Bernoulli serial lines with batching machines: Performance analysis and system-theoretic properties

Abstract

Aiming at Bernoulli serial lines with batching machines and finite buffers, this study develops analytical methods for performance analysis and system-theoretic properties. Batching machines can process several jobs simultaneously as a batch, as long as the number of jobs in a batch does not exceed the machine’s batch capacity. The batch capacities of all machines are not necessarily equal. Batching machines bring about a new characteristic of state transitions depending on batch capacities and machine states. For two-machine lines, the joint impacts of batching machines on state transitions are analyzed. Theoretically, the state transition rules are revealed. Based on the state transition rules, this study proposes a hierarchical state transition diagram, proves the ergodicity condition, and derives analytical formulas to evaluate the performance measures. Then, for multi-machine lines, this study develops a computationally efficient aggregation method with high accuracy. Furthermore, the impacts of system parameters, including machine efficiency pattern, batch capacity pattern, batch capacity mismatch, and system size, on the accuracy are qualitatively analyzed. Finally, this study investigates the reversibility and monotonicity properties. These analytical methods and results help production managers to scientifically evaluate, accurately predict, and continuously improve Bernoulli serial lines with batching machines.