Stochastic Scheduling Research Articles

A Kronecker Algebra Formulation for Markov Activity Networks with Phase-Type Distributions

The application of theoretical scheduling approaches to the real world quite often crashes into the need to cope with uncertain events and incomplete information. Stochastic scheduling approaches exploiting Markov models have been proposed for this class of problems with the limitation to exponential durations. Phase-type approximations provide a tool to overcome this limitation. This paper proposes a general approach for using phase-type distributions to model the execution of a network of activities with generally distributed durations through a Markov chain. An analytical representation of the infinitesimal generator of the Markov chain in terms of Kronecker algebra is proposed, providing a general formulation for this class of problems and supporting more efficient computation methods. This entails the capability to address stochastic scheduling in terms of the estimation of the distribution of common objective functions (i.e., makespan, lateness), enabling the use of risk measures to address robustness.

Scheduling jobs with normally distributed processing times on parallel machines

We consider a stochastic parallel machine scheduling problem, where the jobs have uncertain processing time described by a normal probability distribution. The objective is to maximize the probability that all the jobs are completed before a common due date. The considered problem has many practical applications, but it is notoriously known to be difficult as it involves several non-linearities which complicates its analysis and solution.In this work, we have developed novel lower and upper bounds on the objective function. The upper bound is computed via a solution to a problem where a subset of machines is represented as a single machine having a modified due date. Furthermore, we study lower and upper bounds on the number of jobs that must be scheduled on a machine in an optimal schedule. Subsequently, we use the bounds to construct an efficient branch-and-price algorithm where the pricing problem is found to be related to an inflatable stochastic Knapsack problem. An advantage of the branch-and-price algorithm is a constraint branching mechanism that mitigates symmetries in the solution space. The performance evaluation of the proposed algorithm shows that our algorithm outperforms the state-of-the-art method.In this paper, we also study a special case of the problem assuming two machines. We developed a scalable method whose efficiency arises from the concavity of the relaxed objective function and a fast procedure to recover optimal integer solution from it. These improvements allowed us to solve instances with 500 jobs within a few seconds.

Stochastic charging scheduling of a parking lot with wind power: a state‐aggregation method based on Markov decision processes

Stochastic charging scheduling of a parking lot with wind power: a state‐aggregation method based on Markov decision processes

Stochastic multi-objective scheduling of a wind farm integrated with high-temperature heat and power storage in energy market

In spite of significant opportunities created by wind energy, the high uncertainty of wind farms is problematic for their operators, making their participation in the energy market quite challenging. The combination of Air-based High-Temperature Heat and Power Storage (HTHPS), which is known as a novel energy storage technology, with a wind farm as an integrated system can make new opportunities for a Generation Company (GenCo) to overcome the wind generation challenges. This paper proposes a novel Stochastic Multi-objective Optimization (SMOO) problem to determine the optimal charging and discharging scheduling and the best bidding strategy in the day-ahead energy market for an integrated energy system including a wind farm and HTHPS unit. The proposed model presents a comprehensive and coherent approach from historical data analysis as input to final decision making as output, that it can maximize Genco’s profit by avoiding incorrect commitment and energy offering. In the phase of uncertainty handling, via a scenario-based approach, the wind uncertainty is modeled by Monte-Carlo Simulation (MCS) method based on wind speed forecast errors. In the optimization phase, the Pareto optimal set is obtained by Non-dominated Sorting Genetic Algorithm-II (NSGA-II), and then, a new method is also provided to choose the best possible solution based on the entropy Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) method and the minimax regret criterion. The historical data related to wind generation and energy prices provided by the Danish energy market in West Denmark is used in simulation analysis, and the results demonstrate pleasantly the effectiveness of the proposed model.

Exploitation of Microgrid Flexibility in Distribution System Hosting Prosumers

Increasing the penetration of renewables on prosumers' side brings about operational challenges in the distribution grid due to their variable and uncertain behavior. In fact, these resources have increased the distribution grid net load fluctuation during recent years. In this article, the flexibility-oriented stochastic scheduling of a microgrid is suggested to capture the net load variability at the distribution grid level. In this scheduling, the flexibility limits are set to manage the net load fluctuation at a desirable level for the main grid operator. The uncertainties of load and renewables are considered, and their uncertainties are under control by the risk-averse strategy. Moreover, multiperiod islanding constraints are added to the problem, preparing the microgrid for a resilient response to disturbances. The model is examined on a typical distribution feeder consisting of prosumers and a microgrid. The numerical results are compared for both flexibility-oriented and traditional scheduling of a microgrid at the distribution level. The proposed model reduces the net load ramping of the distribution grid using an efficient dispatch of resources in the microgrid. A sensitivity analysis is also carried out to show the effectiveness of the model.

Stochastic Single Machine JIT Scheduling with Geometric Processing Times and Due Dates

In this paper, we investigate a static stochastic single machine JIT scheduling problem in which the jobs’ processing times are stochastically independent and follow geometric distributions whose mean is provided, due dates are geometrically distributed with a common mean, and both the unit penalty of earliness/tardiness and the fixed penalty of earliness/tardiness are deterministic and different. The objective is to minimize the expected total penalties for quadratic earliness, quadratic tardiness, and early and tardy jobs. We prove that the optimal schedule to minimize this problem is V-shaped with respect to the ratio of mean processing time to unit tardiness penalty under the specific condition. Also, we show a special case and two theorems related to this JIT scheduling problem under specific situations where the optimal solutions exist. Finally, based on the V-shaped characteristic, a dynamic programming algorithm is designed to achieve an optimal V-shaped schedule in pseudopolynomial time.

A multi-objective resilience-economic stochastic scheduling method for microgrid

In this paper, the applicability of Microgrids (MGs) is reviewed for power system resilience against low-probability high-impact (LPHI) events. Financial issues have been always one of the major priorities in the scheduling of MGs. Although these systems can feed their loads in islanding mode, resilient operation of them under critical situations caused by LPHI events is a challenging problem. Improving resilience increases MG costs, therefore it is necessary to establish a trade-off between resilience and economic metrics. Therefore, the main purpose of this paper is to develop a novel multi-objective resilience-economic stochastic MG scheduling model. The proposed bi-level resilience-oriented stochastic scheduling integrates the economic perspective along with resilience function simultaneously using a multi-objective mixed-integer linear programming approach. The considered MG resilience function includes various metrics such as the ability to withstand, quick recovery, and the technical criteria in the face of low-probability high-impact events. The proposed method is tested on the modified IEEE 33-bus power system with a set of distributed energy resources, energy storage systems, and electric vehicle parking lots. The results outlined that, although, the integration of the resilience metrics in the MG scheduling problem has increased the operation cost of the MG approximately 25%, but improved the MG resilience more than 70%. On the other hand, the proper management of the independent distributed energy resources enhanced the resilience of the MG approximately 16% while decreased the operation cost of the MG by at least 28%.

Performance comparison of approximate dynamic programming techniques for dynamic stochastic scheduling

This paper focuses on the performance comparison of several approximate dynamic programming (ADP) techniques. In particular, we evaluate three ADP techniques through a class of dynamic stochastic scheduling problems: Lagrangian-based ADP, linear programming-based ADP, and direct search-based ADP. We uniquely implement the direct search-based ADP through basis functions that differ from those used in the relevant literature. The class of scheduling problems has the property that jobs arriving dynamically and stochastically must be scheduled to days in advance. Numerical results reveal that the direct search-based ADP outperforms others in the majority of problem sets generated.

Control-aware batch process scheduling

Batch processes are inevitably affected by disturbances. The process control system can often reject them and ensure that the final product is “in spec.” Nevertheless, processing times and the quality of the final product and any intermediates can fluctuate as a result. In turn, this impacts the computation and execution of production schedules. We propose a new scheduling framework that considers the effect of disturbances and the impact of process control on short-term production scheduling of batch processes. Processing time expressions are derived using historical closed-loop process operating data. Subsequently, a two-stage stochastic scheduling problem is formulated, whereby exogenous and endogenous uncertainties are considered at the first stage, with the exception of product demand, which is dealt with in the second stage. Two case studies are presented in detail.

Energy Minimization in UAV-Aided Networks: Actor-Critic Learning for Constrained Scheduling Optimization

In unmanned aerial vehicle (UAV) applications, the UAV's limited energy supply and storage have triggered the development of intelligent energy-conserving scheduling solutions. In this paper, we investigate energy minimization for UAV-aided communication networks by jointly optimizing data-transmission scheduling and UAV hovering time. The formulated problem is combinatorial and non-convex with bilinear constraints. To tackle the problem, firstly, we provide an optimal algorithm (OPT) and a golden section search heuristic algorithm (GSS-HEU). Both solutions are served as offline performance benchmarks which might not be suitable for online operations. Towards this end, from a deep reinforcement learning (DRL) perspective, we propose an actor-critic-based deep stochastic online scheduling (AC-DSOS) algorithm and develop a set of approaches to confine the action space. Compared to conventional RL/DRL, the novelty of AC-DSOS lies in handling two major issues, i.e., exponentially-increased action space and infeasible actions. Numerical results show that AC-DSOS is able to provide feasible solutions, and save around 25-30% energy compared to two conventional deep AC-DRL algorithms. Compared to the developed GSS-HEU, AC-DSOS consumes around 10% higher energy but reduces the computational time from second-level to millisecond-level.

Risk‐adjustable stochastic schedule based on Sobol augmented Latin hypercube sampling considering correlation of wind power uncertainties

Risk‐adjustable stochastic schedule based on Sobol augmented Latin hypercube sampling considering correlation of wind power uncertainties

Nonlinear State Estimation With Multisensor Stochastic Scheduling

In this article, the problem of a nonlinear system states estimation with multisensor stochastic scheduling is investigated. In order to solve the non-Gaussian property induced by the nonlinear transformation, the unscented transformation (UT) technique is applied. Since the sensor networks channel is limited, the stochastic event-triggered mechanisms (SETMs) are proposed to reduce the network transmission burden. Under the SETMs, the modified unscented Kalman filter is proposed. Additionally, the sufficient conditions are given to guarantee the stabilities of the error covariance and the estimation error. Finally, extensive examples are carried out. Performances evaluation and comparison with existing methods are given to demonstrate the superiority of the proposed methods.

Corrigendum: Two-Stage Stochastic Scheduling of Integrated Electricity and Natural Gas Systems Considering Ramping Costs with P2G Storage and Wind Power

Corrigendum: Two-Stage Stochastic Scheduling of Integrated Electricity and Natural Gas Systems Considering Ramping Costs with P2G Storage and Wind PowerName of all authors as they appear in the published original article Affiliations of all authors as they appear in the published original version of the article * Correspondence: Tao Jiang, tjiang@neepu.edu.cnKeywords: Power-to-gas, ramping cost, wind power accommodation, stochastic programming, natural gas systemCorrigendum on: Two-Stage Stochastic Scheduling of Integrated Electricity and Natural Gas Systems Considering Ramping Costs With Power-to-Gas Storage and Wind Power. Front. Energy Res. 8:596774. doi: 10.3389/fenrg.2020.596774. Incorrect Funder NameThere is an error in the Funding statement. The correct Name for the Funder is ** science and technology project of State Grid Jilin Corporation (SGJL0000DKJS2000287)**. This is the only funder. The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated.

Markov automata with multiple objectives

Markov automata combine probabilistic branching, exponentially distributed delays and nondeterminism. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and stochastic scheduling. Their verification so far focused on single objectives such as (timed) reachability, and expected costs. In practice, often the objectives are mutually dependent and the aim is to reveal trade-offs. We present algorithms to analyze several objectives simultaneously and approximate Pareto curves. This includes, e.g., several (timed) reachability objectives, or various expected cost objectives. We also consider combinations thereof, such as on-time-within-budget objectives—which policies guarantee reaching a goal state within a deadline with at least probability p while keeping the allowed average costs below a threshold? We adopt existing approaches for classical Markov decision processes. The main challenge is to treat policies exploiting state residence times, even for untimed objectives. Experimental results show the feasibility and scalability of our approach.

Optimal stochastic scheduling of reconfigurable active distribution networks hosting hybrid renewable energy systems

Renewable energy sources (RESs) have a remarkable role in advancing the goals of restructured power systems to reduce greenhouse gas emissions and increase the level of reliability. However, due to the non-uniform utilisation of these resources in various sectors of power grids, a major part of the generated renewable energies is spilled to satisfy the power system constraints. Motivated by this challenge, the role of the reconfiguration mechanism in maximising the utilisation of RESs in active distribution networks (ADNs) is investigated herein. To this end, a two-stage stochastic model is presented for optimal scheduling of reconfigurable distribution networks in the presence of high-power hybrid wind/photovoltaic systems. The main goal of the presented model is to maximise the hybrid system owner's profit. In the first stage of the presented structure, the optimal hourly bilateral dispatches between the hybrid system and the ADN in the day-ahead electricity market are determined to maximise the hybrid system owner's profit. In the second stage, the power spillage of the hybrid renewable energy systems are minimised using reconfiguration technology in the real-time electricity market. For practical implementation, the proposed operational strategy is applied to the modified 33-bus and 69-bus distribution test systems, and is solved using GAMS software. The simulation results indicate that the proposed strategy can considerably reduce renewable power spillage, increase the hybrid system owner's profit, and decrease total active power loss of the ADN. According to the obtained results in the 33-bus test system, the profit of the hybrid system owner is increased by up to 6.8% as well as the total active power loss being decreased by up 75.58% through the presented structure.

Stochastic energy management and scheduling of microgrids in correlated environment: A deep learning-oriented approach

Regarding the operation, reliability, security, and cost-effectiveness of microgrids (MGs), optimal energy management and data security are essential issues that must be taken into consideration. In this regard, this paper proposes a secured stochastic energy management scheme for both grid-connected and islanded hybrid AC-DC MGs (HMGs) considering renewable energy sources (RESs), plug-in hybrid electric vehicles (PHEVs), and energy storage devices (ESs). In this work, the operation of HMGs is formulated as a single objective optimization problem, which is solved using the interior search optimization algorithm (ISOA). In order to reinforce data security in HMGs, a deep learning-based intrusion detection system (IDS) based on the long short-term memory (LSTM) and prediction interval is proposed to detect false data injection attacks (FDIA) on advanced metering infrastructures (AMIs). In this work, the 2 m point estimation method is utilized to model uncertainties associated with the forecasted output power of RESs, energy market price, charging demand of PHEVs, and load demand. The performance of the proposed scheme is evaluated using IEEE 33 bus test system for both operation modes.

Wind power scenario generation with non-separable spatio-temporal covariance function and fluctuation-based clustering

Short-term wind power scenarios significantly affect the economic efficiency of the stochastic power system scheduling. In order to better capture the nonlinear spatio-temporal correlations of wind power, this paper proposes a scenario generation method integrated with non-separable spatio-temporal covariance function and fluctuation-based clustering for short-term wind power output. By taking advantage of well-calibrated marginal distribution modeled by Gaussian mixture model, the non-separable covariance function is incorporated in the scenario generation method to capture the complex interactions between spatial and temporal components of wind power. To estimate the covariance matrix more precisely, the historical data is grouped into K clusters with different fluctuations using the K-means clustering algorithm. Two indices are proposed to evaluate the scenarios in capturing the spatial and temporal correlations from the perspective of system operators. The proposed method is applied to a modified IEEE-118 system with four wind farms. Simulation results verify the superiority of the proposed method in capturing spatial and temporal correlations, and validate the economic benefits for the power system operation.

A semantic-level component-based scheduling method for customized manufacturing

• Information model obtains the job shop state through semantic reasoning. • Computation model generates the optimal schedules for guiding the control of manufacturing resources. • The integration of information model and computation model reduces the search of the solution space. To meet the increasingly complex needs of customers, scheduling faces challenges of the high uncertainty of product arrival in customized manufacturing (CM). This paper proposes a semantic-level component-based scheduling method to solve the uncertainty via the integration of the information model and the computation model. In our proposal, we first construct a component-based framework to illustrate the composition and execution mechanism of a component. Then we present a semantic-enriched information model to obtain the state of the shop floor through automatic semantic reasoning. Additionally, we build a computation model to abstract the stochastic scheduling process of CM. Finally, we design an iteration algorithm to solve the computation model through the interaction between the information model and computation model. In experiments, we show that for random arrivals of products, our proposal can ensure the timeliness of the learning and decision-making, and the task assignment performance is the best compared with the other two methods.

Stochastic control and time scheduling for irregular robots

Vehicles of different sizes are difficult to navigate in close vicinity. In this paper, we propose multi-vehicle coordination strategy by stochastic control and time scheduling to guarantee no collisions. We use contours and relative motions of vehicles to calculate collision time and use it in multi-vehicle scheduling and reduce computation burden. The proposed strategy enables the vehicles to add calculation delay when vehicles are moving towards the destinations. To avoid complicated control rule design for motion-restricted irregular vehicles, we propose stochastic control to provide satisfactory performance. By changing the frequency of control update, a modification is proposed to take congestion into account. Simulation examples are given to demonstrate the effectiveness of the proposed approach.

Two-stage robust stochastic scheduling for energy recovery in coal mine integrated energy system

During the mining process, many energy resources are produced additionally, which have a promising prospect to supply electricity, heat and cooling energy. However, different energy inertia and diverse uncertainties from photovoltaic, wind turbine and gushing water outputs will pose challenges to the operation of a coal mine integrated energy system. This paper constructs a coal mine integrated energy system operation model considering energy resources recovery. Coal mine integrated energy system consists of energy supply subsystem, energy recovery subsystem, and energy storage subsystem, and it integrates multiple energies such as electricity, heat and cooling. A two-stage robust stochastic optimization method is proposed to adapt to the uncertainties. At the day-ahead stage decision, the optimal operation problem is solved at long time intervals to determine the heat dispatching. Meanwhile, the intra-day stage decision is focused on dealing with diverse uncertainties at short time intervals to enhance operational robustness. Heat energy equipment is scheduled at intra-day stage with the day-ahead dispatching result. A real case of coal mine is demonstrated to validate the effectiveness and robustness of the proposed method. The result reveals that the proposed method, compared to the conventional methods, can fully improve the economic benefits, the energy recovery and the system operational robustness.