A Real-Time Human–Machine–Logistics Collaborative Scheduling Method Considering Workers’ Learning and Forgetting Effects

Abstract

In the era of Industry 5.0, human-centric manufacturing necessitates deep integration between workers and intelligent workshop scheduling systems. However, the inherent variability in worker efficiency due to learning and forgetting effects poses challenges to human–machine–logistics collaboration, thereby complicating multi-resource scheduling in smart workshops. To address these challenges, this study proposes a real-time task-driven human–machine–logistics collaborative framework designed to enhance multi-resource coordination in smart workshops. First, the framework incorporates a learning-forgetting model to dynamically assess worker efficiency, enabling real-time adjustments to human–machine–logistics resource states. Second, a task-driven self-organizing approach is introduced, allowing human, machine, and logistics resources to form adaptive groups based on task requirements. Third, a task slack-based matching method is developed to facilitate real-time, adaptive allocation of tasks to resource groups. Finally, the proposed method is validated through an engineering case study, demonstrating its effectiveness across different order scales. Experimental results indicate that, on average, completion time is reduced by no less than 10%, energy consumption decreases by at least 8%, and delay time is reduced by over 70%. These findings confirm the effectiveness and adaptability of the proposed method in highly dynamic, multi-resource production environments.

1. Introduction

As an extension of Industry 4.0, Industry 5.0 emphasizes human-centered manufacturing [1], with a focus on the collaboration between humans and machines. By harnessing the cognitive and practical abilities of humans in the manufacturing process, it aims to improve product quality, reduce waste, and create a more humane, intelligent, and sustainable manufacturing system. This trend signifies a transition in the manufacturing industry towards human-centric and value-driven production, emphasizing distributed production, intelligent supply, and personalized customization to enhance sustainability [2,3,4,5].

Human–machine collaboration in smart workshops is now central to production management, with the role of workers becoming increasingly important [6]. The learning and forgetting effects of workers significantly impact system efficiency [7], as changes in worker performance influence processing times and energy consumption. In an internet-of-things and cloud manufacturing environment, tasks in smart workshops are dynamically allocated and managed in real time through cloud platforms, enhancing collaboration. The dynamic interaction among workers, production equipment, and logistics creates a complex and evolving system, adding to the challenges of resource scheduling.

To manage the complexity and uncertainty caused by fluctuations in worker efficiency, scheduling systems must be flexible and adaptive, allowing for quick adjustments in resource allocation and scheduling strategies in changing environments. Developing accurate and dynamic scheduling models is crucial. These models help smart scheduling systems respond effectively to complex production demands and environmental changes, optimizing the coordination of production, logistics, and human resources to improve efficiency. They also offer adaptable solutions for smart manufacturing systems, enhancing responsiveness and sustainability.

Most current smart workshop scheduling systems focus primarily on production [8] and logistics [9] resources, overlooking the crucial role of workers. Without a deep understanding of worker efficiency fluctuations and their dynamic nature, these systems struggle to incorporate the human-centric principles of Industry 5.0, making them inadequate for meeting the needs of smart workshops in complex environments.

To address these issues, this paper proposes a real-time human–machine–material collaborative scheduling method considering workers’ learning and forgetting effects (HMLCS). The real-time scheduling method includes three main components: First, a mathematical model of learning and forgetting is used to calculate workers’ real-time efficiency, which updates the real-time state of manufacturing resources accordingly. Second, the real-time state of human–machine–material resources is modeled, and a method for grouping these resources is proposed. Finally, an adaptive scheduling algorithm that accounts for worker learning and forgetting is presented. The paper is structured into three main parts: (1) building a collaborative scheduling framework for smart workshops that considers worker learning and forgetting; (2) proposing a real-time scheduling method considering these effects; and (3) validating the proposed strategy through a case study of a coal machinery company’s workshop using a simulation platform built with Tecnomatix Plant Simulation software.

2. Related Work

To establish a solid foundation for our research, we first review existing studies on scheduling methodologies. This section explores the role of learning and forgetting effects in scheduling and discusses multi-resource collaborative scheduling approaches that have been developed in previous studies.

2.1. Application of Learning and Forgetting Effects in Scheduling

In recent years, research on human behavior in socio-technical systems has gained widespread attention [10]. In complex technical systems, factors such as workers’ cognition, emotional responses, and social skills directly influence decision-making processes and system efficiency [11,12]. However, workers’ learning and forgetting effects are also affected by these behavioral factors. Therefore, to achieve more efficient resource management, it is essential to fully consider learning and forgetting effects in production scheduling, making it a current research hotspot.

The study of human learning and forgetting effects dates back several decades. In the 1990s, Biskup [13,14] pioneered research on learning effects in the scheduling field, proposing two fundamental learning effect models: a position-based learning model and a model based on cumulative processing times. Building on Ebbinghaus’ forgetting curve theory, John et al. [15] introduced a forgetting effect model to describe the relationship between worker forgetting and idle time. Subsequently, Lee [16] established two learning and forgetting effect curves and demonstrated that the problem is polynomially solvable when the objective is to minimize either the maximum or total completion time. Jaber and Kher [17], along with Jaber and Bonney [18], further integrated learning and forgetting curves, creating a model that better reflects real-world production scenarios, significantly improving its accuracy and applicability.

Initially, the impact of learning and forgetting effects on shop floor scheduling was primarily studied in single-machine scheduling problems. Pan et al. [19] proposed a comprehensive single-machine group scheduling model that considered both learning and forgetting effects as well as preventive maintenance to enhance scheduling efficiency and equipment utilization. Muştu and Eren [20] studied a single-machine scheduling problem with sequence-independent setup times and time-dependent learning and forgetting effects, introducing a dual learning–forgetting model, formulating an integer nonlinear programming model, and proposing a pseudo-polynomial dynamic programming solution. Zhang et al. [21] introduced a multi-objective optimization model that integrates production scheduling and machine maintenance, taking into account learning and forgetting effects to optimize production sequences and preventive maintenance (PM) decisions for more efficient production and maintenance management. Heuser and Tauer [22] incorporated category-based learning and forgetting effects into single-machine scheduling to explain skill development processes and the actual processing of different types of products on the same production line.

In addition, Zhang et al. [23] considered human factors and learning effects in unrelated parallel machine scheduling, proposing a model for scheduling with limited human resources and learning effects, suitable for sequence-dependent machine environments. Kurniawan et al. [24] addressed the synchronization of batch scheduling and operator allocation with learning and forgetting-induced time variation by proposing an algorithm that incrementally increases the number of batches to find the optimal solution. Zhang et al. [25] proposed a metaheuristic algorithm combining search frameworks and multiple search operators to solve hybrid flow shop scheduling problems with learning and forgetting effects. Lou et al. [26] developed a multi-objective flexible job shop scheduling problem that considers worker flexibility and learning and forgetting effects, formulating a multi-objective mixed-integer nonlinear programming model and introducing a learning and decomposition-based multi-objective memetic algorithm that integrates adaptive local search with a decomposition-based multi-objective evolutionary algorithm. Renna [27] proposed a scheduling method for manufacturing systems under learning and forgetting effects to address processing time variability.

2.2. Multi-Resource Collaborative Scheduling

With the widespread application of next-generation information technologies such as cloud computing, industrial internet, and artificial intelligence in manufacturing, traditional workshops are evolving toward smart workshops. In smart workshops, the state of various manufacturing resources changes in real time, and dynamic scheduling methods that achieve resource collaboration not only meet customer demands but also significantly improve production efficiency.

Burdett et al. [28] studied multi-resource collaboration in production processes, defining primary resources (e.g., machines) and secondary auxiliary resources (e.g., personnel) and generating optimal scheduling solutions using a mixed-integer programming model. Pizon et al. [29] highlighted that technological advancements have led to a resurgence of human involvement in production, emphasizing the importance of human creativity and potential in shaping human–machine relationships. Wang et al. [30] proposed a human–machine collaborative decision-making method based on confidence, where intelligent devices make initial decisions and humans modify inappropriate decisions. Wang et al. [31] also proposed a human–machine collaboration mechanism that achieves effective cooperation through task allocation and introduced an adaptive scheduling method to integrate human and machine intelligence. Zhang et al. [32] developed a dynamic human–machine task allocation framework that optimizes task allocation by assessing task complexity and economic benefits. Liu et al. [33] tackled the human–machine task allocation problem using a directed acyclic graph for task modeling, inspired by graph path search, and developed an ant colony optimization-based human–machine task allocation method to find optimal solutions in the search space. In the context of human–machine interactive learning, Wang et al. [34] emphasized the role of workers and scheduling models (SM) in dynamic scheduling decisions, introducing active learning techniques to reduce labeling costs and improve learning efficiency.

In terms of production–logistics collaboration, Qu et al. [35] pointed out that logistics activities account for more than 90% of production time in manufacturing, making production–logistics coordination crucial for smart manufacturing. Guo et al. [36] proposed an adaptive production–logistics collaboration method based on Petri nets, while Zhang et al. [37] introduced a production–logistics collaboration method based on objective cascading, enabling self-organizing configuration. The Qu team [38,39] further proposed optimization control methods and dynamic linkage decision frameworks for production–logistics systems to support collaborative operation and autonomous decision-making. In a customized production setting, Luo et al. [40] proposed a real-time edge scheduling model that prevents dynamic disturbances in workshops and improves customer satisfaction by dynamically inserting orders. Lin et al. [41] introduced a cloud-based production–logistics collaboration service infrastructure (CPLSS), which experimental results showed could reduce operational costs and improve finished product storage efficiency. Guo et al. [42] developed an adaptive collaborative control (SCC) model for intelligent production–logistics systems using an Analytical Target Cascading (ATC) approach, which has proven highly effective and applicable. Zhang et al. [43] built an intelligent product service system that uses a real-time information-driven logistics task optimization method to improve task completion efficiency. Yang et al. [44,45] proposed a real-time reactive scheduling framework for production–logistics resource collaboration based on information entropy, achieving adaptive collaboration between production and logistics resources. In the area of real-time scheduling for complex dynamic job shops, Cai et al. [46] proposed a new real-time scheduling model and algorithm that adapts to dynamic environments involving logistics elements. This model extends the preparation time for AGV tasks and designs a real-time information update mechanism to improve schedule robustness. Zhao et al. [47] proposed a flexible job shop scheduling model that addresses the coupling of production and logistics scheduling and developed a boosted multi-objective jellyfish search (BMOJS), which demonstrated better productivity and balanced equipment load in workshops with multi-level job priority constraints. Pan et al. [48] achieved production–logistics synchronization control in a dynamic environment through a multi-level digital twin architecture, a two-stage, three-level synchronization mechanism, and a genetic algorithm-based objective cascading method. [49] Zhang et al. utilized the Term Frequency–Inverse Document Frequency algorithm to filter low-distinctiveness data and built a logistics resource allocation recommendation model based on a similarity algorithm-based recommendation system (Recsys) to optimize production logistics management.

In summary, most current research on collaborative scheduling in workshops focuses on the coordination between human–machine or machine–logistics resources, while research on the collaborative scheduling of human–machine–logistics resources in smart workshops is still relatively limited. However, under the context of Industry 5.0, the coordinated scheduling of workers, intelligent logistics equipment, and processing equipment will become a critical aspect of workshop management. Therefore, this paper proposes a human–machine–logistics collaborative scheduling method for smart workshops that considers worker learning and forgetting effects (LFE). By leveraging the computational and communication capabilities of industrial internet of things (IIOT), radio frequency identification (RFID), and device-to-device (D2D) technologies, this method aims to achieve real-time collection of worker processing efficiency and other manufacturing resource data, enabling multi-resource real-time interaction. Consequently, task collaboration and allocation can be based on the real-time state of production and logistics resources, achieving high levels of human–machine–logistics synergy and production efficiency, ultimately enabling multi-objective dynamic optimization based on the real-time status of various resources.

3. A Collaborative Scheduling Framework for Human–Machine–Logistics Considering Workers’ LFE

Building upon the insights from previous research, this section introduces a collaborative scheduling framework that integrates human, machine, and logistics resources while considering workers’ learning and forgetting effects.

3.1. Problem Description and Mathematical Model

In the context of Industry 5.0, with the increasing prevalence of human–machine collaborative work scenarios, the role of humans as an indispensable part of the production system has become more prominent. The scope of resource scheduling should not only include processing and logistics equipment but also encompass workers as a critical factor. Due to the learning and forgetting effects experienced by workers during their tasks, worker efficiency exhibits dynamic variability, significantly impacting production efficiency and task allocation.

Specifically, worker efficiency is not constant but gradually improves with accumulated work experience. However, once work is interrupted, efficiency begins to decline. This phenomenon is known as the learning and forgetting effect, which directly affects workers’ ability to complete tasks over different time periods. Therefore, effectively quantifying and incorporating workers’ learning and forgetting effects into human–machine–material collaborative scheduling is a critical issue that needs to be addressed.

To address this issue, we developed a time-based mathematical model to quantify the impact of learning and forgetting on worker efficiency [7,50], providing a more accurate description of how efficiency changes over time.

$${p_r}^{\prime }=p_r\left\{max\left[1+{\left({\sum }_1^{r-1}{p_{[r-1]}}^{\prime }\right)}^a,\theta \right]-1\right\}{e}^{-bt}+p_r$$

(1)

where ${p_r}^{\prime }$ represents the actual working time, $p_r$ represents the theoretical working time, ${\sum }_1^{r-1}{p_{[r-1]}}^{\prime }$ represents the cumulative processing time of the worker, $\theta$ is limiting parameter, $0<\theta <1$, a is the learning factor, $a<0$, b is the forgetting factor, $0<b$, and t represents the interruption or break time between two consecutive operations.

As can be seen from the model, this effect is influenced not only by work time but also by individual learning and forgetting factors. A worker’s efficiency directly affects the production capacity of the equipment, which in turn impacts the collaborative operation of production–logistics units. Therefore, workshop scheduling must include workers in the scope, comprehensively considering the relationships between workers, machines, and logistics to deal with the uncertainties and complexities brought about by workers’ learning and forgetting effects. This will achieve efficient collaborative scheduling.

The scheduling problem can be described as follows: Given a set of jobs, each job has two time attributes—arrival time and deadline. If a job is completed after its due date, a penalty cost for lateness is generated. There is a set of AGVs (Automated Guided Vehicles) $A=\left\{a_i|i=1, 2, \dots , I\right\}$, a set of machines $M=\left\{m_j|j=1, 2, \dots , J\right\}$, and a set of workers $H=\left\{h_j|j=1, 2, \dots , J\right\}$. The objective of this method is to provide an adaptive task allocation strategy under the influence of workers’ learning and forgetting effects, optimizing multiple objectives simultaneously. The assumptions for the problem are as follows:

• Jobs arrive randomly, and the deadlines vary.
• Each machine can only process one job at a time, and each job can only be processed on one machine at a time.
• Each AGV can only transport one job at a time, and the speed of AGVs is identical.
• Jobs’ arrival times and deadlines are only known upon their arrival.
• Each machine has a buffer zone with a capacity of 10 jobs.
• Each production unit provides loading and unloading areas for logistics units, and loading/unloading times are included in logistics time.
• Each worker can only operate one machine at a time.
• Each worker has a fixed location.
• Each worker has different learning and forgetting effects, and their learning capabilities and forgetting speeds vary.
• Workers’ efficiency fluctuations conform to the learning-forgetting mathematical model.

The objective of the intelligent workshop scheduling layer is to minimize job completion time, total energy consumption of production and logistics equipment, and average task delay.

$$F=min\left\{f_1,f_2,f_3\right\}$$

(2)

$$f_1=max\left\{C^k\right\}$$

(3)

$$f_2={\sum }_{i=1}^I{E}_v^i+{\sum }_{j=1}^J{E}_m^j$$

(4)

$$f_3=\left({\sum }_{k=1}^K{L}^k\right)/K$$

(5)

S.t

$$i=\left\{1, 2, \dots , I\right\}$$

(6)

$$j=\left\{1, 2, \dots , J\right\}$$

(7)

$$k=\left\{1, 2, \dots , K\right\}$$

(8)

$$L^k=max\left(0,C^k-D^k\right)$$

(9)

In this mathematical model, $f_1$ denotes the makespan; $f_2$ denotes the total energy consumption, which includes energy consumption of machine and energy consumption of AGVs; and $f_3$ denotes the mean tardiness of jobs.

To facilitate reading and understanding,

Table 1. The notation used in this study.

Notations	Description
${job}^k$	The k_th workpiece
$h_j$	The number of worker j
$m_j$	The equipment number of machine j
$a_i$	The number of AGV i
$O_n^k$	The n_th operation of the ${job}^k$
$E_v^i$	Total energy consumption of $a_i$
$E_m^j$	Total energy consumption of $m_j$
$L^k$	Delay time of the ${job}^k$
$C^k$	Completion time of the ${job}^k$
$D^k$	Due date of the ${job}^k$
$g_j$	Human–machine collaborative production group
$g_j^t$	Real-time state of $g_j$ at time t
$h_j^t$	Real-time state of worker resource $h_j$ at time t
$m_j^t$	Real-time state of machine resource $m_j$ at time t
$a_i^t$	Real-time state of logistics resource $a_i$ at time t
${sp}_{ni}^{kt}$	Time at which logistics task $a_i$ starts processing operation $O_n^k$
${fp}_{n\widehat{J}}^{kt}$	Time at which machine completes operation $O_{n-1}^k$
${sp}_{nj}^{kt}$	Time at which machine $m_j$ starts processing operation $O_n^k$
${fp}_{nj}^{kt}$	Time at which machine completes operation $O_n^k$
${mp}_{ni}^{kt}$	Time at which logistics task arrives at the location of operation $O_n^k$
${fp}_{\widehat{n}j}^{\widehat{k}t}$	The completion time of the last operation before processing by the machine $m_j$

lists the mathematical symbols used in this article.

3.2. A Real-Time Human–Machine–Logistics Collaborative Scheduling Framework Considering Workers’ LFE

The real-time reactive scheduling framework, illustrated in Figure 1, integrates three key components: (1) a real-time state model of the human–machine–material resources that accounts for workers’ learning and forgetting effects, (2) dynamic self-organization of human–machine–material resources based on real-time worker states and task demands, and (3) an adaptive scheduling method leveraging real-time self-organization, while also considering learning and forgetting effects. Each module operates as follows:

In intelligent workshops, technologies such as RFID, sensors, and processors enable manufacturing resources to communicate and execute tasks intelligently. These modules facilitate the monitoring of resource state changes, thereby improving the coordination of workshop operations. However, worker efficiency remains challenging to assess directly due to the influence of numerous factors. To address this, a mathematical model incorporating learning and forgetting dynamics is employed to estimate workers’ real-time efficiency, allowing for continuous adjustment of resource states in the workshop.

The random arrival of tasks and constantly changing resource availability in intelligent workshops necessitate a highly flexible approach to multi-resource collaboration. To meet these requirements, we propose a dynamic self-organization strategy for human–machine–material resources, which reflects the real-time nature of tasks. This strategy effectively meets the workshop’s task demands by dynamically matching and integrating available service resources based on their real-time capabilities, thereby achieving optimal resource organization in response to task requirements.

An adaptive allocation method based on task slackness is then implemented to optimize task assignment. Task slackness serves as a metric for evaluating the suitability of a service group for a specific task, ensuring that the most appropriate resources are allocated to balance completion time, energy consumption, and delay. Additionally, a conflict resolution mechanism for Automated Guided Vehicles (AGVs) is integrated, prioritizing urgent tasks and minimizing delays caused by resource conflicts. This ensures that critical tasks are handled efficiently, maintaining the overall productivity of the workshop.

4. Human–Machine–Logistics Collaborative Scheduling Method Considering Workers’ LFE

Real-time adaptability is crucial for scheduling systems in smart manufacturing. This section expands on the proposed framework by incorporating real-time resource management and self-organization mechanisms.

4.1. Real-Time Status Model of Human–Machine–Logistics Resources

In the Industrial Internet-of-Things (IIoT) environment, the real-time status of critical resources in an intelligent workshop forms the foundation for the human–machine–object collaborative scheduling system. The capability status of manufacturing resources includes both resource attributes and real-time states. Resource attributes cover operational capabilities, energy consumption, and service quality, while real-time states encompass anomaly detection, dynamic queues, workload, and service processes. To accurately depict the real-time status of human–machine–object resources, this study constructs state models for workers, processing equipment, and handling equipment. The concept of “operation ratio” is introduced as a key indicator of worker real-time efficiency, reflecting human factors in a more comprehensive manner.

Definition 1.——Worker’s Real-time Efficiency.

The slackness of a real-time task is a key factor that influences the matching between tasks and service groups, and predicting the remaining processing time of a real-time task is essential for calculating slackness. In the human–machine–logistics collaborative work environment, the learning and forgetting characteristics of workers affect the processing duration, and the operational efficiency of production resource groups exhibits dynamic characteristics, making it difficult to estimate the actual time accurately. Therefore, this paper defines the ratio between the actual task processing time and the theoretical task processing time at a given moment as the task time ratio, and the product of the task time ratio and the theoretical remaining time is used as the estimate for the remaining processing time of the task $O_n^k$.

In the production process, processing equipment and workers work in combination, so a production resource group model consists of one piece of production equipment and one worker operating the equipment.

$$g_j=\left(h_j,m_j\right)$$

(10)

At time t, the real-time state model of production resources is composed of the real-time states of workers and processing equipment and can be expressed as follows:

$$g_j^t=\left(h_j^t,m_j^t\right)$$

(11)

$$h_j^t=\left(h_j,a_j^{LI},b_j^{FI},T_j^{cum},T_j^{down},{\theta }_j,E_{nj}^k\right)$$

(12)

$$m_j^t=\left(m_j,S_j^t,L_j^{pos},{p_{nj}^k,e}_j^{sta},e_j^{act},{sq}_j\right)$$

(13)

where $a_j^{LI}$ represents the worker’s learning ability, $b_j^{FI}$ represents the forgetting speed, $T_j^{cum}$ represents the total working time, $T_j^{down}$ represents the idle time, ${\theta }_j$ represents the worker’s maximum learning efficiency, and $E_{nj}^k$ represents the worker’s processing efficiency at time t when handling the current task. $S_j^t$ represents the types of services that can be provided, $L_j^{pos}$ represents the location information, $p_{nj}^k$ represents the service time for the current task, $e_j^{sta}$ represents the idle power, $e_j^{act}$ represents the operating power, and ${sq}_j$ represents the service queue.

The real-time state model of logistics equipment includes eight characteristic values, such as service options $S_i^t$, resource location $L_i^{pos}$, transport time $p_{ni}^k$, standby energy $e_i^{sta}$, transport energy $e_i^{act}$, transport speed $\overline{v},$ and service queue ${sq}_i$.

$$a_i^t=\left(a_i,S_i^t,L_i^{pos},{p_{ni}^k,e}_i^{sta},e_i^{act},\overline{v},{sq}_i\right)$$

(14)

4.2. Real-Time Self-Organization of Human–Machine–Logistics Resources for Real-Time Tasks

In the dynamic environment of an intelligent production workshop, the collaborative logic between manufacturing resources is complex and variable. This paper considers not only processing resources and logistics resources but also the factor of workers. The impact of workers’ learning and forgetting effects further complicates the dynamic properties of all manufacturing resources in the workshop, making it difficult to predict and increasing the flexibility needed for the dynamic reorganization of manufacturing resources. To clearly describe the dynamic self-organization of individual manufacturing resources for tasks based on their current status and the uncertainty of task arrival in production workshops, a human–machine–logistics dynamic self-organization method for real-time tasks is proposed. This method is based on D2D technology and is guided by real-time task demands in the workshop. It integrates and matches available service resources according to the service capabilities of human–machine–logistics, achieving real-time self-organization of resources for specific tasks.

The construction of the self-organization method for human–machine–logistics resources involves two components:

Self-Organization Strategy for Real-Time Tasks: When a workpiece enters the workshop, all its operations are divided into individual tasks. Each operation task requires a set of services: one logistics service and one processing service (the processing service requires both a worker and a machine). Each operation task requires a worker, a machine, and an AGV to provide production and logistics services.

Real-Time Self-Organization of Human–Machine–Logistics Resources Based on D2D Interactions: The resource interaction mode in the intelligent workshop is shown in Figure 2, where tasks and represent two consecutive operations of task $k$. The completion of each operation requires a service group composed of a production machine, a worker, and a logistics device to provide support. When facing the real-time task, the scheduling center can query the available production resource set and the available logistics resource set based on the task type. Machines initiate communication with logistics units via D2D technology and quickly form service groups based on real-time information and their respective service capabilities. Obtain the set of service groups that meet the service requirements of task $O_n^k$. The most suitable service group is selected to execute task $O_n^k$. Before the completion of task, the processing resource publishes the next task $O_{n+1}^k$. The D2D-based human–machine–logistics self-organization mechanism includes four key elements: a service object, task publisher, production service provider, and logistics service provider. The service group formation process also includes two roles: Group Leader and Group Member. The Group-Leader is responsible for gathering Group Members, while Group Members provide feedback on task costs to the Group Leader. Production resources, typically fixed equipment connected to industrial buses, are less costly in terms of communication overhead. Therefore, the production resource in the service group for the current operation acts as the Group Leader and the task publisher for the next operation $O_n^k$. After completing the collaborative task, the service group dissolves, and the resources are released for reallocation to new tasks.

4.3. Adaptive Real-Time Scheduling Considering Workers’ Learning and Forgetting Effects

Building on the self-organization concept, this subsection presents an adaptive scheduling mechanism that takes into account workers’ learning and forgetting effects to optimize efficiency.

4.3.1. Adaptive Real-Time Allocation Considering Workers’ Learning and Forgetting Effects

The real-time matching between task demands and service combinations is the essence of adaptive scheduling for human–machine–logistics collaboration and is central to implementing multi-resource task allocation. Based on the division of manufacturing resource groups, this method selects the optimal service group as the task service provider for real-time tasks, aiming to enhance the ability of multi-resource collaboration to respond to disturbances and improve the efficiency of manufacturing execution. In selecting the optimal service group, the worker’s work efficiency, which is affected by learning and forgetting effects, must be considered as a key factor influencing the service group’s capability.

Based on prior research [39], this paper proposes an adaptive scheduling method considering the learning and forgetting effects of workers. The proposed algorithm is a real-time task allocation method based on minimizing service cost and dynamic priority. It is also an adaptive weighted task allocation strategy, aiming to match human–machine–logistics combinations with real-time tasks while considering the impact of workers’ learning and forgetting effects. The method is described as follows.

For a real-time task, the states of the production resource set and logistics resource set are as follows:

$${\overline{G}}^t=\left\{g_j^t|g_j^t=\left(h_j^t,m_j^t\right),j=1, 2, \dots , J\right\}$$

(15)

$${\overline{A}}^t=\left\{a_i^t|i=1, 2, \dots , I\right\}$$

(16)

At time t the set of service groups that meet the requirements of task can be obtained ${RT}_Z$:

$${RT}_Z=\left\{\left(g_j,a_i\right)|g_j\in \overline{G},a_i\in \overline{A}\right\}$$

(17)

Assume it is a set of service combinations. Among them, ${RT}_Z=\left\{{rt}_z|z=1, 2, \dots , Z\right\}$, ${rt}_z=\left(g_j,a_i\right)=\left(h_j,m_j,a_i\right)$, $Z=I\times J.$

In human–machine collaborative work, the service time of the machine tool changes with the worker’s efficiency, and the worker’s efficiency is influenced by their individual learning and forgetting effects. At time t, based on the worker real-time state model and the corresponding Formula (1), the actual service time of the task on the processing equipment can be obtained:

$$p_{nj}^{tk}=p_{nj}^k\left\{max\left[1+{\left(T_j^{cum}\right)}^{a_j^{LI}},{\theta }_j\right]-1\right\}{e}^{-b_j^{FI}{T}_j^{down}}+p_{nj}^k$$

(18)

Furthermore, we can obtain that the worker’s real-time processing time is $p_{nj}^{tk}$ and the machine’s actual processing energy consumption is ${e_j^{act}p}_{nj}^{tk}$.

Assume that task is processed on machine and task will be processed on machine $m_j$. Assume that an AGV provides transportation services for task and $L_i^{pos}$ is the position of the AGV when it starts executing task $O_n^k$. The distance between machine $m_{\widehat{j}}$ and is denoted as $Dist\left(L_{\widehat{j}}^{pos},L_i^{pos}\right)$. The time cost for the AGV to execute the pickup task is represented as: $p_{ni\widehat{J}}^{kta}=Dist\left(L_{\widehat{j}}^{pos},L_i^{pos}\right)/\overline{v}$. The time cost for the AGV to execute the delivery task is represented as $p_{nij}^{ksen}=Dist\left(L_{\widehat{j}}^{pos},L_j^{pos}\right)/\overline{v}$. The total transportation time cost is $p_{ni}^k=p_{ni\widehat{J}}^{kta}+p_{nij}^{ksen}$. The transportation energy consumption is $e_i^{act}{p}_{ni}^k.$

At time $t$, for each service group in the service group set ${RT}_Z$, the service time and service energy consumption are as follows:

$$T_f^t=p_{nj}^k+p_{ni}^k+max\left({sp}_{ni}^{kt}-{fp}_{n\widehat{J}}^{kt},0\right)+max\left({sp}_{nj}^{kt}-{fp}_{nj}^{kt},0\right)$$

(19)

$$W_f^t={e_j^{act}p}_{nj}^k+e_i^{act}{p}_{ni}^k+e_i^{sat}max\left({sp}_{ni}^{kt}-{fp}_{n\widehat{J}}^{kt},0\right)+e_j^{sat}max\left({mp}_{ni}^{kt}-{fp}_{\widehat{n}j}^{\widehat{k}t},0\right)$$

(20)

where $max\left({sp}_{ni}^{kt}-{fp}_{n\widehat{J}}^{kt},0\right)$ represents the waiting time for the AGV $a_i$ to pick up task $O_n^k$, $max\left({sp}_{nj}^{kt}-{fp}_{\widehat{n}j}^{kt},0\right)$ represents the waiting time for task at the corresponding machine before being processed, and $max\left({mp}_{ni}^{kt}-{fp}_{\widehat{n}j}^{kt},0\right)$ represents the waiting time for AGV $a_i$ to pick up task $O_n^k$.

Resource groups typically face a trade-off between completion time and energy consumption: high-power machines complete tasks in a shorter time but consume more energy, while low-power machines take longer to complete tasks but consume less energy. Therefore, it is difficult to achieve a combination of resources that is both low in energy consumption and short in time, and it is necessary to consider both the duration and energy consumption of service groups during scheduling. To select the optimal service group, this paper uses the actual task slack to allocate tasks from the task pool.

The smaller the slack, the more biased the task allocation will be towards the combination of good machine–resource–worker groups, while larger slack will make the allocation lean towards combinations with relatively lower efficiency to improve the worker’s learning effect.

The following formulas are based on adding consideration of the worker’s learning efficiency, considering the impact of learning and adaptation on the worker’s processing time.

Suppose at time t, a task is issued, and the task’s estimated average processing time is calculated as

$$\begin{array}{c}rp\left(O_n^k\right)={\sum }_n^r{\sum }_1^j{\displaystyle \frac{p_{nj}^k·E_j^t}{r-n}}\end{array}$$

(21)

where r is the total number of tasks, j is the selected machine sequence for a specific worker, and $E_j^t$ represents the actual learning efficiency of worker $h_j$ at time t.

The estimated transportation time is given by

$$\begin{array}{c}rl \left(O_n^k\right)=d_n^k/\overline{v}\end{array}$$

(22)

In this formula, $d_n^k$ is the predicted average material handling distance for the remaining flow tasks, and $\overline{v}$ is the movement speed of the material handling resources.

Thus, the estimated remaining service time for the job is the sum of the remaining processing time and the remaining transportation time:

$$\begin{array}{c}rt \left(O_n^k\right)=rp\left(O_n^k\right)+rl \left(O_n^k\right)\end{array}$$

(23)

At time t, the remaining time to complete job is

$$rd\left(O_n^k\right)=D^k-t$$

(24)

The slackness of task $O_n^k$ is the ratio of the estimated remaining service time to the remaining completion time. At time t, the slackness of task is

$$\begin{array}{c}Z\left(O_n^k\right)={\displaystyle \frac{rt \left(O_n^k\right)}{rd \left(O_n^k\right)}}\end{array}$$

(25)

Task slackness is used to measure the difference between the actual completion time of a task and its theoretical completion time, reflecting whether the task is delayed. When the slackness is large, the task may have already been delayed or is about to be delayed, so the system should prioritize selecting resource combinations with shorter completion times to reduce delays. When the slackness is small, it indicates that the task has enough time to be completed, and the system can select resource combinations with lower energy consumption to reduce overall energy use.

Based on this, this paper proposes an adaptive weighting evaluation function that uses task slackness as a weighting factor to dynamically adjust the resource allocation strategy. Through this method, we can achieve comprehensive optimization of completion time, energy consumption, and delay, thereby improving the overall efficiency and stability of production scheduling.

The service group’s capability is adaptively weighted, and a function is constructed as a real-time evaluation function:

$$f_0^t=\mu \times {\displaystyle \frac{T_f^t-{T_f^t}_{min}}{{T_f^t}_{max}{{-T}_f^t}_{min}}}+(1-\mu )\times {\displaystyle \frac{W_f^t-{W_f^t}_{min}}{{W_f^t}_{max}-{W_f^t}_{min}}}$$

(26)

$$\begin{array}{c}\mu =1-Z\left(O_n^k\right)\end{array}$$

(27)

where ${T_f^t}_{min}$ and ${W_f^t}_{min}$ represent the minimum service time and energy in the service group, while ${T_f^t}_{max}$ and ${W_f^t}_{max}$ represent the maximum service time and energy in the service group. We use $f_0^t$ to assess the quality of the service group and select the service group with the lowest overall cost. Based on the matching result between the service group and any task in the task pool, the task is assigned to the optimal processing group and the AGV.

4.3.2. AGV Conflict-Handling Mechanism

In intelligent workshops, AGVs and machines handle transportation and processing tasks in a multi-task environment. In such environments, it is possible that multiple tasks may simultaneously select the same AGV and machine, resulting in resource contention. However, since machines are fixed resources and have buffers as storage units, even when multiple tasks contend for the same machine, as long as different AGVs are responsible for transportation, each task can still be transported to the current optimal machine in the first instance. The presence of the buffer ensures that this situation does not cause task blocking, so the overall scheduling is only slightly affected.

In contrast, AGVs, being mobile resources with limited capacity, cannot handle multiple tasks simultaneously. When multiple tasks select the same AGV for transportation, the AGV can only process these tasks sequentially. This not only leads to task blocking but also changes the slackness of subsequent tasks due to the transportation delay of the preceding task. This can cause the selected service group to no longer be the optimal choice, having a more significant impact on the overall scheduling process.

To resolve this issue, a resource conflict handling mechanism is proposed in this paper. By reasonably allocating AGV resources, the system ensures that higher-priority tasks are handled first, effectively avoiding resource conflicts and task delays.

When multiple tasks in the scheduling pool are assigned to the same AGV for logistics execution, the system selects the task with the highest urgency based on the task priority selection rule. At time t, the priority of task is calculated as

$$F_0^t={\theta }_{O_n^k}\times {\displaystyle \frac{T_{O_n^k}^{tf}-T_{min}^{tf}}{T_{max}^{tf}-T_{min}^{tf}}}+(1-{\theta }_{O_n^k})\times {\displaystyle \frac{W_{O_n^k}^{tf}-W_{min}^{tf}}{W_{max}^{tf}-W_{min}^{tf}}}$$

(28)

where represents the slackness of task at time t, $T_{O_n^k}^{tf}$ represents the processing time of task and $W_{O_n^k}^{tf}$ represents the energy consumption for processing task $O_n^k$. $T_{min}^{tf}$ and $W_{min}^{tf}$ represent the minimum service time and energy consumption among all tasks waiting to be executed at time t, while $T_{max}^{tf}$ and $W_{max}^{tf}$ represent the maximum values.

This mechanism ensures that the most urgent tasks are processed promptly, avoiding delays in important tasks due to resource conflicts. For tasks that are not selected, the system unbinds them from the current AGV and returns them to the scheduling pool for reallocation. These tasks’ statuses are updated based on real-time feedback and are re-entered into the resource allocation process based on resource availability. This mechanism ensures that not selected tasks are handled flexibly, preventing long-term blocking in resource contention. After being returned to the scheduling pool, the system continuously monitors the resource status of the task. If the resource status changes (e.g., another AGV becomes available), the system re-evaluates the not selected task, adjusts its priority, and reallocates resources according to real-time conditions.

4.3.3. Human–Machine–Logistics Collaborative Process

The human–machine–logistics collaboration process consists of three main parts: human–machine collaborative processing, production logistics collaboration for real-time tasks, and material transportation. To further demonstrate the detailed process of each part and the relationship between them, an example service group is described, as shown in Figure 3.

Human–Machine Collaborative Processing: When the workpiece arrives at the buffer area of the processing equipment, the worker confirms the task, while the machine calculates the worker’s real-time efficiency based on their working time and idle time. Once the worker confirms the task, the human–machine collaboration starts, and the next task is triggered. After processing is completed, the workpiece undergoes a quality inspection and is placed in the buffer area.

Production–Logistics Collaboration: Once the next operation of the task is triggered, the task slackness is calculated, and the task is broadcast to the available production groups. The selected production group broadcasts the logistics task to the surrounding AGVs, forms a service group with the AGV, and evaluates and selects the optimal service combination to place in the execution pool.

Logistics Execution and Priority Checking: The system checks the tasks in the execution pool for AGV conflicts. If multiple tasks contend for the same AGV, the system determines the task priority. If the current task has the highest priority, the AGV acquires the workpiece information and moves to the pickup point (i.e., the output buffer area). After loading the workpiece, the AGV transports it to the delivery point (i.e., the input buffer area of the optimal service combination). If the current task does not have the highest priority, the system reselects a service group.

Repeat the Process: The process repeats until no tasks remain or all workpieces have been processed.

5. Case Study

To validate the effectiveness of our proposed framework, we conduct a case study based on a realistic industrial scenario. This section presents our case study design, followed by an analysis of the experimental results.

5.1. Case Description

This paper uses Siemens Tecnomatix Plant Simulation 16 to validate the proposed method. The application scenario involves a hydraulic valve block production workshop at a coal mining machinery company. The method addresses the difficulties of multi-resource scheduling considering workers’ learning and forgetting effects. Based on an actual production case, the proposed human–machine–logistics dynamic collaborative methods and theories were comprehensively tested on the simulation platform, and the performance of the proposed framework and methods was evaluated, verifying their feasibility and effectiveness. The simulation case architecture is shown in Figure 4.

In the case workshop described in this chapter, a hydraulic valve block is considered a workpiece. Each workpiece can be completed through a series of specific production processes. There are eight types of processing tasks involved in the manufacturing process: face milling, positioning hole drilling, four-side milling, joint hole processing, main hole processing, side hole processing, top hole processing, and deburring. The hydraulic valve block production workshop of the case company has six machining centers, each equipped with multiple functions. Each machine can perform manufacturing tasks with different expected service times.

To evaluate the effectiveness of the proposed method, several performance indicators are defined. The simulation parameters for the manufacturing resources are shown in

Table 2. Manufacturing resource simulation parameters.

Parameter	Value	Parameter	Value
Workers	8	(Learning Index, Forgetting Index)	(0~1)
Production Equipment	8	Order Quantity	20, 40, 60
Processing Rate	1	Equipment Idle Power	5 (KW)
Logistics Devices	4	Logistics Power	4 (KW)
Logistics Speed	1 (m/s)	Logistics Idle Power	1 (KW)

.

The distances between the warehouse and the machines are shown in

Table 3. Distance matrix between machines in the workshop layout.

Distance (m)	S/D	${\mathit{m}}_1$	${\mathit{m}}_2$	${\mathit{m}}_3$	${\mathit{m}}_4$	${\mathit{m}}_5$	${\mathit{m}}_6$	${\mathit{m}}_7$	${\mathit{m}}_8$
S/D	0	16	24	32	40	48	40	56	48
$m_1$	40	0	8	16	24	32	24	40	32
$m_2$	48	40	0	24	16	24	16	32	24
$m_3$	56	24	16	0	16	24	32	32	40
$m_4$	64	32	24	16	0	16	24	24	32
$m_5$	24	40	32	24	16	0	16	16	24
$m_6$	32	56	48	40	32	24	0	16	8
$m_7$	40	48	40	32	24	16	24	0	16
$m_8$	48	64	56	48	40	32	40	24	0

. At the initial moment, movable resources (such as AGVs) are located in the same position as the warehouse.

In this case study, each workpiece consists of eight operations.

Table 4. Estimated processing time for each process.

Time [s]	${\mathit{m}}_1$	${\mathit{m}}_2$	${\mathit{m}}_3$	${\mathit{m}}_4$	${\mathit{m}}_5$	${\mathit{m}}_6$	${\mathit{m}}_7$	${\mathit{m}}_8$
Job	135	105	135	105	120	144	105	126
	105	135	120	105	135	120	135	90
	105	135	120	105	135	105	120	90
	120	105	135	150	120	120	126	114
	132	135	102	120	90	114	120	126
	129	120	114	108	120	150	130	120
	180	195	165	150	195	225	180	165
	225	210	195	210	165	180	195	180

and

Table 5. Energy consumption of the machine tools during operation.

Machine	${\mathit{m}}_1$	${\mathit{m}}_2$	${\mathit{m}}_3$	${\mathit{m}}_4$	${\mathit{m}}_5$	${\mathit{m}}_6$	${\mathit{m}}_7$	${\mathit{m}}_8$
Operational Power [KW/h]	22.5	13.0	24.1	24.5	23.5	22.8	23.4	24.0

show the estimated processing time and power consumption for each operation on different machines.

Through conducting a workshop case study, it was discovered that not only do new and experienced workers have different learning and forgetting rates, but even among experienced workers, the learning and forgetting rates vary based on age [51]. Additionally, some workers possess exceptional talent, learning faster than the average. Therefore, four scenarios were designed.

Older Experienced Workers (OEW): Workers are all older experienced employees. The Learning Index is (0.4, 0.5), the Forgetting Index is (0.2, 0.3), and the learning capacity limit is constrained at 0.7.

Younger Experienced Workers (YEW): Workers are all younger experienced employees. The Learning Index is (0.5, 0.6), the Forgetting Index is (0.1, 0.2), and the learning capacity limit is constrained at 0.65.

New and Novice Workers (NNW): Workers are all new employees. The Learning Index is (0.3, 0.4), the Forgetting Index is (0.2, 0.3), and the learning capacity limit is constrained at 0.8.

Special Workers (SW): All workers are highly capable employees with strong learning abilities. The Learning Index is (0.7, 0.9), the Forgetting Index is (0.1, 0.3), and the learning capacity limit is constrained at 0.75.

Due to individual differences, learning and forgetting rates are not uniform across workers. Therefore, for each worker, a uniform fuzzy function is applied to define their specific learning and forgetting indices within the boundary values of each scenario. When the learning and forgetting effects are disregarded (No Learning and Forgetting, NLF), the learning and forgetting rates for all workers are set to zero.

5.2. Effectiveness Analysis of the Proposed Method

Due to fluctuations in the number of workshop orders, which vary with peak and off-peak seasons, three different order quantities were selected for this case study: small, medium, and large. This section presents the results of experiments conducted under three order quantity scenarios, considering five different worker learning and forgetting speeds. In each scenario, the order arrival rate follows a normal distribution. By conducting multiple simulations, the experimental results for each scheduling method under different worker learning and forgetting speeds were collected and compared. The proposed method was evaluated against five scheduling rules from Erol et al. [52] and Baruwa and Piera [53], including First-Come-First-Served (FCFS), Shortest Processing Time + Shortest Transportation Time (SPT + STT), Longest Processing Time + Longest Transportation Time (LPT + LTT), Shortest Remaining Processing and Transportation Time (SRPTT), and Longest Remaining Processing and Transportation Time (LRPTT). The comparison also includes an order insertion rule (OC) [35] from the previous literature. The proposed human–machine–logistics collaborative scheduling method (HMLCS) was tested both with and without considering the learning and forgetting effects of workers.

The following

Table 6. Comparison of results with and without Worker LFE (NNW vs NLF).

Without Learning and Forgetting Effects (NLF)					Considering Learning and Forgetting Effects (NNW)
Algorithm	Order Size	Makespan (s)	Energy Consumption (KJ)	Tardiness (s)	Algorithm	Order Size	Makespan (s)	Energy Consumption (KJ)	Tardiness (s)
HCML CS	20	3558	573,172	40	HCML CS	20	3464	535,336	21
	40	6464	1,109,272	111		40	5944	989,220	47
	60	9087	1,635,784	499		60	8121	1,407,748	102
OC	20	3967	590,400	99	OC	20	3553	538,448	37
	40	7299	1,146,788	472		40	6065	1,004,932	108
	60	10,071	1,674,104	1043		60	8257	1,443,756	388
FCFS	20	3977	590,216	90	FCFS	20	3755	552,464	78
	40	7146	1,144,348	360		40	6923	1,056,896	264
	60	11,158	1,751,944	1261		60	10,180	1,543,460	695
SPT+ STT	20	3703	575,264	62	SPT+ STT	20	3826	550,168	29
	40	6980	1,129,000	293		40	6540	1,024,008	154
	60	10,066	1,677,836	638		60	9061	1,477,712	277
LPT+ LTT	20	3851	577,984	95	LPT+ LTT	20	3461	503,136	47
	40	6893	1,128,296	227		40	6104	1,002,832	69
	60	9818	1,668,320	829		60	8365	1,453,240	313
SRP TT	20	3912	586,904	49	SRP TT	20	3736	548,532	28
	40	7508	1,147,084	396		40	6695	1,034,884	61
	60	10,135	1,686,340	591		60	8887	1,463,496	185
LRP TT	20	3963	591,972	147	LRP TT	20	3618	544,396	49
	40	7343	1,151,672	358		40	6945	1,033,268	225
	60	10,493	1,695,692	816		60	8748	1,455,264	432

shows a comparison of the results between considering (NNW) and not considering worker learning and forgetting effects (NLF):

When considering the learning and forgetting effects (NNW), the HCMLCS algorithm demonstrates significant performance improvements in completion time, energy consumption, and delay time compared to all scheduling methods under the no-learning-and-forgetting (NLF) scenario. Specifically, for an order size of 20, the completion time, energy consumption, and delay time were reduced by an average of 10.65%, 8.52%, and 73.04%, respectively. For an order size of 40, the three indicators decreased by 17.63%, 12.76%, and 86.26% on average, respectively. For an order size of 60, the improvements were even more significant, with reductions of 20.79%, 16.43%, and 88.35%, respectively. Particularly in terms of delay time, as the order size increases, the optimization effect of HCMLCS with learning and forgetting effects becomes more pronounced, indicating its strong advantage in large-scale order scenarios. To comprehensively evaluate the performance of HCMLCS under different conditions, the following section compares its performance with and without considering the learning and forgetting effects (NLF vs NNW) and explores its optimization effects across various order sizes.

Even without considering the learning and forgetting effects, the HCMLCS algorithm still exhibits significant advantages in completion time and delay control. For order sizes of 20, 40, and 60, completion time was reduced by 9.63%, 10.31%, and 12.4%, respectively. Similarly, the reductions in delay time were also remarkable, at 55.9%, 69.2%, and 41.0%, respectively. When considering workers’ learning and forgetting effects, the performance of HCMLCS was further optimized. For small, medium, and large order sizes, completion time was further reduced by 5.20%, 6.35%, and 10.32%, while average delay time was reduced by 53.0%, 67.7%, and 70.7%, respectively. These improvements ensure efficient production processes, allowing enterprises to respond to customer demands more quickly, thereby enhancing customer satisfaction and loyalty. Moreover, while the reduction in energy consumption was relatively smaller, the overall optimization effect remains significant, demonstrating that the HCMLCS method exhibits strong flexibility and adaptability in dynamic production environments.

The above analysis indicates that the HCMLCS algorithm demonstrates unique advantages compared to existing scheduling methods in the literature. Many traditional scheduling methods focus primarily on individual task scheduling, overlooking task collaboration, dynamic resource variations, and fluctuations in worker efficiency (such as learning and forgetting effects). For example, classical scheduling approaches such as Shortest Processing Time (SPT) and First-Come-First-Served (FCFS), while effective in certain scenarios, may lead to inefficient resource allocation, task delays, and reduced overall production efficiency in multi-resource, high-disturbance production environments. Even when some traditional methods take worker learning and forgetting effects into account, their scheduling optimization results still fall short of the HCMLCS algorithm, further highlighting the limitations of conventional scheduling strategies in complex, high-dynamic production environments. Additionally, although the Order Insertion (OC) method from literature [35] performs well in logistics-intensive production settings, experimental results indicate that in high-disturbance, low-logistics-priority, and multi-resource collaborative production environments, the OC method exhibits lower adaptability and inferior scheduling performance compared to the HCMLCS algorithm.

In summary, the HCMLCS algorithm demonstrates superior adaptability and optimization capabilities in multi-resource, high-disturbance production environments, effectively enhancing production efficiency and scheduling stability, thereby proving its practical value in real-world manufacturing scenarios. However, current research on human–machine–logistics collaborative scheduling in multi-resource, high-dynamic environments remains limited, with almost no publicly available code resources, which hinders broader comparative studies and slows research progress in this field. Therefore, this study not only fills a research gap but also provides a novel approach and methodology for future scheduling optimization research.

5.3. Analysis of the Impact of Learning and Forgetting Effects on Scheduling

To further prove the impact of learning and forgetting effects on scheduling, comparative experiments were conducted between scenarios with and without considering worker learning and forgetting effects for all types of workers. The results for three different order sizes are shown in Figure 5, Figure 6 and Figure 7.

According to the charts, across all order sizes, all scheduling methods that consider learning and forgetting effects show varying degrees of improvement in completion time, energy consumption, and average delay. The impact of workers’ learning and forgetting rates on production scheduling is significant. Workers with higher learning abilities and lower forgetting rates (e.g., YEW and SW) can complete tasks in a shorter time with lower energy consumption and shorter delays. This indicates that they quickly adapt to tasks and execute them efficiently, thereby enhancing overall production efficiency. In contrast, workers with weaker learning abilities and higher forgetting rates (e.g., NNW) exhibit longer completion times, higher energy consumption, and greater delays, suggesting that a lower learning rate and a higher forgetting rate lead to lower efficiency and slower adaptation during task execution.

As order size increases, the scheduling performance of all workers improves, especially for experienced workers (e.g., OEW and SW). This suggests that as order size grows, workers become more adaptable to tasks, particularly experienced workers, whose learning and adaptation processes are more efficient. However, it is important to note that although larger order quantities lead to greater optimization effects, this improvement is limited. Each worker’s learning ability has an upper limit (parameter θ), beyond which further improvements in scheduling performance will plateau.

Although this study has validated the effectiveness of the HCMLCS algorithm through simulations, the experimental environment remains idealized and does not fully consider complex real-world factors such as equipment failures, material shortages, or other unexpected disruptions. Additionally, worker-to-worker variations were only preliminarily considered. Future research could enhance the robustness and adaptability of the algorithm by conducting field tests in more complex and uncertain production environments.

Overall, the proposed method not only holds significant theoretical value in the field of production scheduling but also provides strong support for the practical application of intelligent manufacturing and scheduling optimization. From a theoretical perspective, this study makes an innovative contribution to the field of production scheduling, particularly in incorporating workers’ learning and forgetting effects. By considering fluctuations in worker efficiency, this study not only optimizes scheduling performance but also introduces a novel research perspective for intelligent scheduling in dynamic production environments. This approach effectively addresses common challenges in production scheduling, such as inefficient resource allocation and task delays, thereby filling a gap in existing research. From a practical application perspective, the HCMLCS algorithm significantly enhances production efficiency, reduces delays, optimizes resource utilization, and enables enterprises to achieve more efficient resource scheduling in complex and dynamic production environments. The algorithm dynamically adjusts resource allocation based on changes in workers’ learning curves, ensuring high execution efficiency across different order sizes, especially for large-scale orders. Additionally, by optimizing resource allocation and task assignment, enterprises can reduce operational costs, improve on-time delivery rates, and enhance customer satisfaction.

6. Conclusions

This paper, set against the backdrop of Industry 5.0, explores the issue of human–machine–logistics collaborative scheduling in intelligent workshops, highlighting the differences between intelligent workshops involving workers and those that do not. A human–machine–logistics collaborative scheduling framework was proposed, considering workers’ learning and forgetting effects. This framework makes several key contributions:

Introduction of a Learning and Forgetting Model: By incorporating a mathematical model for learning and forgetting, this paper addresses the scheduling challenges posed by variable worker efficiency. The model effectively captures the state changes in workers under the influence of learning and forgetting effects, providing reliable data for further scheduling optimization.

Development of Real-Time State Models: The framework establishes real-time status models for human–machine–logistics resources, integrating dynamic information on workers, equipment, and materials within the workshop. This allows the scheduling system to self-organize based on real-time data, improving flexibility and response speed.

Adaptive Scheduling Algorithm: An adaptive scheduling algorithm based on real-time worker efficiency is proposed. This algorithm dynamically adjusts scheduling strategies in real time according to worker states, ensuring production stability and high efficiency.

Through case study validation, the proposed method demonstrated significant advantages in enhancing production efficiency, increasing scheduling system flexibility, and handling variations in worker states. The validation results showed that the scheduling framework considering workers’ learning and forgetting effects could maintain stable system operation in complex and changing production environments.

In conclusion, the method proposed in this paper provides an innovative and effective solution to intelligent workshop scheduling, fully reflecting the importance of human-centered manufacturing in the Industry 5.0 era. However, there is still room for further exploration. Some indicators did not show better performance in cases where learning speed was high, and forgetting speed was low, suggesting that the impact of workers’ learning and forgetting effects on collaborative scheduling involves complex triggering mechanisms that could affect overall scheduling outcomes. Future research could delve deeper into these mechanisms. Additionally, combining intelligent algorithms, such as deep learning or genetic algorithms, with human–machine–logistics collaborative scheduling could further improve scheduling precision and efficiency, providing new solutions for complex, dynamic scheduling problems. This would create smarter management modes for coordinating workers, machines, and logistics and offer theoretical foundations and practical references for future research.