Lean buffering in serial production lines with nonidentical exponential machines

Lean buffering is the smallest buffer capacity, which is necessary and sufficient to ensure the desired production rate of a manufacturing system. Literature offers methods for designing lean buffering in production systems with identical machines. The current paper extends these methods to serial production lines with nonidentical machines, assuming that they obey the exponential reliability model. For two-machine lines, exact formulas for lean buffering are derived, while for longer lines estimates are obtained. These results can be useful for production line designers and production managers to maintain the required production rate with the smallest possible inventories. Note to Practitioners-In production systems with unreliable machines, operation with no-buffers (i.e., JIT) leads to low throughput. Very large buffers lead to high throughput but undesirable quality and economics properties. So, which level of buffering is good? This is the question addressed in this paper. The good level of buffering is addressed in terms of line efficiency, i.e., the fraction of the maximum of the throughput, which is acceptable for the system. For example, assume that the desired line efficiency is 0.9 (i.e., 90% of the maximum throughput is viewed as satisfactory). Under such an assumption, this paper offers methods for calculating the smallest (i.e., lean) level of buffering, which guarantees the desired throughput, provided that uptime and downtime of the machines are distributed exponentially with arbitrary mean time to failure and mean time to repair.