Scheduling Policy Research Articles

Joint Learning of Volume Scheduling and Order Placement Policies for Optimal Order Execution

Order execution is an extremely important problem in the financial domain, and recently, more and more researchers have tried to employ reinforcement learning (RL) techniques to solve this challenging problem. There are a lot of difficulties for conventional RL methods to tackle the order execution problem, such as the large action space including price and quantity, and the long-horizon property. As naturally order execution is composed of a low-frequency volume scheduling stage and a high-frequency order placement stage, most existing RL-based order execution methods treat these stages as two distinct tasks and offer a partial solution by addressing either one individually. However, the current literature fails to model the non-negligible mutual influence between these two tasks, leading to impractical order execution solutions. To address these limitations, we propose a novel automatic order execution approach based on the hierarchical RL framework (OEHRL), which jointly learns the policies for volume scheduling and order placement. OEHRL first extracts the state embeddings at both the macro and micro levels with a sequential variational auto-encoder model. Based on the effective embeddings, OEHRL generates a hindsight expert dataset, which is used to train a hierarchical order execution policy. In the hierarchical structure, the high-level policy is in charge of the target volume and the low-level learns to determine the prices for a series of the allocated sub-orders from the high level. These two levels collaborate seamlessly and contribute to the optimal order execution policy. Extensive experiment results on 200 stocks across the US and China A-share markets validate the effectiveness of the proposed approach.

Improving QoS in cloud resources scheduling using dynamic clustering algorithm and SM‐CDC scheduling model

SummaryQuality of Service (QoS) regulates and controls network resources by setting priorities for specific data types. Many clustering algorithms are used to cluster cloud workloads, most of which are static. However, the lack of dynamic algorithms is seen in the face of huge databases that are real‐time and according to the existing clustering conditions. Additionally, fair allocation of tasks on servers and efficient resource utilization pose challenges. In this research, two solutions are proposed to improve the quality of service: the first solution uses the chameleon dynamic algorithm, a method to improve service quality. The chameleon algorithm has been able to show significant performance due to its high accuracy in detecting the smallest distance between clusters. This dynamic algorithm outperforms static algorithms with classification accuracy and response speed, which are the most important parameters of service quality. The second part of the proposed solution is to use the Scheduling Model using Cloud Data Centers (SM‐CDC) system to select the best service provider based on the clustering done in the previous step. A SM‐CDC technique is developed to handle cloud storage center tasks that are stored in electronic devices. According to the comparison with existing scheduling policies, SM‐CDC offered 36% decrease on response time, 50% reduction on cost of resources, and 40% improvement on QoS Satisfaction.

Cooperative multi-agent reinforcement learning for multi-area integrated scheduling in wafer fabs

The existing scheduling methods of wafer fabs focus on single area, achieving local optimisation while failing to realise global optimisation due to neglecting the coordination of multi-area. Therefore, it is necessary to consider the complex opposing relationships between multi-area caused by constraints such as batch processing, re-entrance, and multiple residency times within and between areas to conduct integrated scheduling and shorten the production cycle time. For this issue, this paper proposes a cooperative multi-agent reinforcement learning for multi-area integrated scheduling. Aiming at the dynamic batching and scheduling considering the dynamic arrival lots in multi-area, a multi-agent reinforcement learning algorithm is presented to learn the optimal dynamic batching and scheduling policy firstly. Subsequently, a cooperative multi-agent framework is raised to achieve the global optimisation and coordination of multi-area. Furthermore, an adaptive exploration strategy is constructed to enhance the global exploration capability of the complex solution space caused by residency time constraints and re-entrant property. Moreover, a policy share enhanced Double DQN is employed to improve the generalisation and adaptability of the multi-agent. Finally, the experiments demonstrate that the proposed integrated scheduling method has better comprehensive performance compared to the previous area-separated scheduling methods.

Knowledge graph-enhanced multi-agent reinforcement learning for adaptive scheduling in smart manufacturing

AbstractSelf-organizing manufacturing network has emerged as a viable solution for adaptive manufacturing control within the mass personalization paradigm. This approach involves three critical elements: system modeling and control architecture, interoperable communication, and adaptive manufacturing control. However, current research often separates interoperable communication from adaptive manufacturing control as isolated areas of study. To address this gap, this paper introduces Knowledge Graph-enhanced Multi-Agent Reinforcement Learning (MARL) method that integrates interoperable communication via Knowledge Graphs with adaptive manufacturing control through Reinforcement Learning. We hypothesize that implicit domain knowledge obtained from historical production job allocation records can guide each agent to learn more effective scheduling policies with accelerated learning rates. This is based on the premise that machine assignment preferences effectively could reduce the Reinforcement Learning search space. Specifically, we redesign machine agents with new observation, action, reward, and cooperation mechanisms considering the preference of machines, building upon our previous MARL base model. The scheduling policies are trained under extensive simulation experiments that consider manufacturing requirements. During the training process, our approach demonstrates improved training speed compared with individual Reinforcement Learning methods under the same training hyperparameters. The obtained scheduling policies generated by our Knowledge Graph-enhanced MARL also outperform both individual Reinforcement Learning methods and heuristic rules under dynamic manufacturing settings.

Nonlinear Analysis of EDF Scheduling Framework for Resource Distribution in Cloud Computing

In modern times, the field of information technology is significantly shifting towards cloud computing. This innovative technology involves the permanent storage of resources on servers, which clients access via the internet. Typically, a cloud comprises a collection of resources known as virtual machines, capable of managing both computational tasks and storage needs. As the demand for cloud services continues to rise, the scheduling of these resources presents a considerable challenge. Scheduling refers to the workflow management necessary to complete tasks within the system. An efficient scheduler adapts its scheduling policy dynamically in response to changing conditions and task requirements. Cloud computing represents a recently developed technology where resources, whether physical or virtual machines, are permanently stored on servers and accessed by users through the internet. The cloud offers various service models, including Platform as a Service (PaaS), Software as a Service (SaaS), and Infrastructure as a Service (IaaS). In this context, IaaS refers to a set of resources, including virtual machines, that provide computational and storage services. Given the increasing adoption of cloud technology, resource scheduling has become a critical task. Hence, optimizing the scheduling of requests to ensure the best utilization of cloud resources is essential. This paper introduces a Nonlinear Analysis of EDF Scheduling Framework for resource allocation that considers deadlines and processing times when assigning resources to specific jobs. The performance metrics, including Average Turnaround Time, Average Waiting Time, and Average Deadline Violation, show a significant improvement when compared to traditional scheduling models such as First-Come, First-Served (FCFS), the Shortest Job First (SJF), and Simple Earliest Deadline First (EDF) models.

Dynamic resource allocation and scheduling for appointment-based systems with walk-ins

Effectively managing constrained and perishable capacity amid fluctuating demands is a common challenge in service industries, often addressed through appointment-based systems that incorporate walk-ins. Balancing appointments and walk-ins is crucial for enhancing system value and maintaining stability. In this article, we study an integrated decision problem for appointment scheduling and resource allocation across multiple facilities, considering stochastic demands from three segments: priority customers, walk-in customers, and appointment customers. We formulate the problem as a sequential scheduling-allocation challenge using stochastic dynamic programming. Leveraging the anti-multimodularity of the value function, we fully characterize the optimal dynamic resource allocation policy and its monotone structural properties under any appointment schedule. Given the complexity and intractability of optimal scheduling with dynamic resource allocation, we introduce two suboptimal scheduling policies—vertical scheduling and horizontal scheduling—and a heuristic allocation policy. Additionally, we create an Upper Bound (UB) for the original problem as a surrogate, establishing an asymptotically optimal UB for the scaled problem through its objective value and a corresponding lower bound through its solution. This UB solution serves as an efficient and effective heuristic, demonstrating superior performance compared with the combined performance of suboptimal scheduling policies with optimal dynamic resource allocation, especially as problem size increases. It also holds significant practical implications for integrated pooling systems.

Coordinated referral and scheduling decisions for specialized healthcare services

This paper studies the coordination of referral and scheduling policies where access to specialized medical services, such as surgical procedures, imaging or other consultations, is managed through a centralized intake system. In this increasingly common mode of operation, a central body makes decisions regarding the allocation of patients between a set of providers, followed by the provider taking control of the scheduling and delivery of the required service. To study the coordination of the allocation and scheduling policies we present a sequential optimization model where both referrer and provider attempt to maximize the proportion of a heterogeneous set of patients receiving treatment within a targeted wait time. Motivated by observations of performance thresholds in queueing systems, we introduce an achievable region model which permits study of providers who vary in ability to coordinate scheduling different patient streams. We characterize optimal referral and scheduling policies for a range of demand patterns and operational abilities. We find that the optimal referral policy can result in large discrepancies in outcomes for different patient types but that the discrepancy in outcomes is muted when operational abilities are higher. In situations where operational abilities are low, it is optimal for the providers to prioritize patients by stream. Low capacity for both providers results in an optimal referral and scheduling policy where certain patients streams are deprioritized and with certainty will not be seen within their wait time targets. We also study the cost of enforcing parity between patient classes and find that the cost is reduced when providers have higher operational abilities. This paper illustrates how operational constraints lead to incentives to prioritize different patient streams. In particular, we show that when operations are challenging, a more hands-on design is required to ensure clinical intake systems maintain equitable access to the service.

Dynamic scheduling of hybrid flow shop problem with uncertain process time and flexible maintenance using NeuroEvolution of Augmenting Topologies

AbstractA hybrid flow shop is pivotal in modern manufacturing systems, where various emergencies and disturbances occur within the smart manufacturing context. Efficiently solving the dynamic hybrid flow shop scheduling problem (HFSP), characterised by dynamic release times, uncertain job processing times, and flexible machine maintenance has become a significant research focus. A NeuroEvolution of Augmenting Topologies (NEAT) algorithm is proposed to minimise the maximum completion time. To improve the NEAT algorithm's efficiency and effectiveness, several features were integrated: a multi‐agent system with autonomous interaction and centralised training to develop the parallel machine scheduling policy, a maintenance‐related scheduling action for optimal maintenance decision learning, and a proactive scheduling action to avoid waiting for jobs at decision moments, thereby exploring a broader solution space. The performance of the trained NEAT model was experimentally compared with the Deep Q‐Network (DQN) and five classical priority dispatching rules (PDRs) across various problem scales. The results show that the NEAT algorithm achieves better solutions and responds more quickly to dynamic changes than DQN and PDRs. Furthermore, generalisation test results demonstrate NEAT's rapid problem‐solving ability on test instances different from the training set.

A Comprehensive IoT edge based smart irrigation system for tomato cultivation

Agriculture industry is the primary engine for a country's economic development. Growing crops using minimum irrigation water is a major challenge for farmers. In conventional farming, crops may be affected by various diseases due to inadequate irrigation scheduling. Recent proposals have suggested using Edge-IoT, AI, and distributed computing to accelerate the inference procedure utilized in smart irrigation applications. The use of resource-constrained edge servers and edge devices used to deliver smart agriculture applications can cause latency-sensitive workloads to interfere with one another. To address this issue, we design a long-range (LoRa) edge IoT computing-based sustainable and customized smart irrigation framework to capture the real-time data of tomato plants. This helps in automatic underground drip irrigation scheduling. This also predicts total water demand and usage, and measure plant growth status. The edge-IoT cloud data transmission control and optimization has been enforced using Smart irrigation data optimization and robust transmission (SIDORT) Message Queuing Telemetry Transport (MQTT) system. We develop a hybrid algorithm named Linked least traversal (LLT) for machine-to-machine communication (M2M). Also, a Reinforcement learning (RL) based Optimal Soil Wetness Closeness Policy (OSWCP) for irrigation scheduling has been proposed. The performance of the proposed smart irrigation models has been validated through extensive experiments using real-time data in which OSWCP performance has been measured at a 97.88 % accuracy rate. Additionally, a comparison of our proposed architecture has been accomplished by resolving the existing smart irrigation system challenges.

EETS: An energy-efficient task scheduler in cloud computing based on improved DQN algorithm

The huge energy consumption of data centers in cloud computing leads to increased operating costs and high carbon emissions to the environment. Deep Reinforcement Learning (DRL) technology combines of deep learning and reinforcement learning, which has an obvious advantage in solving complex task scheduling problems. Deep Q Network(DQN)-based task scheduling has been employed for objective optimization. However, training the DQN algorithm may result in value overestimation, which can negatively impact the learning effectiveness. The replay buffer technique, while increasing sample utilization, does not distinguish between sample importance, resulting in limited utilization of valuable samples. This study proposes an enhanced task scheduling algorithm based on the DQN framework, which utilizes a more optimized Dueling-network architecture as well as Double DQN strategy to alleviate the overestimation bias and address the shortcomings of DQN. It also incorporates a prioritized experience replay technique to achieve importance sampling of experience data, which overcomes the problem of low utilization due to uniform sampling from replay memory. Based on these improved techniques, we developed an energy-efficient task scheduling algorithm called EETS (Energy-Efficient Task Scheduling). This algorithm automatically learns the optimal scheduling policy from historical data while interacting with the environment. Experimental results demonstrate that EETS exhibits faster convergence rates and higher rewards compared to both DQN and DDQN. In scheduling performance, EETS outperforms other baseline algorithms in key metrics, including energy consumption, average task response time, and average machine working time. Particularly, it has a significant advantage when handling large batches of tasks.

Intelligence Model based Routing with Channel Assignment in Multichannel Mobile Ad-Hoc Networks

Multiple wireless channels in MANET promise to enhance QoS, and their well-coordinated use can lead to major operational enhancements. For coordination & synchronization across numerous channels, existing approaches for developing multi-channels in mobile ad hoc networks (MANETs) employ a control channel-based technique. Offering QoS via resource reservation, routing, mobility management, & access/admission control has become the most important problems recently in MANETs. Nevertheless, due to obvious interference caused by mobility, several existing solutions fail to offer good QoS. This paper intends to introduce a novel routing and channel assignment in multichannel MANET. Here, the optimal routing is performed via selecting the cluster head under the certain constraints like Delay, distance, QoS, RSSI, and security. For this, (Chaotic Functions influenced spider monkey optimization) CFISMO algorithm is used. The assignment of channels as the scheduling policy is introduced through senders while it has packets to transmit. In this work, the channel assignment will be initiated via machine learning model that predicts the availability of the channels, which is based on the paths (channels) generated under the selected cluster head. Here, Optimized Neural Network (NN) will be used. Thus, the final output shows the paths (channel) to be assigned for data transmission. At the end, the performance of the adopted routing approach is evaluated over other traditional schemes based on various metrics like distance, PDR, delay, energy, alive nodes, QoS, security, and trust, respectively.

Trailblazer: A proactive caching, blockchain, minimum content retrieval latency, and energy cost-aware resource and job orchestration scheme for publisher-subscriber based 6G ICN services

With the rise of information-centric networks (ICN), the user can access the caching content from nearby caching nodes rather than the remote content server through in-network caching facilities. The existing articles did not look into minimum caching content retrieval latency, user energy consumption, user financial cost, and maximum service provider profit-aware proper resource orchestration and job scheduling policies all at once, taking into account multiple publishers and subscriber-based caching jobs, blockchain, user-owned and service provider cache, pre-caching, neighbor collaboration, and available resources. To suppress these challenges, this article offers a proactive pre-caching, collaboration, blockchain, minimum latency-aware resource, and job scheduling policy for 6G ICN services that takes into account publishers’ and subscribers’ caching job requests, user-owned and service provider cache, available resources, and deadline. The experimental results visualized that at least 16% content retrieval delay, 66% energy, and 22% service provider profit gain are attained in the proposed scheme over the existing techniques.

An Optimization Model for Offline Scheduling Policy of Low-Density Parity-Check Codes

An Optimization Model for Offline Scheduling Policy of Low-Density Parity-Check Codes

Shaping closed-loop supply chain dynamics: Mitigating the bullwhip effect and improving customer satisfaction in production systems with material reuse

Modern societies are currently transitioning towards more circular economic models to reduce environmental impacts and leverage economic opportunities. Managing the emerging supply chains, more complex and uncertain, poses a considerable challenge for many organisations. This work examines the dynamic behaviour of these closed-loop systems under different replenishment policies and varying levels of product returns and lead times. We model a generalised multi-level, closed-loop supply chain of a production system with material reuse, drawing inspiration from the real-world operations of cider makers in Spain. We investigate its ability to effectively and efficiently satisfy the consumer through four performance metrics: fill rate, bullwhip ratio, inventory cover, and reuse demand share. Through experimentation techniques, we observe that the highest performance is generally obtained when the retailer applies a pure pull policy while the manufacturer adopts a level scheduling policy. This strategy, built on lean principles, can achieve much lower operational costs while providing similar, or even better, service levels compared to more popular and complex alternatives. Based on our findings, we provide a set of actionable managerial implications that would help supply chain professionals successfully implement and manage these supply chains.

Bereavement scheduling policy for emergency medicine residents: A descriptive pilot study.

The Accreditation Council for Graduate Medical Education has tasked residency programs to prioritize resident wellness, reduce trainee stress, and prevent burnout. Grief and bereavement can significantly impact residents' wellness during difficult clinical training schedules. There are no best practices on how to support residents during this time. In a split academic county emergency medicine (EM) residency, this pilot study documents a resident-driven change to scheduling practices for bereavement leave. An advisory group of residents, chief residents, and program directors informally polled peer institutions to develop bereavement leave guidelines. Considerations were made to balance resident wellness, education, and patient care in developing a bereavement scheduling policy. The bereavement policy was adopted in January 2023, aiming to "support the resident during a difficult time and reduce concerns around shift coverage" following the death of a family member without impacting sick call. The number of covered days depended on the relationship of the resident to the deceased. Residents covering bereavement days for their peers were financially compensated. During the first 7 months following implementation, five residents utilized the policy. These residents noted this to be the most positive impact on the residency during the past year. Based on resident feedback, the scope was expanded to include grave medical illness of a family member as an implementation criterion. This article outlines the creation, implementation, and benefits of a bereavement scheduling policy within an EM residency. Describing this approach will provide guidance for other residencies to adopt similar wellness-focused strategies.

Design of an Iterative Method for MapReduce Scheduling Using Deep Reinforcement Learning and Anomaly Detection

Due to high complexities within distributed computing environments, there's a critical need for advanced scheduling frameworks that are capable of optimizing MapReduce systems. Current approaches have static policies that limit their capability to adapt to changing system dynamics and workload variations for different cloud scenarios. To overcome these issues, this study introduces a robust MapReduce framework empowered by intelligent scheduling algorithms, tailored to enhance system efficiency and resilience levels. The framework introduces three novel scheduling models: Deep Reinforcement Learning for Dynamic Job Scheduling (DRDJS), Anomaly Detection-driven Adaptive Scheduling (ADAS), and Cluster-based Job Categorization and Scheduling (CJCS). DRDJS utilizes deep reinforcement learning to dynamically generate optimal scheduling policies based on multiple metrics that include historical job data, system metrics, and workload characteristics. This adaptive approach leads to significant reductions in job completion times, outperforming static scheduling methods by up to 30%. Next, ADAS leverages anomaly detection to prioritize critical tasks and efficiently allocate resources in response to anomalies, resulting in a notable improve scheduling speed by up to 40%. Finally, CJCS employs clustering algorithms to categorize jobs based on their resource requirements and execution profiles, enabling more accurate resource allocation and reducing average job completion times by up to 25%. By integrating these methods into a unified scheduling framework, the proposed solution addresses the variability in job characteristics and system performance, thereby enhancing the overall throughput and stability of MapReduce operations.

Scheduling for additive manufacturing with two-dimensional packing and incompatible items

Additive manufacturing technology can enable low-cost, efficient production of low-demand, highly-complex customized items with reduced lead time if production is judiciously planned. This paper addresses the assignment of requested items into batches and the scheduling of the batches onto 3D printers. The objective is to minimize the manufacturing makespan while satisfying items’ compatibility, two-dimensional no-overlap and containment packing constraints within a batch, and machine’s capability to manufacture a batch. The problem is modeled as a mixed integer linear program (MIP) that solves instances up to 100 items. For hard and large instances, this paper proposes a matheuristic that fathoms packings using a step-wise check procedure. Computational results reveal that the proposed heuristic improves the makespan of MIP solutions of hard instances by 12% on average, with improvements reaching up to 72% for instances with 150 items. They further show that the proposed heuristic finds the best makespan for 88% of all cases. Finally, we provide useful managerial insights for production flexibility and scheduling policies.

A DRL-Based Reactive Scheduling Policy for Flexible Job Shops With Random Job Arrivals

In real-life production systems, arrivals of jobs are usually unpredictable, which makes it necessary to develop solid reactive scheduling policies to meet delivery requirements. Deep reinforcement learning (DRL) based scheduling methods are capable of quickly responding to dynamic events by learning from the training data. However, most of policy networks in DRL algorithms are trained to choose priority dispatching rules (PDR), thus, to some extent, the efficiency of obtained scheduling plans is limited by the performance of PDRs. This paper investigates a dynamic flexible job shop scheduling problem with random job arrivals for the total tardiness minimization. A DRL-based reactive scheduling method, proximal policy optimization with attention-based policy network (PPO-APN), is proposed to make real-time decisions for the dynamic scheduling environment, where the attention-based policy network (APN) is able to directly select pending jobs distinguished from the action space that consists of PDRs. Additionally, a global/local reward function (GLRF) is designed to address the reward sparsity issue during training processes. The proposed PPO-APN is tested on randomly generated instances with different production configurations, and is compared with frequently-used PDRs and DRL-based methods. Numerical experimental results indicate that APN and GLRF components significantly improve the training efficiency, and the PPO-APN shows better overall performance compared with other methods. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work is motivated by a typical production scenario in discrete manufacturing systems, where orders randomly arrive at the shop floor and require to be scheduled in a short time to ensure the on-time delivery. Previous research work tends to apply DRL algorithms to choose suitable dispatching rules for the ease of implementation. Nevertheless, the jobs that can be selected by dispatching rules are rather limited, thus many possible high-quality scheduling plans are ignored. This work first sorts all the unscheduled jobs by a heuristic algorithm, and puts some of top-ranked jobs to a pool. When a machine becomes available, it will directly choose a job from the pool as the next processing task. The job selection policy is represented by a novel attention-based network, and is trained by a powerful DRL algorithm. The aforementioned process is repeatedly executed in a simulation environment to collect the training data. Therefore, after being trained for a certain period of time, the policy will become smarter and can be applied to make right decisions in real-time. The proposed reactive scheduling method has been proved to be more efficient than dispatching rules and DRL-based approaches, and is effective in the production scheduling for a wide variety of discrete manufacturing scenarios, such as automobile and electronics industries. Moreover, the proposed method can be further extended to address dynamic scheduling problems with some production characteristics via adding constraints for the job selection or re-defining calculations for the completion time of operations accordingly.

Stochastic resource leveling in projects with flexible structures

In project management, efficient utilization of resources plays a key role in project success, and resource leveling is an effective technique to optimize resource usage. During project execution, there are often uncertainties that complicate resource leveling. Furthermore, existing research on resource leveling typically assumes a fixed project structure. However, this is not always the case in practice, because there may be a variety of optional technical solutions for some activities, leading to a flexible project structure. Therefore, considering both stochastic activity durations and flexible project structures, we propose and study the stochastic resource leveling problem with flexible project structures (SRLP-PS). The solution of the SRLP-PS is in the form of a scheduling policy. We design two algorithms for solving the NP-hard SRLP-PS: (a) an exact algorithm based on stochastic programming, in which we formulate a scenario-based non-linear stochastic programming model and linearize it into an equivalent deterministic mixed-integer linear programming model that can be directly solved by CPLEX; and (b) an improved differential evolution algorithm, which is equipped with several problem-specific components, such as two mutation operators balancing exploration and exploitation, initialization, and local improvement search. Extensive computational experiments on a large number of benchmark instances are performed to validate our algorithms, which are also compared with state-of-the-art meta-heuristics. The computational results reveal the effectiveness and competitiveness of our algorithms. We also analyze the value of stochastic information based on the exact algorithm and the meta-heuristics, respectively.

S-Graph-Based Reactive Scheduling with Unexpected Arrivals of New Orders

Manufacturing processes are often disrupted by unexpected events, such as machine breakdowns, raw material shortages, and the arrival of new orders. Effectively managing these uncertainties is crucial for maintaining the feasibility and optimality of the production system. The efficiency of a manufacturing system is heavily dependent on the optimality of its scheduling plan. In this study, we present a reactive scheduling approach based on the S-graph framework. The proposed method is specifically designed to handle the arrival of new jobs and generate schedules with the shortest makespan, i.e., the minimum total completion time. Whenever a new order is received, the method dynamically adjusts the production plan through rescheduling. Three distinct scheduling policies are identified that determine which tasks require scheduling or rescheduling and which tasks should remain unchanged in their schedules. To evaluate the effectiveness of the algorithm, we solve several examples from the literature and analyze the results. The findings demonstrate the efficiency and efficacy of the proposed approach. The ability to accommodate new job arrivals and generate schedules with a minimized makespan highlights the practical relevance and benefits of the S-graph-based reactive scheduling method.