Analyzing throughput is very important for the design, optimization, and management of production lines. In this paper, we present an efficient throughput analysis approach for production lines with merging, splitting, and recirculating topologies. In particular, we define a decomposition regulation based on queue modules for the decomposition of the various topologies, and we improve an iterative approximation method for calculating and iterating the queue module state probabilities until the throughput of the production line is obtained. To decrease the computation time and automate the calculation process of the queue module state probabilities, we build a queue module database that includes the solution equations of common queue module state probabilities. The numerical examples show that our approach calculates the throughput of production lines with merging, splitting, and recirculating topologies with high accuracy (≥90%) and efficiency (completed in ten min). Our contribution is an efficient throughput evaluation methodology that can be used to rapidly estimate the performance and the cost of production lines with various topologies in the conceptual design phase of production lines in the industry. INDEX TERMS Approximation method, production engineering, queueing analysis, topology, throughput. The associate editor coordinating the review of this manuscript and approving it for publication was Huaqing Li. FIGURE 1. Recirculating production line that includes merging, splitting, and recirculating topologies simultaneously.

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An analytic flow design algorithm for an automated distribution center with multiple shipping areas is presented. The main elements of the analytic flow design are the number of devices and the volumes of product flow between the devices. In the design of an automated distribution center, it is necessary to satisfy the demand throughput while minimizing construction costs. In the conventional design process, system engineers utilize experimental and intuitional approaches. However, conventional approaches are time-consuming and the design outcome is dependent on the skill of the designer. Therefore, a theoretical design algorithm is needed. We propose an analytic flow design algorithm using a dynamic network flow model and considering time-variable flow volumes according to shipment and storage schedules. To verify the feasibility of the proposed method, we perform analytic flow design using real data and confirm that the proposed method can yield a feasible analytic flow design in several minutes.

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