Accompanying the unceasing progress of integrated circuit manufacturing technology, the mainstream production mode of current semiconductor wafer fabrication is featured with multi-variety, small batch, and individual customization, which poses a huge challenge to the scheduling of cluster tools with single-wafer-type fabrication. Concurrent processing multiple wafer types in cluster tools, as a novel production pattern, has drawn increasing attention from industry to academia, whereas the corresponding research remains insufficient. This paper investigates the scheduling problems of dual-arm cluster tools with multiple wafer types and residency time constraints. To pursue an easy-to-implement cyclic operation under diverse flow patterns, we develop a novel robot activity strategy called multiplex swap sequence. In the light of the virtual module technology, the workloads that stem from bottleneck process steps and asymmetrical process configuration are balanced satisfactorily. Moreover, several sufficient and necessary conditions with closed-form expressions are obtained for checking the system's schedulability. Finally, efficient algorithms with polynomial complexity are developed to find the periodic scheduling, and its practicability and availability are demonstrated by the offered illustrative examples.

To advance energy conservation and emissions reduction in urban logistics systems, this study focuses on the green vehicle routing problems with time windows (GVRPTWs), which remains underexplored in balancing environmental and service quality objectives. We propose a comprehensive multi-objective optimization framework that addresses this gap by simultaneously minimizing total distribution costs and carbon emissions while maximizing customer satisfaction, quantified based on the vehicle’s arrival time at the customer location. The rationale for adopting this tri-objective formulation lies in its ability to reflect real-world trade-offs between economic efficiency, environmental performance, and service level, which are often considered in isolation in previous studies. To tackle this complex problem, we develop an improved Non-Dominated Sorting Genetic Algorithm III (NSGA-III) that incorporates three key enhancements: (1) an integer-encoded initialization method to enhance solution feasibility, (2) a refined selection strategy utilizing crowding distance to maintain population diversity, and (3) an embedded 2-opt local search operator to prevent premature convergence and avoid local optima. Comprehensive validation experiments using Solomon’s benchmark instances and a real-world case demonstrate that the presented algorithm consistently outperforms several state-of-the-art multi-objective optimization methods across key performance metrics. These results highlight the effectiveness and practical relevance of our approach in advancing energy-efficient, low-emission, and customer-centric urban logistics systems.

In wafer fabrication, it is imperative to minimize the transient process of cluster tools for the sake of on-demand and preventive maintenance. Due to the trend of multi-type and small-batch production, transient processes appear more and more frequently. Thus, the optimization problems of transient processes have gained increasing attention from both industry and academia. The requirement for wafer revisiting tend to complicate this problem significantly. However, only a few studies take such a challenge for cluster tools with wafer revisiting. This paper focuses on the schedule optimization of transient processes for dual-arm cluster tools with wafer revisiting. To accelerate transient processes, including both start-up and close-down ones, we adopt a program evaluation and review technique to analyze and harness a cluster tool's state evolution. We then propose computationally efficient algorithms to speed up transient processes. Finally, we provide illustrative examples to show their applications and validate their effectiveness.

As the wafer size increases and consumption demand changes, wafer fabrication mode tends to be multi-type and small-batch production. However, most of existing scheduling methods focus on the control problems of single wafer type, which is not suitable for the scheduling of multiple wafer types. With wafer residency time constraints considered, this paper concentrates on the scheduling and control problems of single-armed cluster tools with multi-type wafers and shared PMs. To balance workloads among processing steps, a virtual processing modules technology is adopted. According to the modified backward scheduling strategy, analytic expressions for testing schedulabilities are derived. Finally, a periodic scheduling algorithm for steady-state is presented. Meanwhile, illustrative examples are given to verify the feasibility and availability of the proposed algorithm.

To describe deadlocks occurring in general nets, some characterizations have been proposed to establish a relationship between liveness and siphons. Among them, the most prominent characterizations are max-controlled siphons and deadly marked siphons. Nevertheless, the former is only a sufficient condition while the latter may lead to some unreasonable operations, i.e., modified markings are necessary if applicable. In this paper, we elaborately discuss the related concepts of deadly marked siphons when liveness analysis is conducted. Subsequently, a new siphon-based characterization of liveness, i.e., undermarked siphons that explain liveness in the original markings, is proposed to demonstrate its more general applicability. Finally, a necessary and sufficient condition is developed to show the relationship between the liveness and undermarked siphons in general nets.