Serial production lines with waiting time limits: Bernoulli reliability model

Production systems with waiting time constraints are frequently encountered in semiconductor, automotive, battery, food, and many other manufacturing industries. Under the waiting time constraints, the residence time of in-process inventories is constrained by a predetermined time limit. A part exceeding the maximal time limit has to be inspected for quality assurance and it is subject to be scrapped with a certain probability. In this paper, performance evaluation of Bernoulli serial lines with waiting time limits is studied. Analytical formulas are derived to predict the system performance of two-machine lines in steady state. For longer lines, direct analysis is no longer viable due to high complexity, thus an aggregation-based iterative procedure is introduced. Based on extensive numerical studies, the convergence of the procedure can be observed and high accuracy in performance estimation is achieved. In addition, to design such lines, an efficient procedure for near optimal buffer assignment to maximize production rate is also proposed. Analogously, we first propose an exact algorithm for two-machine lines and then extend it to a recursive procedure for longer lines. We then numerically verify that the procedure provides a near optimal solution within a very short computation time. Finally, the impacts of relaxing waiting time constraints on line performance and buffer design are discussed, and operational strategies to achieve better performance are also presented.