Key Takeaways & Executive Findings
- •• FJSP_PT jointly optimizes machine processing and transportation vehicle scheduling, capturing real-world flexible manufacturing logistics. • The review provides a systematic taxonomy of solution approaches: exact algorithms, heuristics, metaheuristics, and swarm intelligence algorithms. • Statistical analysis of literature up to 2023 reveals increasing research interest and diverse algorithmic developments for FJSP_PT. • The coupling of processing and transportation stages remains a central challenge, driving future research toward more efficient integrated scheduling methods.
Abstract
The flexible job shop scheduling problem for processing machines and transportation vehicles (FJSP_PT) has garnered significant attention from academia and industry. Due to the inclusion of transportation vehicle scheduling in the scheduling problem of flexible manufacturing systems, solving FJSP_PT becomes more challenging and significantly more practically relevant compared to the flexible job shop scheduling problem. We summarize the assumptions, constraints, objective functions, and benchmarks of FJSP_PT. Then, statistical analysis is conducted on the literature up to 2023, including journals, number of articles published each year, and solution algorithms. We analyze recent literature on FJSP_PT, categorizing it based on algorithms into exact algorithms, heuristic algorithms, meta-heuristic algorithms, and swarm intelligence based algorithms. Finally, the research trends and challenges faced by FJSP_PT are summarized.
1. Introduction
With the upgrading of the consumption structure, the demand of markets and consumers for personalization and customization is increasing. Many countries are trying to promote the reform of manufacturing industries, such as Industry 4.0 in Germany and Made in China 2025. The traditional production mode is being changed to a more flexible and intelligent manufacturing mode to accelerate the construction of manufacturing power. With the widespread application of transportation equipment like cranes and automated guided vehicles (AGVs) in the flexible manufacturing system (FMS), the logistics procedures transporting jobs between machines have a significant impact on production efficiency and have been considered into the job shop scheduling problem. Compared with other traditional logistics devices like conveyor belts, transportation vehicles can accomplish the logistics tasks of processing jobs in a more efficient and flexible manner.
From a theoretical standpoint, as an extension of the flexible job shop scheduling problem (FJSP), the flexible job shop scheduling problem for processing machines and transportation vehicles (FJSP_PT) is highly complex. In the production flow of a job, the transportation stages and the processing stages occur alternately. Correspondingly, the transportation time and the processing time together constitute the flow time of a job in FMS. In the past, most research on the traditional scheduling problem in FMS focused on the processing time and ignored the transportation time. However, flexible transportation procedures are playing more and more important roles in modern manufacturing systems. Due to the coupling between processing and transportation stages, the increase in types of scheduling entities makes solving FJSP_PT more difficult. From a practical perspective, FJSP_PT is widely found in manufacturing industries characterized by product diversification and small batches, such as the hardware and container terminal industries. Therefore, FJSP_PT represents an optimization problem that is both practically significant and theoretically intricate.
An FJSP_PT can be described as follows: In an FMS such as the one depicted in Fig. 2, there exists an order comprising NJ jobs. Each job has multiple operations to be processed. The FMS requires scheduling NM machines and a finite number, NA, of vehicles to effectively execute both the processing and transporting tasks for all jobs, optimizing the makespan or other related objectives. Throughout production, the transportation and processing procedures for each job will be carried out alternately. Consequently, the transportation time and processing time collectively impact the job completion duration. Therefore, FJSP_PT cannot be readily decoupled into FJSP or logistics scheduling problems. The flexibility in this problem is evident in the following areas:
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Bin Xin, Sai Lu, Qing Wang, Fang Deng (2025). A review of flexible job shop scheduling problems considering transportation vehicles. Frontiers of Information Technology & Electronic Engineering. https://doi.org/10.1631/FITEE_2300795
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Frequently Asked Questions
What is FJSP_PT in manufacturing scheduling?
FJSP_PT stands for the flexible job shop scheduling problem for processing machines and transportation vehicles. It extends the classical flexible job shop scheduling problem by jointly optimizing machine processing and transportation vehicle scheduling in flexible manufacturing systems.
Why is transportation vehicle scheduling important in flexible job shop scheduling?
In flexible manufacturing systems, jobs alternate between processing and transportation stages. Transportation time directly affects job flow time and overall makespan, so neglecting transportation can lead to suboptimal production schedules.
What solution algorithms are reviewed for FJSP_PT?
The review categorizes solution algorithms into exact algorithms, heuristic algorithms, meta-heuristic algorithms, and swarm intelligence based algorithms, and analyzes recent literature on these approaches.
What are the main challenges of solving FJSP_PT?
The coupling between processing and transportation stages, the increase in the number of scheduling entities, and the need to handle realistic manufacturing constraints make FJSP_PT highly complex and computationally challenging.
What future research directions are highlighted for FJSP_PT?
The authors summarize research trends and challenges, pointing toward more efficient integrated scheduling methods, advanced metaheuristics, and the incorporation of real-world manufacturing constraints.
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