Buffer Capacity

Most of the studies on parallel merging assembly lines (also known as fork-join or split-merge) have focused on line balancing. For a comprehensive literature review of merging line balancing methods, see Battaïa and Dolgui, Sivasankaran and Shahabudeen and Weiss et al.. Other studies, however, focused on merging lines with uneven buffer capacities. Merging line studies can be divided into two broad categories: reliable and unreliable merging lines. Below is a review of pertaining works.

Literature on uneven buffer allocation in reliable merging lines is sparse. Powell and Pyke presented general strategies on the efficient placement of buffers in unbalanced assembly systems with random processing times. Leung and Lai provided more guidance by discussing strategies on how to install parallel workstations for improved cycle times, compared to simple assembly systems. They concluded that off-line parallel systems are superior in reducing buffer requirements and reducing sensitivity to imbalance, compared to on-line and tunnel-gated systems. Applying interdisciplinary techniques to improve assembly systems, Bulgak used a genetic algorithm and simulation to yield maximum output, while optimising the buffers in merge and split unpaced assembly systems.

More recently, Shaaban et al. assessed the performance of unbalanced, reliable, unpaced merging lines with asymmetric buffer storage sizes. Lines were simulated with varying line lengths, mean buffer capacities and uneven buffer allocation configurations. They found that higher throughput (TR) and lower average buffer level (ABL) (as compared to an equivalent balanced merging line) were obtained when total available buffer capacity is allocated as evenly as possible and with a higher buffer capacity concentration towards the end of the line, respectively.

For unreliable merging lines, Gershwin first analysed a class of unreliable assembly/disassembly tree-network systems in which buffers are finite and machines perform operations when none of their upstream buffers are empty and none of their downstream buffers are full. An approximate decomposition method to estimate TR was presented at that time. Bhatnagar and Chandra later focused on three-station assembly systems, and used simulation to study the effect of variability due to unreliable stations and imperfect yields on assembly systems. More significant TR improvements were found from increasing the production rate of individual stations than from increasing the size of buffers. Subsequently, Jeong and Kim investigated buffered production systems with feeder stations merging into an assembly station. They developed heuristics to determine the line configuration which would bring a desired TR at a minimal cost with finite buffer sizes, and assumed exponential times to failure and repair, as well as exponential processing times.

Tan studied an unreliable merging system comprised of two stations in parallel with unbalanced processing rates feeding a common merge station. A decomposition method for determining the production rate and expected buffer contents was developed. Yuan and Liu focused on an unreliable assembly system where different types of components are processed by two separate work centres before merging into an assembly station with random breakdowns. They developed formulas for the probabilities of blocking, starvation, stockout, and station availability in steady state, and also obtained the probability distributions of blocking and failure times.

Liu and Li contributed to work on unreliable systems by proposing a decomposition algorithm to estimate the throughput of split and merge unreliable manufacturing systems with two parallel lines. They also presented three structural properties of split and merge manufacturing systems: conservation of flow, monotonicity (higher machine reliability and/or buffer size result in higher throughput) and reversibility (symmetrical split and merge lines are equivalent). More recently, Jia et al. studied the transient behaviour of assembly systems with merging serial lines, comprised of Bernoulli machines (subject to failure) with finite buffers. They derived formulas to efficiently measure TR, work-in-process, and probability that any station will be blocked or starved, and also developed an analytical method for dealing with larger and more complex assembly systems, with multiple feeder lines and merge stations. Following this, Yegul et al. studied the optimal configuration of a real complex manufacturing system using a simulation-optimisation approach. Their study attempted to maximise the profit of the manufacturing system by optimising buffer sizes, number and speed of parallel machines, and allocation of workers to some of the system's stations. They considered stochastic setup times, processing times, time-to-failure and time-to-repair, as well as costs associated with labour, machine investments and inventory. They suggested that due to the very specific problem considered in their study, the allocation of machines and workers in a specific subset of stations were the most important factors in the profit function of the system.

Current work by Romero-Silva and Shaaban has suggested that an unbalanced assignment of buffer capacities along the line, i.e. concentrating buffer towards the central or final stations of the line, results in higher throughput for unreliable lines, while the throughput of reliable lines is better served with a balanced assignment of buffers. However, they did not assess the impact of different degrees of machine efficiency (ε) and different values of MTTF and MTTR on the performance of a merging line, despite the fact that the influence of different production line design factors (e.g. buffer capacity) is highly dependent on ε, MTTF and MTTR. Moreover, they did not investigate the profit-related trade-off between investing in additional buffer capacity to generate more throughput and the cost of that investment.

The above review reflects a history of merging line research that has mostly focused either on developing line balancing and mathematical optimisation methods, or on developing of analytical and approximation methods. To the best of our knowledge, there are no studies which integratively study the influence of both buffer allocation patterns and degrees of unreliability on the performance of TR and ABL in merging lines, considering inventory holding costs and buffer capacity investment costs. Therefore, the performance of unreliable merging lines with uneven buffer sizes is examined here to bridge this gap and contribute to both theory and practice. This study applies simulation and statistical analysis to assess if uneven buffer size allocation can generate better results than those obtained from balanced buffer allocation along the line, considering different degress of unreliability.