thermal comfort can reduce MGs costs remarkably since it adds more flexibility.

Stochastic competitive release and adaptive chemotherapy.

We develop a finite-cell model of tumor natural selection dynamics to investigate the stochastic fluctuations associated with multiple rounds of adaptive chemotherapy. The adaptive cycles are designed to avoid chemoresistance in the tumor by managing the ecological mechanism of competitive release of a resistant subpopulation. Our model is based on a three-component evolutionary game played among healthy (H), sensitive (S), and resistant (R) populations of N cells, with a chemotherapy control parameter, C(t), which we use to dynamically impose selection pressure on the sensitive subpopulation to slow tumor growth and manage competitive release of the resistant population. The adaptive chemoschedule is designed based on the deterministic (N→∞) adjusted replicator dynamical system, then implemented using the finite-cell stochastic frequency dependent Moran process model (N=10K-50K) to ascertain the cumulative effect of the stochastic fluctuations on the efficacy of the adaptive schedules over multiple rounds. We quantify the stochastic fixation probability regions of the R and S populations in the HSR trilinear phase plane as a function of the control parameter C∈[0,1], showing that the size of the R region increases with increasing C. We then implement an adaptive time-dependent schedule C(t) for the stochastic model and quantify the variances (using principal component coordinates) associated with the evolutionary cycles over multiple rounds of adaptive therapy. The variances increase subquadratically through several rounds before the evolutionary cycle begins to break down. Despite this, we show the stochastic adaptive schedules are more effective at delaying resistance than standard maximum tolerated dose and low-dose metronomic schedules. The simplified low-dimensional model provides some insights on how well multiple rounds of adaptive therapies are likely to perform over a range of tumor sizes (i.e., different values of N) if the goal is to maintain a sustained balance among competing subpopulations of cells to avoid chemoresistance via competitive release in a stochastic environment.

Risk‐based stochastic scheduling of centralised and distributed energy storage systems

AbstractThe authors propose a continuous‐time two‐stage stochastic optimisation model for the integration of centralised and distributed energy storage (ES) systems into power systems with high levels of volatile renewable generation. In the proposed model, centralised and distributed ES systems, respectively, controlled by the independent system operator and distribution system operator, can offer energy and flexibility to the operation of the power system in order to help accommodate the uncertainties of renewable generation and load. The proposed model considers the power network constraints and minimises the day‐ahead and real‐time operation costs of the system in the first and second stages. The proposed model utilises energy and ramping flexibility trajectories of ES systems to enhance the cost‐effective operation of the power system, countering the financial risks imposed by the integration of uncertain load and renewable generation. Simulations are conducted on the IEEE 24‐bus reliability test system with multiple risk‐aversion levels for the power system operator, and the results demonstrate the efficiency of the proposed model in utilising the ES systems to provide energy and ramping flexibility and reducing the financial risks measured by the conditional value at risk.

Stochastic optimal scheduling strategy of cross-regional carbon emissions trading and green certificate trading market based on Stackelberg game

Under the urgent goal of "carbon peaking and carbon neutralization" in China and based on the distribution characteristics of renewable energy, it is essential to promote the large-scale consumption of renewable energy and increase the proportion of large-scale renewable energy in market transactions. Therefore, a stochastic optimal scheduling model that combines the Stackelberg game, cross-regional carbon emissions trading, and tradable green certificate transaction to consider the uncertainty of renewable energy power generation is proposed. To encourage more market participants to participate in the tradable green certificate trading, the model uses Stackelberg game theory to analyze the complex interest relationship between different market participants and obtain a scheduling scheme that balances the interests of different participants. To give full play to the role of the trading mechanism on the cross-regional system, the tradable green certificate trading mechanism and the carbon emission trading mechanism are combined to optimize the overall allocation of green certificates and carbon emission rights, to stimulate renewable energy generation, limit the carbon emission of traditional thermal power units and promote energy conversion. Finally, the modified IEEE 39-bus system and Hami power grid (in Western China) are used as examples to illustrate the feasibility and effectiveness of the proposed scheduling model. The results show that the proposed strategy improves the cross-regional system economy and reduces emissions, fully reflects the monetary value of the external characteristics of renewable energy, guides renewable energy investment and power grid planning, and promotes the consumption of renewable energy.

Technical Note—Stochastic Scheduling with Abandonment: Necessary and Sufficient Conditions for the Optimality of a Strict Priority Policy

Strict priority policies in a stochastic system with abandonment In the technical note “Stochastic scheduling with abandonment: Necessary and sufficient conditions for the optimality of a strict priority policy,” Chen, Gayon, and Lemaire consider a stochastic scheduling problem in which jobs abandon when their waiting time exceeds their lifetime. Such a problem arises, for example, in call centers or emergency systems. It is known that the optimal policy is a strict priority policy under some sets of conditions. The authors provide the first set of necessary and sufficient conditions for a problem with two types of jobs. They also provide conjectures to guide toward generalizations of the proposed conditions.

Optimal stochastic scheduling in residential micro energy grids considering pumped-storage unit and demand response

Improving energy efficiency, production costs, greenhouse gas emissions, and reliability are some of the most important problems in the energy industry. Energy storage systems and demand-side management (DSM) programs are among the existing solutions for removing such problems. This study presents an improved micro energy grid (MEG) to reduce operating costs as well as greenhouse gas emissions using combined cooling, heating, and power (CCHP) systems, wind turbines (WTs), photovoltaic (PV) units, pumped-storage units, and heating and cooling storage units. In this system, pumped-storage units are employed to store energy. Price- and incentive-based programs are employed to obtain better performance on the demand side. Uncertainties of wind speed, solar power, electricity price, and electrical load are considered to achieve more accurate results. In this paper, the Latin hypercube sampling (LHS) method is applied to generate various scenarios. Then, K-means clustering approach is employed to reduce the number of scenarios. By producing and reducing the proposed scenario, the inherent uncertainty in renewables can be covered, which will result in a more efficient model. Meta-heuristic whale optimization algorithm (WOA) and Pareto model are used to solve single- and multi-objective functions and to optimally design the proposed structure considering contradictory functions, respectively. The features of the proposed developed algorithm are simplicity in execution and absence of derivative operator, increase of local and global search capability and consideration of objective functions with different nature. Moreover, fuzzy decision-making mechanism is proposed to select the optimal solution from the Pareto set of solutions. Finally, the proposed approach in different scenarios on the microgrid with various sources is discussed. The results indicate the proposed method properly obtains the optimal solution.

Demand response scheduling of copper production under short-term electricity price uncertainty

Marketing demand response of industrial processes on electricity spot markets can reduce operational cost. We apply our simultaneous day-ahead and intraday electricity market participation approach (Germscheid et al., AIChE J. 2022;68:e17828) to analyze the demand response potential of power-intensive copper production with our previously derived resource–task network model (Röben et al., J. CLEAN. PROD. 2022;362:132221). Specifically, we tackle intraday price uncertainty by stochastic scheduling optimization considering both risk-neutral and risk-averse market participation. Risk-averse participation allows for 1.9% weekly savings compared to only participating on the day-ahead market. Risk-neutral participation allows for 6.4% savings, but is connected to higher financial risks on weekends. Moreover, we show that load-shifting capabilities significantly depend on modeling on/off decisions either as first or second-stage integer decisions and that sequential day-ahead and intraday scheduling allows to participate in both markets while balancing financial risk, expected cost, and computational complexity compared to stochastic scheduling.

Optimizing teleconsultation scheduling to make healthcare greener

Some international organizations have called for greener healthcare in the post-pandemic era. Telemedicine has made an important contribution to achieving the goal of green healthcare by reducing the travel distance of patients. From the perspective of operation management, we put forward the teleconsultation room scheduling problem to get a better scheduling scheme to make telemedicine more low-carbon and green. First, we propose a deterministic teleconsultation room allocation scheduling model and a stochastic teleconsultation room allocation scheduling model. Then, we utilize some transformation techniques to simplify the models and solve them through numerical experiments. Next, we put the obtained scheduling schemes into the actual situation and compare them with the staff scheduling scheme. The results show that the stochastic programming model performs the best. In addition, the instability of the teleconsultation service duration has a great impact on the scheduling scheme. The telemedicine center should encourage experts from higher-level hospitals to provide more stable service time.

A multi-time scale coordinated control and scheduling strategy of EVs considering guidance impacts in multi-areas with uncertain RESs

With the increased electrification of transportation sector, the electric vehicles (EVs) are deemed to be key players in energy scheduling act to realize more economical operation of distribution networks. EVs have the function of energy space–time transfer, and energy-space coupling effects need to be considered in scheduling. In this paper, EVs’ spatial characteristics from multi-areas and characteristics of transferable charging power are both taken into account, then a multi-time scale coordinated control and scheduling strategy is proposed to achieve optimal schedules in both day-ahead (DA) and real-time (RT) periods. First, in DA periods, EVs are modeled as shiftable and location-flexible loads to participate in multi-areas’ scheduling task managed by a unified distribution system operator (DSO). To attract more spatially distributed EVs to different charging stations and avoid charging congestion, a price-based transfer model (PBTM) is established to realize EVs charging guidance in different areas while integrated into the DA stochastic scheduling. Next, in RT periods, EVs are modeled as controllable loads to compensate RT power errors caused by uncertain renewable energy sources (RESs) and inaccuracies associated with DA prediction. Both DA and RT scheduling are coordinated with a RT control strategy for EVs, in which a state space model (SSM) is constructed to calculate charging power and then form 1-min control signals to realize the tracking of multi-time scale schedule. Simulation results demonstrate that the proposed coordinated control and scheduling strategy can guide more EVs to be grid-connected, promote multi-time scale economic scheduling, and benefit the EV users meanwhile.

Information Gap Decision Theory-Based Stochastic Optimization for Smart Microgrids with Multiple Transformers

Multi-microgrid collaborative scheduling can promote the local consumption of renewable energy in the smart grid and reduce the operating costs of the power grid park. At the same time, the access of the distributed energy storage (ES) system provides an opportunity to further enhance the park’s peak shaving and valley filling capacity, thereby reducing costs. However, the uncertainty of photovoltaic (PV) power generation and load demand seriously affects the profit maximization of the microgrid in the park. To address this challenge, this paper proposes a stochastic optimal scheduling strategy for industrial park smart microgrids with multiple transformers based on the information gap decision theory (IGDT). We first introduce a revenue maximization model for industrial parks, incorporating a two-part tariff system and distributed ES. Subsequently, we employ an envelope constraint model to accurately represent the uncertainty associated with PV generation and load demand. By integrating these components, we establish the IGDT stochastic optimization scheduling model for industrial parks with multiple transformers. Finally, we simulate and analyze the performance of the proposed IGDT model under various cost deviation factors during typical spring and summer days. The simulation results demonstrate the effectiveness of the proposed control strategy in mitigating the impact of PV generation and load uncertainty on industrial parks. The IGDT-based scheduling approach provides an efficient solution for maximizing revenue and enhancing the operational stability of industrial park microgrids.