Stochastic Scheduling Research Articles

Multi-modal cargo logistics distribution problem: Decomposition of the stochastic risk-averse models

This paper aims to develop a solution framework for large size scheduling problems by a novel multi-modal stochastic model in order to help the decision-makers to create a desirable schedule for the Belt & Road (B&R) corridors and North–South corridor, which provide a big trade market for the China–Europe routes. The model incorporates risk measures to resolve the stochastic scheduling problem where the uncertainty of demand, transit time and unloading time are taken into account. The developed model considers the transit cargoes and the various transportation options under time window limitations. In order to select the most effective risk measure, four well-known risk measures are evaluated including Value at Risk (VaR), Conditional Value at Risk (CVaR), Tail Value at Risk (TVaR) and Mean Absolute Deviation (MAD). A two-phase hierarchical algorithm with an integrated novel Golden Search (GS) algorithm is developed to deal with the proposed bi-objective model. In order to cope with the large scale problems, the Sample Average Approximation (SAA) and Scenario Decomposition (SD) methods are further proposed. A Lagrangian Decomposition (LD) algorithm is then developed to estimate the best lower bound of the SD. The efficiency and effectiveness of the proposed model and solution framework has been validated via sets of sensitivity analysis tests. The results of analysis define the optimal flows of the cargoes across the most economic corridor.

Two-stage optimal operation of integrated energy system considering multiple uncertainties and integrated demand response

Integrated energy system (IES) is considered an effective way to alleviate energy supply pressure and improve energy efficiency, which has attracted considerable attentions worldwide. However, in existing studies, the coordination of uncertainty addressing and demand responses over different scheduling stages have not been fully considered in IES operation. Based on these considerations, a two-stage optimal operation method considering multiple uncertainties and integrated demand response is proposed for a community integrated energy system (CIES). First, given the CIES structure, various energy equipment are modeled and analyzed from the perspective of energy conversion and storage. Moreover, a generic optimal operation framework and model that comprises day-ahead and intraday stages is developed for a two-stage CIES scheduling. While the day-ahead stage introduces the time-shifted demand response (DR) to establish a robust optimization operation model, the intraday stage performs a stochastic scheduling with the adoption of replaced DR. Finally, a case study is carried out to demonstrate the operation model, and simulation results show that the proposed method can give play to the complementary advantages of multi energy sources and effectively promote the energy supply and demand balance in the presence of multiple uncertainties and demand responses.

Adaptive Computing Scheduling for Edge-Assisted Autonomous Driving

This paper investigates computing resource scheduling for real-time applications in autonomous driving, such as localization and obstacle avoidance. In our considered scenario, autonomous vehicles periodically sense the environment, offload sensor data to an edge server for processing, and receive computing results from the server. Due to mobility and computing latency, a vehicle travels some distance in the duration between the instant of offloading its sensor data and the instant of receiving the computing result. Our objective is finding a scheduling scheme for the edge sever to minimize the above traveled distance of vehicles. The approach is to determine the processing order according to individual vehicle mobility and computing capability of the edge server. We formulate a restless multi-arm bandit (RMAB) problem, design a Whittle index based stochastic scheduling scheme, and determine the index using a deep reinforcement learning (DRL) method. The proposed scheduling scheme avoids the time-consuming policy exploration common in DRL scheduling approaches and makes effectual decisions with low complexity. Extensive simulation results demonstrate that the proposed indexed-based scheme can deliver computing results to the vehicles promptly while adapting to time-variant vehicle mobility.

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

Stochastic single machine scheduling problem as a multi-stage dynamic random decision process

In this work, we study a stochastic single machine scheduling problem in which the features of learning effect on processing times, sequence-dependent setup times, and machine configuration selection are considered simultaneously. More precisely, the machine works under a set of configurations and requires stochastic sequence-dependent setup times to switch from one configuration to another. Also, the stochastic processing time of a job is a function of its position and the machine configuration. The objective is to find the sequence of jobs and choose a configuration to process each job to minimize the makespan. We first show that the proposed problem can be formulated through two-stage and multi-stage Stochastic Programming models, which are challenging from the computational point of view. Then, by looking at the problem as a multi-stage dynamic random decision process, a new deterministic approximation-based formulation is developed. The method first derives a mixed-integer non-linear model based on the concept of accessibility to all possible and available alternatives at each stage of the decision-making process. Then, to efficiently solve the problem, a new accessibility measure is defined to convert the model into the search of a shortest path throughout the stages. Extensive computational experiments are carried out on various sets of instances. We discuss and compare the results found by the resolution of plain stochastic models with those obtained by the deterministic approximation approach. Our approximation shows excellent performances both in terms of solution accuracy and computational time.

Stochastic day-ahead unit commitment scheduling of integrated electricity and gas networks with hydrogen energy storage (HES), plug-in electric vehicles (PEVs) and renewable energies

This study investigates stochastic day-ahead unit commitment scheduling of integrated natural gas and power systems that consist of a non-gas-fired unit (NGFU), gas-fired unit (GFU), combined heat and power (CHP) unit, and renewable production units considering AC power flow. Natural gas storage is incorporated into the problem to support the gas network during peak natural gas demand hours by reducing pipeline congestion. Moreover, integrating hydrogen energy storage (HES) along with new flexible technologies, such as power to gas (P2G) system and demand response program (DRP) is proven to reduce total operation cost by facilitating renewable energy dispatch and shifting peak load demand to off-peak hours. A sensitivity analysis is carried out to evaluate the impact of thermal load increment on the operation of the CHP unit as its thermal and electrical output are interrelated variables. A residential plug-in electric vehicle (PEV) charging station is integrated into the problem to observe its impact on the operation of the networks, as PEVs introduce a new unplanned and uncertain load to the system. Furthermore, the sensitivity of the problem for PEV penetration is investigated. The uncertain parameters of the problem are electrical load demand, PEVs’ load demand, and wind power. Eventually, the proposed mixed integer non-linear problem (MINLP) is applied to several case studies involving an integrated 6-bus power system and 6-node gas network.

Data clustering based probabilistic optimal scheduling of an energy hub considering risk-averse

An energy hub (EH) is a multi-carrier energy system supplying various types of energy demands. Optimal management of these systems is a non-linear, non-convex, and complicated problem. This complexity is increased because of the unpredictable renewable generation and consumption patterns. Inattention to the probabilistic nature of the uncertain variables may increase the risk of encountering undesired conditions. The use of accurate and low computational probabilistic assessment methods is very important in this problem.This paper presents risk-constrained stochastic scheduling for an EH considering the uncertainties of renewable generations and load demands. The risk is assessed by the conditional value at risk (CVaR) method. A trade-off between decrement of the operation and emissions cost and increment of the risk aversion is offered. The proposed method is applied on an energy hub consisting of a wind turbine (WT), photovoltaic (PV) cells, a fuel cell power plant (FCPP), a combined heat and power generation unit (CHP) and plug-in electric vehicles (PEVs). The wind speed, solar irradiation, all types of demands as well as the market prices are considered as uncertain variables. In order to get maximum profit and enhance the consumption curve, electrical, thermal and cooling demand response programs (DRPs) are applied. Uncertainties in input random variables are managed by the efficient k-means data clustering method. The results, which show considerable flexibility in the energy management of the energy hub, are comprehensively discussed. Simulation results indicate that 1.97%, 6.25%, and 10.17% reduction in the operation cost of the proposed EH can be achieved with the integration of the PEVs, FCPP, and DRPs, respectively. Additionally, the risk cost of the EH is improved by 1.95%, 6.2%, and 9, 68% with consideration of the PEVs, FCPP, and DRPs, respectively.

Minimizing activity exposures in project scheduling under uncertainty

We propose a model to solve a project scheduling problem where resource assignments and activity schedules need to be determined to achieve a set of due-date requirements as well as possible. The concept of activity duration tolerance levels is introduced to describe the longest activity durations over which the due-dates are guaranteed to be achieved. Based on this, we propose a due-date achievement model using a proposed performance measure termed as the activities exposure level, which accounts for the total amount of durations exceeding tolerance levels for a given scheduling solution. We describe various properties and characteristics of the proposed scheduling optimization model and its practical implications. We show that the associated stochastic scheduling problem with resource constraints can be equivalently computed as the solution of a modest-sized mixed-integer linear program using the sample average approximation approach. Computational results show that our proposed models perform well when compared to different standard approaches across various performance measures.

NPSCS: Non-Preemptive Stochastic Coflow Scheduling With Time-Indexed LP Relaxation

Coflows model a scheduling setting that is commonly found in a variety of applications in distributed and cloud computing. A stochastic coflow task contains a set of parallel flows with randomly distributed sizes. Further, many applications require non-preemptive scheduling of coflow tasks. This article gives an approximation algorithm on the weighted expected completion time for non-preemptive stochastic coflow scheduling. The proposed approach uses a time-indexed linear program relaxation, and uses its solution to come up with a feasible schedule. This algorithm is shown to achieve an approximation ratio of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(2\log {m}{+}1)(1{+}\sqrt {m {\Delta }})(1{+}m\sqrt {{\Delta }}){(1{+}{\Delta })}$ </tex-math></inline-formula> for zero-release times, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2(2\log {m}{+}1)(1{+}\sqrt {m{\Delta }})(1{+}m\sqrt {{\Delta }})(1{+}{\Delta })$ </tex-math></inline-formula> for general release times, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\Delta }$ </tex-math></inline-formula> represents the upper bound of squared coefficient of variation of processing times, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> is the number of servers.

A stochastic scheduling, allocation, and inventory replenishment problem for battery swap stations

Electric vehicles and drones promise to transform transportation systems and supply chains. However, long recharge times and battery degradation inhibit adoption. To overcome these barriers, swap stations enable quick battery exchange. We introduce a stochastic scheduling, allocation, and inventory replenishment problem which determines the charging, discharging, and replacement decisions at a swap station over time. The decisions are complex because recharging is necessary for short-term operation but causes degradation and the need for future replacement. We model the problem as a Markov Decision Process, solve it using backward induction, and show that the problem suffers from the curses of dimensionality. Hence, we propose two approximate methods, a heuristic benchmark policy and a reinforcement learning method, which provide high-quality solutions. Using a designed experiment, we deduce effective operational insights.

Integrating Schedule Risk Analysis with Multi-Skilled Resource Scheduling to Improve Resource-Constrained Project Scheduling Problems

Construction projects are planned in a complex and dynamic environment characterized by high risks and uncertainties amidst resource constraints. Assessing construction schedule risk facilitates informed decision-making, especially in a resource-constrained situation, and allows proactive actions to be taken so that project objectives are not jeopardized. This study presents a stochastic multiskilled resource scheduling (SMSRS) model for resource-constrained project scheduling problems (RCSPSP) considering the impact of risk and uncertainty on activity durations. The SMSRS model was developed by integrating a schedule risk analysis (SRA) model (developed in MS Excel) with an existing multiskilled resource scheduling (MSRS) algorithm for the development of a feasible and realistic schedule. The computational experiment carried out on three case projects using the proposed SMSRS model revealed an average percentage deviation of 10.50%, indicating the inherent risk and uncertainty in activity durations of the project schedule. The core contribution of the proposed SMSRS model is that it: (1) presents project practitioners with a simple tool for assessing the risks and uncertainty associated with resource-constrained project schedules so that necessary response actions can be taken to ensure project success; (2) provides the small-scale construction businesses with an affordable tool for evaluating schedule risk and developing a feasible and realistic project schedule.

Optimal Dynamic Appointment Scheduling of Base and Surge Capacity

Problem definition: We study dynamic stochastic appointment scheduling when delaying appointments increases the risk of incurring costly failures, such as readmissions in healthcare or engine failures in preventative maintenance. When near-term base appointment capacity is full, the scheduler faces a trade-off between delaying an appointment at the risk of costly failures versus the additional cost of scheduling the appointment sooner using surge capacity. Academic/practical relevance: Most appointment-scheduling literature in operations focuses on the trade-off between waiting times and utilization. In contrast, we analyze preventative appointment scheduling and its impact on the broader service-supply network when the firm is responsible for service and failure costs. Methodology: We adopt a stochastic dynamic programming (DP) formulation to characterize the optimal scheduling policy and evaluate heuristics. Results: We present sufficient conditions for the optimality of simple policies. When analytical solutions are intractable, we solve the DP numerically and present optimality gaps for several practical policies in a healthcare setting. Managerial implications: Intuitive appointment policies used in practice are robust under moderate capacity utilization, but their optimality gap can quadruple under high load.

Optimal Dynamic Appointment Scheduling of Base and Surge Capacity

Problem definition: We study dynamic stochastic appointment scheduling when delaying appointments increases the risk of incurring costly failures, such as readmissions in health care or engine failures in preventative maintenance. When near-term base appointment capacity is full, the scheduler faces a trade-off between delaying an appointment at the risk of costly failures versus the additional cost of scheduling the appointment sooner using surge capacity. Academic/Practical Relevance: Most appointment scheduling literature in operations focuses on the trade-off between waiting times and utilization. In contrast, we analyze preventative appointment scheduling and its impact on the broader service supply network when the firm is responsible for service and failure costs. Methodology: We adopt a stochastic dynamic programming (DP) formulation to characterize the optimal scheduling policy and evaluate heuristics. Results: We present sufficient conditions for the optimality of simple policies. When analytical solutions are intractable, we solve the DP numerically and present optimality gaps for several practical policies in a health care setting. Managerial Implications: Intuitive appointment policies used in practice are robust under moderate capacity utilization, but their optimality gap can quadruple under high load.

Scenario Reduction for Stochastic Day-Ahead Scheduling: A Mixed Autoencoder Based Time-Series Clustering Approach

Scenario based stochastic scheduling has drawn a tremendous amount of interests worldwide in tackling the uncertainty of renewable energy and accounting for risks. It is important to generate representative time-series scenarios of renewable energy, while keeping the dimensionality of the scenario set tractable. This article presents a mixed autoencoder based clustering approach to select a reduced scenario set from high-dimensional time series. In contrast to other techniques targeting on minimizing different probability distances, the proposed architecture accounts for the pattern recognition within a large set of scenarios. The effectiveness of the model is verified in the case studies, where the data sets from the Bonneville Power Administration and Elia are used. The numerical results show that the model outperforms the state of the art, in terms of statistical metrics and through empirical analysis.

Day-ahead Risk-constrained Stochastic Scheduling of Multi-energy System

As an increasing penetration of renewable energy sources can potentially impact voltage profile and compromise system security, the security continues to be the most critical concern in power system operations. A risk-constrained stochastic scheduling model is proposed to leverage the latent scheduling capacity of a multi-energy system to seek an economic operation solution while maintaining system operation risk level against uncertain renewable generation. Overvoltage risk constraints, as compared to the straightforward voltage boundary limits, are incorporated into the stochastic scheduling model to guarantee the operation security and economics. Linearized AC power flow model is applied to enable overvoltage risk assessment within the coordinated scheduling model. The proposed stochastic scheduling model is tackled via the improved progressive hedging approach with an enhanced relax-round-polish process, which overcomes the convergence issues of the traditional progressive hedging in handling nonconvex stochastic scheduling model with binary variables on both stages. Numerical simulation results of IEEE 30-bus system and IEEE 118-bus system illustrate the efficacy of the proposed model in ensuring voltage security and improving economic operation of systems.

Enhancing the Resilience of Operational Microgrids Through a Two-Stage Scheduling Strategy Considering the Impact of Uncertainties

This article deals with the stochastic scheduling of a microgrid (MG) to balance the economical and resilience metrics. In the proposed model, the MG resilience indices are integrated into the economic criteria to ensure the resilience of MG operation alongside the main MG actors’ profit/loss. The MG fragility index, recovery efficiency index, MG voltage index, and lost load index are considered in the proposed planning model. Further, to make the results more realistic, the uncertainties associated with energy price and wind production, alongside with planning of energy storage systems and electric vehicles parking lots are considered. To achieve a better solution for the security-constraint operation of MG, AC network equations are included in the system modeling. Finally, a large-scale MG based on the IEEE-33 bus testbed is utilized to evaluate the effectiveness of the proposed stochastic scheduling program.

Optimal Decomposition of Stochastic Dispatch Schedule for Renewable Energy Cluster

The correlated renewable energy farms are usually aggregated as a cluster in economic dispatch to relieve computational burden. This strategy can also achieve better performance since the precision of predicting the power generation of a cluster can be higher than those of individual farms. This paper proposes an optimal decomposition method to allocate dispatch schedules among renewable energy farms (REFs) in the cluster under existing stochastic optimization framework. The proposed model takes advantage of probabilistic characteristics of renewable generation to minimize the curtailment and ensure the feasibility of dispatch schedule of the clusters. Approximated tractable formulation and efficient solution method are the proposed to solve the proposed model. Numerical tests show that the proposed method achieves the optimal decomposition of dispatch schedule among REFs and facilitates the utilization of renewable generation.

Dispatching fuel-cell hybrid electric vehicles toward transportation and energy systems integration

With an increasing integration of traditional electric vehicles (EVs), the ensuing congestion and overloading issues have threatened the reliability of power grid operation. Hydrogen has been advocated as a promising energy carrier to achieve a low-carbon transportation and energy (trans-energy) systems, which can support the popularization of fuel cell hybrid EVs (FCHEVs) while enhancing the flexibility of power grids. In this paper, we propose an optimal scheduling framework for trans-energy systems that evaluates the merits of hydrogen supply chain from water electrolysis, compressed storage and transportation to FCHEV utilization. A detailed FCHEV model is established, and mileage is modeled as a function of the stored electricity and hydrogen mass. A stochastic programming-based scheduling model is formulated, which minimizes the total cost of unit commitment and hydrogen supply chain. Dijkstra algorithm is adopted to search the shortest path for hydrogen transportation. Case studies demonstrate that FCHEVs can reduce the operation costs of the trans-energy systems and facilitate the accommodation of renewable energy compared to traditional EVs.

Paired discrete competition with a free route choice

The paper considers the problem of optimizing the operation schedule for multiprocessor systems. The solution to this problem involves the formation of a rigid work schedule, which determines the rhythm of the processes, but in practice the functioning of systems is influenced by many side factors that make the intervals of work execution random. In the work, a semi-Markov model of the formation of a stochastic schedule in conditions of pair competition is constructed. It is shown that if during the functioning of the system it is possible to execute the items of the schedule in an arbitrary order, then the evolution of the semi-Markov process follows the Hamiltonian path. It is proved that all possible realizations of Hamiltonian paths form a complete group of incompatible events. It is noted that, due to the imposition of restrictions on the nature of evolution, the evolution process is not strictly semi-Markov, and therefore a method of forming a strictly semi-Markov process with a tree structure from the primary model is proposed. Dependences are obtained for calculating the distribution densities and the probabilities of switching from states of a semi-Markov process to conjugate states, as well as the time of walking from the starting to absorbing states. Using the concept of paired discrete competition and a distributed penalty, the effectiveness of the choice of a Hamiltonian path by one of the subjects is estimated, taking into account the fact that the algorithm of his opponent’s behavior is known up to the construction of a semi-Markov model.

A multi-energy complementary virtual power plant operation optimization model for distributed energy aggregation is considered

In this paper, a stochastic scheduling optimization model of virtual power plant (VPP) is established to maximize the net operating income of VPP considering the loss of uncertain risks. Firstly, the model of conventional scheduling optimization of virtual power plant is presented. Then, the risk conditional value (CVaR) theory is introduced to quantify the operational risk level of VPP, and the constraint conditions containing random variables are converted by the confidence method to establish the risk avoidance scheduling optimization model of VPP. Finally, an improved IIEEE30 node system is used as a simulation system to verify the validity and applicability of the proposed model.