Abstract Serial production lines consisting of heterogeneous workstations and limited buffers represent a principal configuration for mass production manufacturing systems. This paper introduces the Traffic Ratio Model (TRM), a new Markovian model developed, tested, and applied to these manufacturing lines. The TRM provides an efficient analytical method for calculating the state probabilities of all workstations, for exponential arrival and process times. When tested against well-known established methods, the TRM meets or surpasses their accuracy; specifically, throughput calculation results agree with discrete-event simulation within 1%. Furthermore, the TRM offers a novel formulation for the accurate calculation of work-in-process inventories directly from state probabilities—a capability absent in previous models. Two significant analytical findings are deduced from the model: first, the necessary condition for maximum throughput (traffic ratio equal to unity); and second, a novel explanation and calculation of the “bowl phenomenon” of optimal work allocation in serial manufacturing lines. Subsequently, with minor modification, the model is extended to unreliable lines with operation-independent failures. Despite the known difficulty of modeling unreliable systems, the TRM remains applicable even for long lines, yielding useful approximate results. Finally, the TRM is used to resolve several practical industrial cases for the design and improvement of manufacturing lines. The TRM represents a dependable analytical alternative to discrete-event simulation for exponential times, facilitating the direct calculation of line performance, optimal work allocation, and the efficient identification of bottlenecks for continuous improvement.
Roque Calvo (Mon,) studied this question.