Introduction
Job scheduling is a basic and critical task in production control (Dolgui et al., Reference Dolgui, Ivanov, Sethi and Sokolov2019). Its effectiveness also contributes to the competitiveness and sustainability of the manufacturing system (Aydilek et al., Reference Aydilek, Aydilek and Allahverdi2013). However, job scheduling is a complex optimization problem, forcing schedulers to resort to artificial intelligence (AI), such as machine learning (ML), deep learning (DL), and bio-inspired algorithm applications (Arinez et al., Reference Arinez, Chang, Gao, Xu and Zhang2020). So far, such applications have focused on preparing required inputs, evolving feasible schedules, optimizing scheduling rules, etc. (Wang and Chen, Reference Wang and Chen2023).
However, existing job scheduling systems are still subject to the following issues:
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• Rigid input formats and inflexible user interfaces make it difficult to consider user requirements (Jia et al., Reference Jia, Fuh, Nee and Zhang2002).
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• Only limited options/functions are available (such as finding the optimal schedule, parameter analysis, sensitivity analysis, etc.) (Jia et al., Reference Jia, Fuh, Nee and Zhang2002; Framinan and Ruiz, Reference Framinan and Ruiz2010).
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• ML, DL, and bio-inspired algorithms employed are black boxes (Priore et al., Reference Priore, Gómez, Pino and Rosillo2014; Chawla et al., Reference Chawla, Chanda, Angra and Rani2019; Kim et al., Reference Kim, Lim and Lee2020; Yue et al., Reference Yue, Wang, Mumtaz, Rauf and Li2023), hampering comprehensibility, communicability, and/or trust.
Two new AI streams, explainable AI (XAI) (Kamath and Liu, Reference Kamath and Liu2021; Sofianidis et al., Reference Sofianidis, Rožanec, Mladenic and Kyriazis2021) and generative AI (GenAI) (Ghobakhloo et al., Reference Ghobakhloo, Fathi, Iranmanesh, Vilkas, Grybauskas and Amran2024), are expected to address these issues. However, GenAI applications in job scheduling are still a challenging task for the following reasons:
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• There are no GenAI systems specifically designed for this purpose.
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• In addition, existing GenAI systems may not be directly applicable to job scheduling because the required data and optimization model need to be extracted from in-factory information systems and uploaded to the cloud GenAI server, subject to very high data security risks. Local GenAI systems need to be built to address this issue (Takaffoli et al., Reference Takaffoli, Li and Mäkelä2024).
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• The scheduler takes multiple communications to teach an existing GenAI service to acquire his/her requirements and understand the job scheduling problem.
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• It is difficult to check the optimality or feasibility of the scheduling results generated by an existing GenAI service.
To overcome these issues, a GenAI job scheduling system is established in this study.
In the GenAI job scheduling system, a user interface is designed for users to input their queries in natural language. Requirements related to the scheduling task are then extracted from the user’s query to build an extended three-field notation (ETFN) of the scheduling problem. Based on the ETFN, the corresponding mathematical programming (MP) model is formulated and solved with the help of a customized genetic algorithm (GA). GAs are adopted because of their wide applications in solving job scheduling problems. In addition, GAs have long been used to generate images, music, poetry, and dialogue based on expressions in typical GenAI applications (Spector and Alpern, Reference Spector and Alpern1994; Jacob, Reference Jacob1995; Manurung, Reference Manurung2003; Hervás et al., Reference Hervás, Robinson and Gervás2007; Collomosse, Reference Collomosse2008). Finally, the scheduling results are presented to the user in tabular or graphic forms through the same user interface. Different from existing GenAI applications, the GenAI job scheduling system established in this study has the following novelties:
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• The GenAI job scheduling system is designed to serve job scheduling purposes that are different from those of existing GenAI applications (Law, Reference Law2024).
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• The GenAI job scheduling system is also among the first attempts of applying GenAI to job scheduling.
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• The GenAI job scheduling system is hosted on a private cloud to eliminate the risk of exposure of confidential data, such as order- or recipe-related information (Wang et al., Reference Wang, Chen and Chiu2023; Huang et al., Reference Huang, Huang, Dawson and Wu2024).
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• In a manufacturing environment, users can be asked to enter queries in a more regulated manner, although still using natural language, to facilitate the extraction of scheduling task-related requirements (Li et al., Reference Li, Lin, Pathak, Li, Fei and Wu2024).
The remainder of this paper is organized as follows. Section 2 reviews the relevant literature. Section 3 introduces the established GenAI job scheduling system. To evaluate the effectiveness of the proposed methodology, it has been applied to a flexible job shop scheduling problem in Section 4. Section 5 discusses the experimental results. Finally, Section 6 concludes this study and puts forth some topics that can be investigated in the near future.
Literature Review
GenAI
GenAI (Chiu et al., Reference Chiu, Moorhouse, Chai and Ismailov2023) is a subset of AI that uses generative models to produce text, images, videos, or other forms of data. GenAI models learn the underlying patterns and structures of the training data to generate new data based on users’ requirements (Kido and Takadama, Reference Kido and Takadama2024; Takaffoli et al., Reference Takaffoli, Li and Mäkelä2024), which often comes in the form of natural language prompts. Improvements in transformer-based deep neural networks (Bengesi et al., Reference Bengesi, El-Sayed, Sarker, Houkpati, Irungu and Oladunni2024), especially large language models (LLMs) (Deng et al., Reference Deng, Khan and Erkoyuncu2024; Gu et al., Reference Gu, Zhu, Zhu, Chen, Tang and Wang2024; Jose et al., Reference Jose, Nguyen, Medjaher, Zemouri, Lévesque and Tahan2024; Vidyaratne et al., Reference Vidyaratne, Lee, Kumar, Watanabe, Farahat and Gupta2024), have made the application of generative AI systems popular. Some references on GenAI applications in manufacturing are reviewed below. The gap left by each reference that needs to be filled is also mentioned.
Kulkarni and Bansal (Reference Kulkarni and Bansal2024) believed that GenAI can be used to collect data on the Internet and analyze the collected data to realize various functions of manufacturers, such as sales and marketing planning, customer review analysis, and automated replies, supply chain optimization, office automation, and so forth However, many of such functions are only possible if suppliers or customers agree to share their data, which has not been addressed in their study. Their research was conceptual only and had no actual cases.
Grashoff et al. (Reference Grashoff, Mayer and Recker2024) interviewed 31 technical and business project leaders and pilot testers from a German automobile manufacturer to identify success factors, challenges, and potential for GenAI applications. They concluded that success factors for GenAI adoption included senior management support, the diverse skillset of the development team, intrinsic curiosity about AI topics, and early selection of an appropriate development strategy. They used expert interviews without practicing any GenAI application.
A logical application of GenAI in manufacturing is to assist in product development, given its ability to generate or modify images, text, and designs. Jide-Jegede and Omotesho (Reference Jide-Jegede and Omotesho2024) also claimed that GenAI can streamline operations in a supply chain by analyzing contract documents, ensuring compliance, and reducing legal loopholes. They also believed that the analytical capability of a GenAI system can be used to monitor and analyze production line performance in real time, identify bottlenecks, and make suggestions for improvement. However, uploading such production data to a cloud-based GenAI system is prone to the risk of data leakage. Jide-Jegede and Omotesho (Reference Jide-Jegede and Omotesho2024) was only a conceptual study.
According to Majstorović et al. (Reference Majstorović, Dimitrijević, Simeunović and Stošić2024) GenAI can be applied to product design, additive manufacturing (AM), materials science, business and technical process optimization, robotics and automation, predictive maintenance, quality control, and supply chain management. However, such GenAI applications are subject to various limitations such as data quality, interoperability, scalability, and network security. The approach adopted by Majstorović et al. (Reference Majstorović, Dimitrijević, Simeunović and Stošić2024) is to summarize the review results of selected literature.
Doanh et al. (Reference Doanh, Dufek, Ejdys, Ginevičius, Korzynski, Mazurek, Paliszkiewicz, Wach and Ziemba2023) conducted a literature review on the applications of GenAI in manufacturing. They concluded that most GenAI applications were for designing new products, optimizing workforce and their skills, enhancing quality control, enabling predictive maintenance, improving demand forecasting, and developing marketing strategies. However, one issue with their review was that GenAI applications were not clearly distinguished from traditional AI applications.
Witkowski and Wodecki (Reference Witkowski and Wodecki2024) studied the potential of GenAI applications in product management at a large international manufacturing company. To this end, they conducted stakeholder interviews and document collection and analysis. In their study, GenAI systems were used as an alternative to hiring more employees in developing roadmaps for various product portfolios. Relevant documents were fed into five agents built by GenAI to generate diverse opinions, which were then aggregated by another agent.
Rath et al. (Reference Rath, Tripathy and Jain2023) jointly applied diffusion of innovation (DOI) theory, technology-organization-environment (TOE) framework, and innovation resistance theory (IRT) to identify key factors influencing the initial acceptance and sustained adoption of GenAI in the manufacturing industry. Three factors, relative advantage, compatibility, and complexity, were thought to influence the initial implementation of GenAI, while five additional factors, technology readiness, absorptive capacity, competitive pressures, functional impairments, and physiological barriers, may influence the continued adoption of GenAI.
After reviewing these references, it is clear that there are gaps that need to be filled. Although many past studies have proposed some possible directions for GenAI in manufacturing, there are few noteworthy actual cases of success. In addition, most past research on the application of GenAI in manufacturing has used general-purpose GenAI tools to capture and summarize data, draw, etc., while GenAI tools specifically designed for manufacturing functions (including job scheduling) are very rare.
Industrial LLMs
This section reviews some developments and applications of LLM in the manufacturing domain.
Jose et al. (Reference Jose, Nguyen, Medjaher, Zemouri, Lévesque and Tahan2024) used an LLM to extract domain knowledge accumulated in unstructured textual materials such as technical documents and maintenance logs into diagnostic models. To this end, they chose GPT2-large (Radford et al., Reference Radford, Wu, Child, Luan, Amodei and Sutskever2019) to balance prediction performance and resource efficiency. Furthermore, they highlighted the importance of pre-processing, including special character management and encoding, before providing the material to the LLM.
Gu et al. (Reference Gu, Zhu, Zhu, Chen, Tang and Wang2024) differentiated normal and abnormal drug capsules using a large visual language model (LVLM). They first partition and encode capsule images to obtain intermediate patch-level features. The distance between each patch and its most similar counterpart in the memory bank was then calculated as the localization result and transformed into prompt embeddings using a prompt learner. Finally, these embeddings were fed into an LLM along with the original image information to produce a corresponding text description of the image.
To generate decision rules or trees for machine troubleshooting, Vidyaratne et al. (Reference Vidyaratne, Lee, Kumar, Watanabe, Farahat and Gupta2024) applied an LL.M. During manual preprocessing, the troubleshooting diagram in each manual was first extracted and replaced with natural language representations (including faults, causes, and repairs). These natural language representations were then paraphrased, expanded, combined, and randomly selected using GPT3.5 Turbos to generate rules for troubleshooting machines.
Deng et al. (Reference Deng, Khan and Erkoyuncu2024) used an LLM to design a one-stage reduction gear system consisting of two gears, in which GPT-4 helped complete three tasks, namely parameter calculation, instruction sequence construction, and coding model scripting. First, the user’s design requirements were input into GPT-4 to calculate parameters and generate design documents, which were manually reviewed and structured into multiple text descriptions with parameters. GPT-4 then parsed a JavaScript object notation (JSON) file to formalize the instructions and tokenize the natural language instructions as a list of keywords and values. Based on the JSON file, GPT-4 selected the most relevant function from a given library and filled it with parameters to script 3D modeling, which was then rendered using CAD software.
Clearly, there is a research gap since most industrial LLM applications were devoted to knowledge management, quality control, and computer-aided product design, with few other uses such as job scheduling. The differences between the proposed methodology and some existing methods are summarized in Table 1.
Table 1. Differences between the proposed methodology and some existing methods
According to Table 1, the contribution of this study is to design a GenAI system specifically for flexible job shop scheduling purposes, which is extremely rare at present, in which schedulers can input their requirements in natural language without the need to formulate optimization models or write any code to apply AI technologies to solve the optimization problems. In addition, since the GenAI system established is not a general GenAI system but a dedicated system, eliminates the need for manual preprocessing by the scheduler to train the GPT software. The output of the established GenAI system also meets the usual requirements of the scheduler and, therefore, does not need to be relayed to other systems for post-processing.
Flexible job shift scheduling
Zhang et al. (Reference Zhang, Gao and Shi2011) proposed a GA to solve a five-machine flexible job shop scheduling problem to minimize the makespan. Different from the common chromosome coding format, in the GA, each chromosome consisted of two consecutive parts describing the machines used and the sequence of operations. Two parent chromosomes were selected using tournament selection and crossed over using two-point crossover or uniform crossover and precedence preserving order-based crossover for the two parts, respectively. The mutation operator then changed the machine used by an operation to another machine with the shortest processing time.
Roshanaei et al. (Reference Roshanaei, Azab and ElMaraghy2013) formulated a three-machine flexible job shop scheduling problem as two mixed integer-linear programming (MILP) models: one location-based and the other sequence-based. For a large-scale flexible job shop scheduling problem, they proposed a metaheuristic approach (Chen et al., Reference Chen, Lin and Wang2025) that was a hybrid of artificial immune system and simulated annealing (SA) method. The artificial immune system associated operations with random numbers to sequence them accordingly. Schedules with lower makespan values (higher affinity values) then had a greater chance of entering the mutation pool through tournament selection. All scheduled clones in the pool underwent hypermutation that made random changes to the scheduled clones using a fast-converging SA.
Mokhtari and Hasani (Reference Mokhtari and Hasani2017) solved a multi-objective flexible job shop scheduling problem (Chen et al., Reference Chen, Zhao, Mumtaz, Guangyuan and Wang2024) in which three objective functions were optimized: minimizing the makespan, maximizing the total availability of the system, and minimizing the total energy cost of production and maintenance operations. Machine availability was measured as an exponential function of repair rate, failure rate, and time, which made the second objective function a nonlinear one. By defining the ideal solution, measuring the distance between each feasible solution and the ideal solution, and then seeking to minimize the distance, the three objective functions were combined, similar to the concept of goal programming. Then, a combination of GA and SA was applied to solve the problem.
Dauzère-Pérès et al. (Reference Dauzère-Pérès, Ding, Shen and Tamssaouet2024) recently conducted a review of the flexible job shop scheduling literature. They first distinguished between studies optimizing regular, nonregular, and multiple criteria. Then, additional constraints considered in past studies were classified into time lag, availability, batching, setup time, blocking, transportation time, and other constraints. Like many previous reviews, they classified solution methods into exact methods, heuristics, and metaheuristics, with a special focus on metaheuristics, where trajectory-based metaheuristics, population-based metaheuristics, and hybrid metaheuristics were reviewed.
Obviously, GA and its variants (Mumtaz et al., Reference Mumtaz, Minhas, Rauf, Yue and Chen2024) are one of the most commonly used methods to solve flexible job shop scheduling problems. However, GenAI has rarely been used to facilitate the application of GA in flexible job shop scheduling, which is an obvious gap to be filled.
Methodology
The job scheduling system based on the GenAI application comprises five main parts (see Figure 1): user interface, ETFN generator, MP model formulator, bio-inspired algorithm-based optimizer, and system database.
Figure 1. Main parts of the job scheduling system based on the GenAI application.
The operational procedure of the job scheduling system based on the GenAI application comprises the following steps:
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Step 1. Formulate the basic MP model considering the type of the manufacturing system.
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Step 2. Receives a user’s query through the user interface.
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Step 3. Analyze the query and generate the ETFN of the scheduling problem.
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Step 4. Construct the MP model for solving the scheduling problem.
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Step 5. Customize the GA program for solving the MP problem: Additional code that fulfills user requirements is embedded into the base GA program. Invalid codes will also be replaced with new codes. For this purpose, the feasible solutions of the initial, intermediate and final populations as well as any production condition variable that may be useful will be stored in the system database.
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Step 6. Retrieve the optimal schedule from the system database and present it to the user in tabular and graphical forms through the user-system interface.
Step 1. Formulate the default MP model
First, a default MP model is first formulated for the scheduling problem. Take a four-machine flexible job shop scheduling problem minimizing the makespan with release time and due date constraints (Pezzella et al., Reference Pezzella, Morganti and Ciaschetti2008) as an example. The default MP model is provided in Appendix A. Flexible job shop scheduling problems are usually NP-hard (Oertel and Ravi, Reference Oertel and Ravi2014). The motivation for using GenAI systems to solve such problems is explained below.
Although many past studies have proposed algorithms and refreshed upper-bound solutions for various flexible job shop scheduling problems using benchmarks (Bekkar et al., Reference Bekkar, Belalem and Beldjilali2019; Ozturk et al., Reference Ozturk, Bahadir and Teymourifar2019; Shahgholi Zadeh et al., Reference Shahgholi Zadeh, Katebi and Doniavi2019; Song et al., Reference Song, Chen, Li and Cao2022; Lei et al., Reference Lei, Guo, Zhao, Wang, Qian, Meng and Tang2022), these algorithms were designed for specific flexible job shop scheduling problems and needed to be modified to apply to scheduling problems with different objective functions or constraints, which is often beyond the capability of the production planning or control engineer in practice. The GenAI scheduling system established in this study eliminates the need for production planning or control engineers to select, understand, and code algorithms. In addition, by issuing instructions to the GenAI scheduling system in plain language, objective functions and constraints can be easily added or changed to accommodate any scheduling problem that may not have been investigated by past research, and the GA algorithm is automatically tailored to the scheduling problem to ensure promising scheduling performance.
Step 2. Inputting a query
A key feature of GenAI methods is that they allow users to enter queries in natural language. Given the arbitrary content that a query may contain, a deep neural network (DNN) may need to be built to extract relevant information to complete the required task. The situation in this study can be greatly simplified for the following reasons:
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• The GenAI approach is designed to meet a narrower functional scope (see Table 2), that is, limited to some functions that a job scheduling system might fulfill. According to Table 2, the most important functions of GenAI applications in job scheduling include reflecting fluctuations in production conditions, considering user-specified constraints, evaluating and optimizing the scheduling performance, and so forth Nevertheless, there will be numerous combinations of these functions, addressing a variety of user needs. As a result, the NLP mechanism for extracting the ETFN of the scheduling problem from the user’s query can be much simplified.
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• Users are factory workers with similar knowledge background and can be asked to input in more professional terminology. As a result, queries will be more structured and contain less arbitrary content.
Table 2. Functional scope of the scheduling system using the GenAI approach
Step 3–1. Analyze the query
The query analysis mechanism proposed in this study is illustrated in Figure 2, which is to perform extractive summarization that comprises the following steps:
Figure 2. Query analysis mechanism proposed in this study.
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Step 1. Extract keywords from queries using word tokenization (Kim et al., Reference Kim, Choi and Seok2021): Keywords considered in the GenAI approach, or their combinations, can be mapped to variables in the MP model that are also present in instances of the functions of the job scheduling system (see Table 3). Both stemming and lemmatization (Korenius et al., Reference Korenius, Laurikkala, Järvelin and Juhola2004) are applied. Therefore, for example, not only does “make span” translate to “makespan,” but “maximum completion time” is also equivalent to “makespan.” In addition, in Table 3, A and B means the positions of A and B are interchangeable; A || B means A is in front of B; proxim({
$ {A}_g $
}) means that the elements of {
$ {A}_g $
} should be close to each other and not necessarily in a specific order. Checking whether specific keywords exist in the query and the relationship between these keywords is sufficient to understanding the user’s needs for the scheduling system.Table 3. Keywords considered in the scheduling system
a A system dictionary has been established for this purpose.
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Step 2. Extract the parameters for each identified keyword, usually the first (or last) value or meaningful encoding that follows the keyword.
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Step 3. Generate the corresponding instance of the function for the user or system administrator to confirm (see Table 4). In Table 4, instances are generated based on generally accepted theory and practice in job scheduling. For example, the makespan is to be minimized rather than maximized. In contrast, a machine can be available earlier or later than a certain point in time, depending on the expected repair progress.
Table 4. Instances generated from keyword combinations and parameters
Step 3–2. Generate the ETFN of the scheduling problem
Depending on the type of the manufacturing system, a basic three-field notation is first specified for the scheduling problem, such as FJm/
$ {r}_j $
,
$ {d}_j $
/Cmax for a m-machine flexible job shop scheduling problem minimizing the makespan with release time and due date constraints. Subsequently, each instance adds an additional term to the three-field notation (see Table 5), thereby forming the ETFN of the scheduling problem. For example, in Table 5, the makespan can appear in the third field as part of the performance measure, or as a constraint and appear in the second field. The steps involved in constructing an ETFN include.
Table 5. Additional term added to the three-field notation
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Step 1. For each keyword combination, lookup and complete the symbols representing the keywords from the system dictionary.
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Step 2. Lookup and complete the required modification associated with each keyword combination from the system dictionary.
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Step 3. Insert the required modification associated with each keyword combination into the corresponding field.
Potential application scenarios of the GenAI job scheduling system are discussed as follows. The flexible job shop scheduling problem with transportation time constraints was studied by Bekkar et al. (Reference Bekkar, Belalem and Beldjilali2019) can be represented by ETFN
$ FJm, TF/{R}_j/{C}_{max} $
(Lee and Chen, Reference Lee and Chen2001). The dynamic multi-objective flexible job shop scheduling problem was solved by Ozturk et al. (Reference Ozturk, Bahadir and Teymourifar2019) can be expressed as
$ FJm/{R}_j/\frac{1}{3}{C}_{max}+\frac{1}{3}\overline{L}+\frac{1}{3}\overline{F} $
. The dynamic flexible job shop scheduling problem with variable processing times is considered by Shahgholi Zadeh et al. (Reference Shahgholi Zadeh, Katebi and Doniavi2019) can be expressed by
$ Jm/{\tilde{p}}_j,{R}_j/{C}_{max} $
. Then, corresponding modifications are automatically made to the GA program code. In this way, the GenAI job scheduling system can be applied to solve any job scheduling problem with a valid ETFN.
Step 4. Modify the basic MP model
The additional terms in Table 5 correspond to changes that should be made to the basic MP model, as shown in Table 6. According to Table 6, the default objective function is replaced by the selected one and new constraints are added to exclude solutions that are no longer feasible.
Table 6. Changes that should be made to the basic MP model
The correctness of the MP model is ensured through two steps. First, Lingo is used to validate the default MP model for the flexible job shop scheduling problem using example data from the literature. Subsequently, any possible change to the objective function or constraints is verified in the same way and then saved to the system database for future applications.
Step 5. Customize the program code of the GA algorithm
The following explains how to use the information from the MP model to generate the code of the GA. In the GA, after generating the chromosomes of the initial population, it is necessary to check the feasibility of each chromosome against each constraint of the MP model according to the following procedure:
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Step 1. Check for redundancy: If any operation appears multiple times, the chromosome is infeasible.
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Step 2. Check for incorrect sequences: An operation may appear only if all its preceding operations have appeared.
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Step 3. Check for user-enforced machine specificity: Operations can be assigned only to machines specified by the user.
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Step 4. Check for user-enforced order of operations: Operations can only be performed in the order enforced by the user.
The same situation occurs when two parental chromosomes are crossed over to generate offspring chromosomes that also undergo feasibility checking. Chromosomes that have been mutated in specific ways may also need to be checked. In addition, the objective function of the MP model is used to evaluate the fitness of each chromosome to select parent chromosomes to be paired accordingly.
Based on the modified MP model, the program code of the GA application for solving the scheduling problem is generated and run. A pseudo code for this purpose is provided in Appendix B, Figure B1. Basically, there is no difference in the codes for the main steps (selection, crossover, and mutation) of different MP models, except for the calculation of the fitness function and the code for checking chromosome feasibility. In addition, the original code of the basic MP model has been generated in advance. The program code for implementing the changes replaces or is simply inserted into the original code.
Since all user queries are more structured and contain less arbitrary content, any change to the objective function and constraints of the MP model can be automated using a MATLAB program by modifying the default MP model (stored in the system database in Lingo format, .lg4) to generate a new one, based on which the code of the default GA (also stored in the system database in MATLAB script file, .m) is updated using another MATLAB function. Therefore, after a user enters his/her query, Steps 4 and 5 will be executed automatically instead of manually, which eliminates the need for the user to formulate MP models and write GA code, which meets the requirements of GenAI and is a characteristic of the proposed methodology.
Step 7. Report the scheduling results to the user
Scheduling results can be reported to users in tabular or graphical form. A tabular form showing the actions taken to implement the scheduling plan. These actions can be arranged by time, job, or machine.
In tabular form, the time-phased scheduling plan lists each operation in chronological order with its start time, completion time and responsible machine. The job-phased scheduling plan summarizes the relevant processing information of all operations of each job and arranges it into a block. The blocks of different jobs are presented in sequence. The machine-phased scheduling plan reports the operations processed on the same machine in chronological order and arranges them into a block. The blocks of different machines are presented in sequence. Various tabular presentations of the scheduling results are shown in Figure 3.
Figure 3. Various tabular presentations of the scheduling results.
The most popular tool for graphically presenting a schedule is a Gantt chart. Parts of the Gantt chart can also be highlighted to reflect that the user’s requirements have been met. In addition, due to the application of a GA, information on the evolutionary process and results can also be reported to the user graphically, such as visualizing the chromosomes of the last population and tracking the scheduling performance during the evolutionary process with a line chart. Various graphical presentations of the scheduling results are shown in Figure 4. In the Gantt chart of Figure 4, some machines have some idle phases, which is reasonable because O21 should precede O12 and O12 should precede O23 in the default MP model.
Figure 4. Various graphical presentations of the scheduling results.
Case study
Background
To evaluate the effectiveness of the proposed GenAI job scheduling system, it has been applied to a precision machining factory in Taichung, Taiwan, to evaluate its applicability and possible advantages/advantages. This case was a FJ6/
$ {r}_j $
,
$ {d}_j $
/Cmax problem with release time and due date constraints, which involved six machines and 10 jobs of various product types that were released at different times to the factory every day. MATLAB codes were written to implement query analysis, customize the GA, and present the scheduling results. The release plan, recipes, and the system dictionary were stored in MySQL databases. In terms of data security, all sensitive data were not entrusted to third-party cloud storage providers. All cloud (job scheduling) services were provided by the GenAI job scheduling system (within the organization) to ensure data security. In addition, various encryption protocols have been used in past research to provide better authentication security (Gajra et al., Reference Gajra, Khan and Rane2014; Olowu et al., Reference Olowu, Yinka-Banjo, Misra and Florez2019; Drozdova et al., Reference Drozdova, Bridova, Uramova and Moravcik2020). In the proposed GenAI job scheduling system, Lightweight Directory Access Protocol (LDAP) and OpenID Connect (OIDC) were employed on MATLAB Web App Server for authentication.
Analyzing the user’s query
The user interface of the GenAI job scheduling system is shown in Figure 5. Users were requested to divide their queries into multiple sections using semicolons to facilitate extraction. The user interface was just a textbox for a user to enter his/her scheduling requirements in plain language. Users could enter anything, but only relevant keywords would be retrieved and processed. The only requirement was to separate the requirements with semicolons. There was no limit to the number of lines or words in the textbox. Therefore, users did not need any training to use the interface. It was straightforward for both novices and experts to use.
Figure 5. User interface of the GenAI job scheduling system.
To evaluate and enhance the effectiveness of query analysis, one hundred queries have been conducted by five production planning or control engineers, and then the corresponding ETFNs were generated and checked by the system administrator to take necessary corrective treatments. After taking the corrective treatments, the queries were reconducted and reanalyzed. The results are summarized in Table 7. According to this table, 8 out of 100 queries have not been correctly interpreted and corresponding treatments were taken to expand the system database. The error rate was only 8% because most of the problems were solved at the beginning of the experiment.
Table 7. Queries conducted by different production planning or control engineers
Table 8 summarizes the modifications to the MP formulation. In some modifications, the new objective function was nonlinear or a compromise of several simple regular measures. In addition, for some modifications, many new constraints have been added to the MP model.
Table 8. Modifications to the MP formulation
Take the first query as an example. First, the basic MP model was formulated. The program code of the GA application for solving the basic MP problem was also generated. Each population involved 10 chromosomes, and each chromosome was composed of 50 genes. The roulette wheel method was applied to select parent chromosomes to be paired. One-point crossover operator was then employed. Crossover and mutation probabilities were set to 0.2 and 0.1, respectively. Subsequently, the basic MP model was modified based on the generated ETFN addressing to the requirements of the user (see Figure 6). In this figure, constraints in red represent the user’s requirements. These additional constraints can be added anywhere in the MP model and have the same effect.
Figure 6. Modified MP model addressing the requirements of the first query.
The GA application for solving the basic MP problem was then modified to solve the modified MP problem (see Figure 7). Unlike modifications to the MP model, the code used to implement the changes must be inserted at specific locations in the original code to take effect. Additionally, some users specified constraints on the scheduling performance, which needed to be evaluated before verifying whether a chromosome was feasible.
Figure 7. GA application for solving the modified MP problem.
The evolution process was illustrated with a dynamic line chart in Figure 8.
Figure 8. Dynamic line chart for illustrating the evolution process.
Finally, the scheduling results were presented in (job-phased, machine-phased, and time-phased) tabular forms and Gantt charts (see Figure 9).
Figure 9. Scheduling results presented in tabular forms and a Gantt chart.
Discussion
The following discussion was conducted on the experimental results:
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• A parametric analysis was performed by varying the crossover rate to observe changes in the convergence speed (in terms of the number of populations), in which the mutation rate was set to 0.1. The results are summarized in Figure 10. Obviously, a crossover rate of 0.5–0.7 seemed to be the best setting to optimize the convergence speed. A crossover rate that was too low reduced the chance of finding the best solution in the beginning, while a crossover rate that was too high made it difficult to improve the average fitness because inferior solutions continued to be included.
-
• However, a similar parametric analysis to assess the effect of mutation rate on the convergence speed could not be replicated. The reason is shown in Figure 11, where the mutation rate was set to 0.2 (and the crossover rate is 0.5). Obviously, such a high mutation rate made the convergence process unstable, because a good solution was likely to become poor after mutation.
-
• Analyzing user queries was clearly a learning process, in which the generated ETFNs were checked and necessary additions to the system dictionary were made accordingly. In this experiment, the learning process converged quickly, which was due to that users in the manufacturing system entered more consistent queries through requirements.
-
• Therefore, there seemed to be no need to run large language models (LLMs) using DNNs to analyze user queries.
-
• It turned out that modifying or adding code to the code of the basic GA was a convenient and effective way to solve special FJSP scheduling problems that incorporated user-specified constraints.
-
• In Figure 8, the dynamic line plot was converted into a contrastive gradient-based saliency map to strengthen the distinguishing effect (Chen et al., Reference Chen, Du, Mumtaz, Zhong and Rauf2025):
$$ {R}_{p_t}=255\bullet {\left(\frac{\frac{p_{t+\Delta t}-{p}_t}{\Delta t}-\underset{s}{\min}\left(\frac{p_{s+\Delta t}-{p}_s}{\Delta t}\right)}{\underset{s}{\max}\left(\frac{p_{s+\Delta t}-{p}_s}{\Delta t}\right)-\underset{s}{\min}\left(\frac{p_{s+\Delta t}-{p}_s}{\Delta t}\right)}\right)}^{\varphi } $$
$$ {G}_{p_t}=255\bullet \left(1-{\left(\frac{\frac{p_{t+\Delta t}-{p}_t}{\Delta t}-\underset{s}{\min}\left(\frac{p_{s+\Delta t}-{p}_s}{\Delta t}\right)}{\underset{s}{\max}\left(\frac{p_{s+\Delta t}-{p}_s}{\Delta t}\right)-\underset{s}{\min}\left(\frac{p_{s+\Delta t}-{p}_s}{\Delta t}\right)}\right)}^{\varphi}\right) $$
$$ {B}_{p_t}=0 $$
where
$ {p}_t $
was the performance/fitness of population t; Δt = 175 and φ = 0.25. The result is shown in Figure 12, which told the scheduler that the fitness value has indeed converged after 1300 populations. The optimal fitness was 0.0048, or equivalently
$ {C}_{max}^{\ast }=208 $
(hrs).
-
• Without user-specified constraints, the optimal fitness was 0.0051, or equivalently
$ {C}_{max}^{\ast }=195 $
(hrs). However, it took 3300 population for the GA evolution process to converge. -
• Obviously, although more user-specified constraints made the optimal solution worse, it also shrank the feasible solution space, thereby accelerating the search for the optimal solution.
-
• According to the experimental results, the contribution/advantages of this study can be verified as follows. First, the established GenAI system could only parse user requests related to flexible job shop scheduling purposes (see Table 7), showing its effectiveness as a dedicated system. A review of relevant literature and reports also confirmed that it was the first of its kind. In addition, after schedulers inputted their requirements for scheduling goals and constraints in natural language, the corresponding MP model and GA program code to solve the MP problem were automatically generated (as shown in Figures 6 and 7), serving the need for GenAI. Schedulers did not perform any manual processing, including pre-training of the GPT system. The scheduling results were not relayed to any other system (such as project management software) for post-processing, but were directly presented in tabular forms, Gantt charts, and contrastive gradient-based saliency maps (see Figures 8 and 10), highlighting its difference from the existing GenAI applications (see Table 1).
-
• A management implication of the experimental results is that every worker simply inputted his/her scheduling requirements in natural language, and then the MP model as well as the GA code were automatically formulated and generated to complete the scheduling task. In this way, even if a worker did not have background knowledge in MP or AI, the worker could still accomplish the optimization of the scheduling goal by himself/herself, which provided a lot of flexibility in selecting the responsible worker, or in other words, any worker could be assigned as the scheduler. In addition, some planning tasks in manufacturing systems also involve the formulation and solution of optimization problems. GAs are one of the popular tools that can assist when the optimal solutions to these optimization problems are difficult to find using existing software packages, similar to the situation faced by schedulers in this study. Therefore, there is no doubt that the proposed methodology can also be applied to solve such problems.
-
• The techniques used in the GenAI job scheduling system, ETFN representation, MP model formula, and customized GA coding, are all general techniques, so the proposed methodology can be directly applied to other types of job scheduling problems, such as flow shops, permutation flow shops, and others.
-
• The established GenAI job scheduling system aimed to help schedulers formulate and solve flexible shop scheduling problems that met their needs, rather than designing a new algorithm with better scheduling performance than existing heuristic or meta-heuristic algorithms. Therefore, flexible job shop scheduling problems from references have been selected as diverse as possible to validate the effectiveness of the GenAI job scheduling system. In contrast, existing benchmark problems (e.g., Brandimarte) were not adopted because these problems were similar despite varying sizes and therefore were not diverse. The validation results are summarized in Table 9. Obviously, for these diverse flexible job shop scheduling problems, the GenAI job scheduling system successfully achieved scheduling performances that were quite close to those of the original studies. Moreover, the schedulers did not need to know how to formulate and solve the relevant optimization problems.
-
• We also tried to apply two general GenAI systems, ChatGPT and DeepSeek, to solve a flexible job scheduling problem with six machines and three product types, i.e.,
$ FJ6//{C}_{max} $
. The results showed that existing general GenAI systems, such as ChatGPT and DeepSeek, also allowed customized scheduling requirements to be input in natural language, but the operation process was lengthy and often required repeated corrections (see Figure 13). In addition, the scheduling results generated by the existing general GenAI systems were often incorrect or unoptimized (see Table 10). -
• Although GA was used in the GenAI job scheduling system, in fact other bio-inspired algorithms, such as ant colony optimization (ACO), spider monkey optimization (SMO), artificial bee colony (ABC), and so forth were also applicable. The GenAI job scheduling system was not tied to a specific bio-inspired algorithm for solving the MP problem.
Figure 10. Parametric analysis results of the crossover rate.
Figure 11. Convergence process when the mutation rate was set to 0.2.
Figure 12. Contrastive gradient-based saliency map for the case.
Table 9. Validation results
Figure 13. Application of an existing general GenAI system (ChatGPT).
Table 10. Comparison of scheduling performances of various GenAI systems
Conclusions
GenAI can be used to address the shortcomings of existing job scheduling systems and provide schedulers with greater flexibility, but this has rarely been discussed in the past. To fill this gap, this study builds a GenAI job scheduling system that is hosted locally to avoid possible leakage of order or recipe-related information through uploading to the cloud-based GenAI service. In the GenAI job scheduling system, a user interface is designed for users to input their queries in natural language. A user’s query is then analyzed to extract his/her requirements related to the scheduling task, thereby building the ETFN of the scheduling problem. The MP model corresponding to the ETFN is formulated and solved with the help of a customized GA, thereby renewing invalid codes or add new codes to the program of the basic GA application.
The effectiveness of the GenAI job scheduling system has been tested in a flexible job shop case. According to the experimental results, the following conclusions were drawn:
-
• User queries to the GenAI job scheduling system were more consistent and simpler than those to other general GenAI systems, making them easier and more efficient to analyze and extract users’ requirements. In the experiment, after a short period of learning, the accuracy of the analysis quickly improved.
-
• The main steps of the GA application (selection, crossover, and mutation) were not altered by the requirements of most users, making them easily embedded in the program for the basic GA application.
-
• It appeared that as the user specified more constraints, the number of populations required to achieve the optimal fitness decreased, apparently due to a shrinking of the feasible solution region. Correspondingly, the scheduling performance deteriorated accordingly.
In the experiment, the user interface, customized GA program, output reports or charts were all created using MATLAB. In order to promote the further application of the proposed methodology, it is a way to go to construct the GenAI job scheduling system using open languages such as Python. However, neither MATLAB nor Python is ideal in terms of the presentation of the scheduling results, compared with professional software like Microsoft Project. Additionally, other bio-inspired algorithms can be used for the same purpose. Although schedulers, do not care which bio-inspired algorithm is used for scheduling, as long as the scheduling performance is good enough. Therefore, it is feasible to apply multiple bio-inspired algorithms simultaneously to find the best scheduling results. Furthermore, in this study, the generation of ETFN is achieved by extracting keywords to form keyword combinations that have been defined in the system dictionary. An extension based on this study is to feed the number, type, and position of each keyword to an artificial neural network (ANN) or a deep neural network (DNN) for processing to generate the type of each field in the ETFN. These constitute some directions for future research.
Data availability statement
Data will be made available on request.
Author contribution
All authors contributed equally to the writing of this paper.
Funding statement
This research received no external funding.
Competing interests
The authors declare none.
Appendix A
A FJm/
$ {R}_j $
,
$ {A}_i $
,
$ {s}_{jk} $
,
$ {X}_{jki} $
/Cmax problem can be formulated as a mixed integer-nonlinear programming (MINLP) model in the following:
$$ \operatorname{Min}\hskip0.24em Z={C}_{\mathrm{max}} $$
s.t.
$$ {C}_{\mathrm{max}}\ge {C}_j;j=1\sim n $$
$$ {C}_j={c}_{jK};j=1\sim n $$
$$ {c}_{jk}={s}_{jk}+\sum \limits_{i=1}^m{X}_{jk i}{p}_{jk i};j=1\sim n,k=1\sim K $$
$$ \sum \limits_{i=1}^m{X}_{jki}=1;j=1\sim n,k=1\sim K $$
$$ {s}_{jk_2}\ge {c}_{jk_1}\forall 1\le {k}_1<{k}_2\le K;j=1\sim n $$
$$ {s}_{j1}\ge {R}_j;j=1\sim n $$
$$ \begin{array}{c}{s}_{j_2{k}_2}\ge \left(\sum \limits_{i=1}^m{X}_{j_1{k}_1i}{X}_{j_2{k}_2i}\right){Y}_{j_1{k}_1{j}_2{k}_2}{c}_{j_1{k}_1};\forall 1\le {k}_1,{k}_2\le K;1\le {j}_1,\\ {}{j}_2\le n;{j}_1\ne {j}_2\end{array} $$
$$ {Y}_{j_1{k}_1{j}_2{k}_2}+{Y}_{j_2{k}_2{j}_1{k}_1}=1;\forall 1\le {k}_1,{k}_2\le K;1\le {j}_1,{j}_2\le n;{j}_1\ne {j}_2 $$
$$ {X}_{jki},{Y}_{j_1{k}_1{j}_2{k}_2}\in \left\{0,1\right\};\forall 1\le k,{k}_1,{k}_2\le K;1\le j,{j}_1,{j}_2\le n;{j}_1\ne {j}_2;i=1\sim m $$
Other variables ∈ R +.
where
$ {s}_{jk} $
and
$ {c}_{jk} $
denote the start time and completion time of the k-th operation of job j.
$ {X}_{jki}=1 $
if the k-th operation of job j is performed on machine i;
$ {X}_{jki}=0 $
if otherwise.
$ {Y}_{j_1{k}_1{j}_2{k}_2}=1 $
if the
$ {k}_1 $
-th operation of job
$ {j}_1 $
precedes the
$ {k}_2 $
-th operation of job
$ {j}_2 $
on the same machine;
$ {Y}_{j_1{k}_1{j}_2{k}_2}=0 $
if otherwise. As mentioned previously, the default objective function is to minimize the makespan, calculated according to Constraints (A2)–(A4). Constraint (A5) is to ensure that each operation can be performed on only a single machine. Constraints (A6)–(A7) mean that an operation can start only when the job has been released to the flexible job shop and the previous operation has been completed. Constraints (A8) and (A9) is to sequence any two operations on the same machine.
Appendix B
Figure B1. Pseudo code for the customized GA application.
Open access
