Stochastic Scheduling Research Articles

Stochastic Event-Based Distributed Fusion Estimation Over Sensor Networks With Fading Channel

The problem of the stochastic event-based distributed fusion estimation for a class of Gaussian systems is investigated. Considering the deterministic event-triggers destroying the Gaussian property of system states, the stochastic event-triggered mechanisms (SETMs) are used, which also can relieve the network transmission burden. Under the stochastic transmission schedules, a two-step fusion estimation method is developed. The first step, with the consideration of channel fading, the local estimation of each sensor is proposed by using the measurements from itself and its neighbors. The second step, the fusion algorithm is designed to eliminate the disagreements among local estimations of each sensor. Finally, experiment is carried out to demonstrate the advantages of the proposed distributed fusion estimation.

Online computation offloading and trajectory scheduling for UAV-enabled wireless powered mobile edge computing

The unmanned aerial vehicle (UAV)-enabled mobile edge computing (MEC) architecture is expected to be a powerful technique to facilitate 5G and beyond ubiquitous wireless connectivity and diverse vertical applications and services, anytime and anywhere. Wireless power transfer (WPT) is another promising technology to prolong the operation time of low-power wireless devices in the era of Internet of Things (IoT). However, the integration of WPT and UAV-enabled MEC systems is far from being well studied, especially in dynamic environments. In order to tackle this issue, this paper aims to investigate the stochastic computation offloading and trajectory scheduling for the UAV-enabled wireless powered MEC system. A UAV offers both RF wireless power transmission and computation services for IoT devices. Considering the stochastic task arrivals and random channel conditions, a long-term average energy-efficiency (EE) minimization problem is formulated. Due to non-convexity and the time domain coupling of the variables in the formulated problem, a low-complexity online computation offloading and trajectory scheduling algorithm (OCOTSA) is proposed by exploiting Lyapunov optimization. Simulation results verify that there exists a balance between EE and the service delay, and demonstrate that the system EE performance obtained by the proposed scheme outperforms other benchmark schemes.

Stochastic optimization in multi-energy hub system operation considering solar energy resource and demand response

The optimal operation of multi-energy systems based on energy hubs (EHs) is a significant challenge for operators due to the mutual impact of different energies and the uncertainty of renewable energy sources, electricity prices, the energy demand of consumers. To address this challenge, a stochastic scheduling framework for multi-energy hub systems is proposed in this paper to simultaneously optimize both EHs and distribution networks. The proposed framework considers RESs, uncertain parameters, DRPs, and emission to ensure system operation in fact. Furthermore, the uncertainty of electrical, heating, and cooling demands, electrical prices, and output power of RESs is modeled by probability density functions. They are divided into states by clustering technique to form the scenario matrix. A scenario reduction technique is then employed to reduce the number of scenarios to 10 to reduce the computational burden. The objective of the proposed framework is to minimize the total operation cost of the system, which is modeled as a mixed-integer nonlinear programming (MINLP) problem. The numerical results from different case studies show that the operation costs of the multi-energy systems using the proposed method are reduced by 2.0–14.5% among different analyzed cases. Additionally, CO2 emission is reduced by 1.9% and 22.3% considering DRPs and RESs, respectively.

Efficient stochastic scheduling for highly complex resource placement in edge clouds

For the edge cloud-based large-scale distributed systems in wide areas, it is important to quickly adjust the deployed resource in multiple edge clouds to maximize the resource revenue and meet the quality of service requirements. The mean values of demands are usually used in the scheduling algorithms for simplicity, but in the real-world scenarios the resource demands may fluctuate greatly, which cannot be effectively modeled in the mean value-based demand model, resulting in the under-utilization of resources. To address the problem, we investigate a general stochastic scheduling problem in the edge clouds, whose objective is to place the given amount of resources into the edge areas, and to maximize the scheduling revenue like the weighted sum of satisfied demands. We then propose an efficient algorithm by identifying the optimal conditions of nested subproblems. Experiments show that in the scenarios with general settings, the algorithm can achieve at least 97% average revenue of the traditional optimal algorithm with much lower time complexity, which can be further reduced through parallelization. The algorithm has the potential to be an effective supplement to the existing algorithms under the time-tense scheduling scenarios with a large number of resources.

Data-Driven Optimal Scheduling Algorithm of Human Resources in Colleges and Universities

At present, the development process of human resource management in Colleges and universities in China has gone through a period of time. In the whole process, the mode of human resource management in colleges and universities is gradually maturing, but there are also some problems. In this paper, data-driven stochastic optimal scheduling algorithm and robust optimal scheduling algorithm are used to model and analyze the human resources. Then, the two models are applied to the human resource management of Nanjing University and Southeast University. The data optimization results show that the robust optimal scheduling algorithm is helpful to the management of new teachers, while the random optimal scheduling algorithm can improve the management of teachers who have been in service for a long time, but there are still some disadvantages. If the combination of two data-driven scheduling algorithms is adopted, it can manage the human resources of colleges and universities well. In short, this paper provides some theoretical and experimental support for the specific application of data-driven human resources optimal scheduling algorithm in colleges and universities.

Stochastic optimal scheduling considering reserve characteristics of retrofitted combined heat and power plants

Increasing the proportion of non-fossil energy and developing renewable energy are greatly conducive to building a clean and low-carbon energy system. However, in the current power system, the strong thermo-electric coupling limits the feasible operating regions of combined heat and power (CHP) units, which causes serious problems about wind curtailment and reserve capacity insufficiency. To cope with this issue, it is technically feasible to retrofit inside and outside CHP units, so as to improve the operation and reserve flexibility of the system. This paper focuses on illustrating the flexible operation and hourly-level reserve characteristics of retrofitted CHP units in a power and heat integrated energy system (PHIES) with high proportion of wind power. The designed flexibility retrofit scheme based on internal thermal storage (ITS) and external thermal storage (ETS) is firstly analyzed. Secondly, the corresponding refined operation model for retrofitted CHP units is proposed to describe their technical features and energy flow process. Then, a coordinated optimization model for operation scheduling and reserve risk is presented from the perspective of the overall system. Finally, numerical simulations are performed to demonstrate the favorable influence of double thermal storage on wind accommodation improvement and reserve risk reduction in the PHIES. The impact of different wind power installed capacity and different thermal energy storage capacity is also studied in the sensitivity analysis.

Stochastic scheduling of multi-hub energy-water nexus in the presence of renewable resources and responsive loads towards achieving sustainability

Free sources such as seawater and solar and wind energy can be converted by interface equipment for different applications. Due to the development of technologies in recent years, such a process has become more feasible. This paper optimizes the scheduling of a renewable energy-water nexus based on multi-hub concept towards achieving sustainability. In this regard, four hubs have been installed, where the first one provides required electricity and potable water by wind turbines, photovoltaics and desalination plant. The second hub supplies gas demand by using the output of first hub and the power to gas unit. The generated gas and electricity are injected into the third hub that is composed of the boiler, electric heat pump and chiller to meet thermal demand. As well, a storage hub is considered to improve system flexibility. To show the impact of responsive loads and simulate realistic conditions, an incentive-based program has been implemented and grid operation is evaluated under uncertainty of wind speed and solar radiation. Moreover, the simulations are compared with the robust optimization to analyze the capability of the proposed approach. The results validate that the framework is practical and viable for coastal areas, load participation has positive effects on the objective function and considering uncertainty enhances robustness against fluctuations of renewable energies.

Power Grid Resilience Enhancement via Protecting Electrical Substations Against Flood Hazards: A Stochastic Framework

Natural disasters, such as floods, may damage power system assets and lead to widespread and long outages. The impact of flood can be alleviated by preventive actions such as installing tiger dams around power substations before the flood. In this regard, it is imperative that critical substations are identified in terms of the connected load and imposed costs to the system. This article presents a stochastic resource allocation approach for protecting power substations against flood events a day ahead of the event. Flood probability distribution functions are used to generate several flood scenarios at each substation. Using flood scenarios and substations’ fragility, damage, and repair time curves obtained from historical data, the failure probability, damage percentage, damage cost, and repair time of substations are estimated. A day-ahead risk-aware stochastic scheduling model is proposed to identify the critical substations whose protection by tiger dams maximizes grid resilience. The risk-aware approach prevents high cost and low resilience if a particular scenario with a low probability is realized. A scenario reduction method is developed to generate representative substation failure scenarios and reduce the computational cost of the optimization problem. The simulation results on a realistic 30-substation system show the effectiveness of the proposed model.

Optimal stochastic scheduling in microgrids under managed risk

This paper addresses the stochastic optimal day-ahead microgrid (MG) energy resources scheduling, considering the uncertain load, price of electricity, and generated electrical power by wind and solar units. Moreover, the vehicle-to-grid (V2G) implementation, load curtailment cost, and spinning reserve requirements are modeled to make the results more practical and applicable. Furthermore, the price elasticity of supply is considered to explore the relation between V2G capability and the optimization process. The stochastic energy resources scheduling problem is formulated in a two-level optimization framework. The unit commitment of dispatchable resources is analyzed in the upper level, and the lower level is formulated as a scenario-based two-stage stochastic programming problem that minimizes the operation cost of MG considering all the constraints. The risk of attaining unfavorable high costs of MG scheduling is considered using the variance approach. The generated scenarios are reduced by using the backward reduction method for each uncertain variable at each hour, independently. The artificial intelligent-based methods, including differential evolution algorithm (DEA), particle swarm optimization (PSO), and covariance matrix adaptation evolution strategy (CMAES) are applied to solve the problem. The effectiveness of the proposed approaches is confirmed by simulations on a modified 13-bus IEEE test system, in two cases of neglecting the risk and including the managed risk by applying the real-world data. The results confirmed the better performance of CMAES for solving such optimization problems.

Differential Evolution Algorithm Combined with Uncertainty Handling Techniques for Stochastic Reentrant Job Shop Scheduling Problem

This paper considers two kinds of stochastic reentrant job shop scheduling problems (SRJSSP), i.e., the SRJSSP with the maximum tardiness criterion and the SRJSSP with the makespan criterion. Owing to the NP-complete complexity of the considered RJSSPs, an effective differential evolutionary algorithm (DEA) combined with two uncertainty handling techniques, namely, DEA_UHT, is proposed to address these problems. Firstly, to reasonably control the computation cost, the optimal computing budget allocation technique (OCBAT) is applied for allocating limited computation budgets to assure reliable evaluation and identification for excellent solutions or individuals, and the hypothesis test technique (HTT) is added to execute a statistical comparison to reduce some unnecessary repeated evaluation. Secondly, a reentrant-largest-order-value rule is designed to convert the DEA’s individual (i.e., a continuous vector) to the SRJSSP’s solution (i.e., an operation permutation). Thirdly, a conventional active decoding scheme for the job shop scheduling problem is extended to decode the solution for obtaining the criterion value. Fourthly, an Insert-based exploitation strategy and an Interchange-based exploration strategy are devised to enhance DEA’s exploitation ability and exploration ability, respectively. Finally, the test results and comparisons manifest the effectiveness and robustness of the proposed DEA_UHT.

Scheduling on-site service deliveries to minimise the risk of missing appointment times

This paper studies the stochastic service task scheduling and vehicle routing problem for a telecommunication provider where each vehicle is driven by an engineer who performs service tasks at customer premises. There is an agreed time window for starting each service task. The service times and travel times are subject to uncertainties, e.g., task taking longer or shorter than expected, traffic situation causing delays. The problem is to schedule the tasks and route the vehicles to minimise the risks of missing appointment times. Models are presented to express the risks and describe the problem. Simulated annealing and tabu search are applied for generating an initial schedule of the day and for re-optimisation during the day based on real-time information updates. The study reported is based on the work in an industrial case. The stochastic nature of the travel times and durations of different task types as well as their distribution parameters have been obtained by applying data analytics on large sets of operations data. These are used in calculating the risks and in making scheduling and routing decisions. Real-time data updates sent back from the engineers are used for re-optimisation to adjust the schedule and routes so that the risks are kept at a lower level. Simulation results show that using risk minimisation as objective and re-optimisation during the day help enhance the on-time start of tasks. With this approach organisations can achieve robust task scheduling and improved customer satisfaction, and so become more competitive in the market.

Optimal maintenance scheduling under uncertainties using Linear Programming-enhanced Reinforcement Learning

Maintenance is of great importance for the safety and integrity of infrastructures. The expected optimal maintenance policy in this study should be able to minimize system maintenance cost while satisfying the system reliability requirements. Stochastic maintenance scheduling with an infinite horizon has not been investigated thoroughly in the literature. In this work, we formulate the maintenance optimization under uncertainties as a Markov Decision Process (MDP) problem and solve it using a modified Reinforcement Learning method. A Linear Programming-enhanced RollouT (LPRT) is proposed, which considers both constrained deterministic and stochastic maintenance scheduling with an infinite horizon. The novelty of the proposed approach is that it is suitable for online maintenance scheduling, which can include random unexpected maintenance performance and system degradation. The proposed method is demonstrated with numerical examples and compared with several existing methods. Results show that LPRT is able to determine the suitable optimal maintenance policy efficiently compared with existing methods with similar accuracy. Parametric studies are used to investigate the effect of uncertainty, subproblem size, and the number of stochastic stages on the final maintenance cost. Limitations and future work are given based on the proposed study.

Integrated Parametric Graph Closure and Branch-and-Cut Algorithm for Open Pit Mine Scheduling under Uncertainty

Open pit mine production scheduling is a computationally expensive large-scale mixed-integer linear programming problem. This research develops a computationally efficient algorithm to solve open pit production scheduling problems under uncertain geological parameters. The proposed solution approach for production scheduling is a two-stage process. The stochastic production scheduling problem is iteratively solved in the first stage after relaxing resource constraints using a parametric graph closure algorithm. Finally, the branch-and-cut algorithm is applied to respect the resource constraints, which might be violated during the first stage of the algorithm. Six small-scale production scheduling problems from iron and copper mines were used to validate the proposed stochastic production scheduling model. The results demonstrated that the proposed method could significantly improve the computational time with a reasonable optimality gap (the maximum gap is 4%). In addition, the proposed stochastic method is tested using industrial-scale copper data and compared with its deterministic model. The results show that the net present value for the stochastic model improved by 6% compared to the deterministic model.

A Monotone Approximate Dynamic Programming Approach for the Stochastic Scheduling, Allocation, and Inventory Replenishment Problem: Applications to Drone and Electric Vehicle Battery Swap Stations

There is a growing interest in using electric vehicles (EVs) and drones for many applications. However, battery-oriented issues, including range anxiety and battery degradation, impede adoption. Battery swap stations are one alternative to reduce these concerns that allow the swap of depleted for full batteries in minutes. We consider the problem of deriving actions at a battery swap station when explicitly considering the uncertain arrival of swap demand, battery degradation, and replacement. We model the operations at a battery swap station using a finite horizon Markov decision process model for the stochastic scheduling, allocation, and inventory replenishment problem (SAIRP), which determines when and how many batteries are charged, discharged, and replaced over time. We present theoretical proofs for the monotonicity of the value function and monotone structure of an optimal policy for special SAIRP cases. Because of the curses of dimensionality, we develop a new monotone approximate dynamic programming (ADP) method, which intelligently initializes a value function approximation using regression. In computational tests, we demonstrate the superior performance of the new regression-based monotone ADP method compared with exact methods and other monotone ADP methods. Furthermore, with the tests, we deduce policy insights for drone swap stations.

The effect of few historical data on the performance of sample average approximation method for operating room scheduling

AbstractWe model the scheduling problem of a single operating room for outpatient surgery, with uncertain case durations and an objective function comprising waiting time, idle time, and overtime costs. This stochastic scheduling problem has been studied in diverse forms. One of the most common approaches used is the sample average approximation (SAA). Our contribution is to study the use of SAA to solve this problem under few historical data using families of log t distributions with varying degrees of freedom. We analyze the results of the SAA method in terms of optimality convergence, the effect of the number of scenarios, and average computational time. Given the case sequence, computational results demonstrate that SAA with an adequate number of scenarios performs close to the exact method. For example, we find that the optimality gap, in units of proportional weighted time, is relatively small when 500 scenarios are used: 99% of the instances have an optimality gap of less than 2.6 7% (1.74%, 1.23%) when there are 3 (9, many) historical samples. Increasing the number of SAA scenarios improves performance, but is not critical when the case sequence is given. However, choosing the number of SAA scenarios becomes critical when the same method is used to choose among sequencing heuristics when there are few historical data. For example, when there are only three (nine, many) historical samples, 99% of the instances have less than 25.38% (13.15%, 6.87%) penalty in using SAA with 500 scenarios to choose the best sequencing heuristic.

Integrated stochastic bicriteria flow shop scheduling problem with preventive maintenance

In this paper, the concept of flexible and multiple preventive maintenance activities is introduced by reformulating classical bicriteria permutation flow shop scheduling problem into stochastic scheduling with objective to minimise system utilisation time with minimum makespan. The mathematical model is formulated to handle the uncertainties in job processing time and the time interval for machine maintenance. The problem of stochastic flow shop scheduling environment with maintenance activities, is NP-hard. Therefore, the advanced metaheuristic is implemented to solve large scale instances of referred problem. Extensive computational analysis is carried out to depict the superiority of proposed metaheuristic in terms of effectiveness and efficacy.

Geometallurgical prediction models of processing plant indicators for stochastic mine production scheduling

This article presents a new geometallurgical framework that builds empirical prediction models of key performance indicators of the processing plant and integrates them into a simultaneous stochastic optimization model for mine production scheduling. The prediction models are created by tracking blended rock properties and matching them with observed responses from the operating processing plant. Several applied case studies in a gold mining complex are presented building prediction models of ball mill throughput, steel ball consumptions, and reagent consumptions from collected data in a gold leaching operation. Finally, the integration of these geometallurgical prediction models into stochastic mine production scheduling is demonstrated to monetize the gained insights. Compared with conventional planning, the resulting mine plans increase yearly profit and are more likely to align with production targets.

Stochastic production scheduling for water-oil displacement by reduced-order models generated using liquid production rates

Stochastic production scheduling for water-oil displacement by reduced-order models generated using liquid production rates

Effective Proactive Policies for the Stochastic Resource-Constrained Project Scheduling Problem with Inventory Consideration

Effective Proactive Policies for the Stochastic Resource-Constrained Project Scheduling Problem with Inventory Consideration

High-Speed Railway Meal Delivery Service: A Stochastic Scheduling Perspective

High-Speed Railway Meal Delivery Service: A Stochastic Scheduling Perspective