Timed marked graphs, a special class of Petri nets, are extensively used to model and analyze cyclic manufacturing systems. Weighted marked graphs are convenient to model automated production systems, such as robotic work cells or embedded systems, and reduce the size of the model. The main problem for designers is to find a tradeoff between minimizing the cost of the resources and maximizing the system's throughput (also called cycle time). It is possible to apply analytical techniques for the cycle time optimization problem of such systems. The problem consists in finding an initial marking to minimize the cycle time (i.e., maximize the throughput) while the weighted sum of tokens in places is less than or equal to a given value. We transform a weighted marked graph into several equivalent marked graphs and formulate a mixed integer linear programming model to solve this problem. Moreover, several techniques are proposed to reduce the complexity of the proposed method. We show that the proposed method can always find an optimal solution

Mobile robots are extensively used to complete repetitive operations in industrial areas such as intelligent transportation, logistics, and manufacturing systems. This paper addresses the path planning problem of multi-type robot systems with time windows based on timed colored Petri nets. The tasks to be completed are divided into three different types: common, exclusive and collaborative. An analytical approach to plan a group of different types of mobile robots is developed to ensure that some specific robots will visit task regions within given time windows. First, a multi-type robot system and its environment are modeled by a timed colored Petri net. Then, some methods are developed to convert the task requirements that contain logic constraints and time windows into linear constraints. Based on integer linear programming techniques, a planning approach is proposed to minimize the total cost (i.e., total travel distance) of the system. Finally, simulation studies are investigated to show the effectiveness of the developed approach.

According to the characteristics of flexible job shop scheduling problems, a dual-resource constrained flexible job shop scheduling problem (DRCFJSP) model with machine and worker constraints is constructed such that the makespan and total delay are minimized. An improved African vulture optimization algorithm (IAVOA) is developed to solve the presented problem. A three-segment representation is proposed to code the problem, including the operation sequence, machine allocation, and worker selection. In addition, the African vulture optimization algorithm (AVOA) is improved in three aspects: First, in order to enhance the quality of the initial population, three types of rules are employed in population initialization. Second, a memory bank is constructed to retain the optimal individuals in each iteration to increase the calculation precision. Finally, a neighborhood search operation is designed for individuals with certain conditions such that the makespan and total delay are further optimized. The simulation results indicate that the qualities of the solutions obtained by the developed approach are superior to those of the existing approaches.

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