## 1 Introduction
To ensure alignment with practical conditions, multiple scenarios with different shop sizes have been designed, each with limited AGV and charger resources. In addition, this study introduces the \"deterioration\" effect of AGVs: as the battery level decreases, the transportation efficiency declines, resulting in prolonged handling time. This assumption is based on engineering observations of AGV operation in industrial scenarios, where AGVs typically reduce their operating speed at lower battery levels to conserve energy or ensure operational safety. Although comprehensive empirical modeling data are currently lacking, the incorporation of this effect enhances the practical applicability of the proposed scheduling model and reflects the actual operating characteristics of AGVs. Future research will focus on collecting empirical data to further validate and optimize the model. Heuristic algorithms [22; 23; 24] and Deep Reinforcement Learning (DRL) approaches [17; 25] are commonly used to solve collaborative scheduling problems in flexible job shops. However, the problem addressed in this paper incorporates several additional decision dimensions--such as charging constraints--compared with traditional models, making it a high-dimensional scheduling problem. DRL, as a fully reactive scheduling method, leverages data to learn the correlation between data distributions and decision behaviors, and has demonstrated superior optimization performance in solving such high-dimensional and complex scheduling tasks [17; 26; 27]. Among DRL methods, PPO and its variants have gained significant attention in recent years for their robustness, stability, and ease of implementation [28; 29; 30; 31; 32]. Accordingly, this study develops a customized PPO-based DRL algorithm named CRGPPO-TKL to solve the FjSPLSP-LTCC. The algorithm samples candidate actions and computes candidate probability ratios to better evaluate policy divergence. Furthermore, it introduces a target KL divergence mechanism to dynamically adjust the clipping range, thus maintaining a balance between exploration and policy stability. In summary, the main contributions of this study are as follows:  
1. A comprehensive modeling framework for collaborative production-logistics scheduling in flexible job shops is proposed, which incorporates limited AGV resources, AGV charging constraints, and the deterioration effect between battery level and transportation speed, thereby enhancing the practical applicability of the scheduling model. 2. Multiple flexible job shop scenarios with varying workshop scales are designed, and a systematic analysis is conducted to determine the optimal AGV configuration for each layout, providing valuable guidance for resource allocation in practical applications. 3. An improved PPO algorithm--CRGPPO-TKL--is developed, which enhances action evaluation through candidate probability ratio sampling and dynamically adjusts the clipping range based on the target KL divergence, thereby improving learning stability and performance in solving complex collaborative scheduling problems. The remainder of this paper is organized as follows: Section 2 reviews related literature on production-logistics collaborative scheduling in flexible job shops. Section 3 defines the proposed FjSPLSP-LTCC problem. Section 4 describes the developed DRL framework. Section 5 presents experimental results and analysis. Finally, Section 6 concludes the paper and outlines future research directions.