Q2. What are the future works mentioned in the paper "Serial production line performance under random variation_ dealing with the ‘law of variability’" ?
Addressing future research directions and opportunities, since most previous studies on simple serial lines focused on the single effects caused by processing time variance in the resulting mean throughput, mean flow time and variance of inter-departure time measures, more efforts are needed to study the impact of specific and various combined factors on particular performance measures. Therefore, further research considering more realistic probability distributions is needed as it has been previously shown that queueing network models are highly sensitive to the choice of the probability distribution modelling input distributions [ 37,39,110,111 ]. In terms of measure development, another worthy research direction would be to extend proposed work by Delp et al. [ 76 ] and Wu et al. [ 56 ], to directly assess the variability of a production line, or more precisely, the impact that the many variability factors ( e. g., variance, skewness and auto-correlation of inter-arrival and processing times, and unreliability, etc. ) have on the overall performance of the production line. A similar reference compilation on more complex production line results, such as assembly lines with merging materials [ 113,118 ], setup times [ 119,120 ], quality concerns [ 121 ], or multiple-product serial lines [ 122–124 ] could be useful to better understand the effects of variability in different production environments and further extend the reach of the ‘ Law of Variability ’.
Q3. What is the widely accepted conclusion about serial line design?
One of the most widely accepted conclusions about serial line design is that balanced stochastic serial lines, if comparing two saturated lines with the same assumed TH̄ , perform worse than unbalanced lines [25,59], which have a protective capacity to deal with processing time uncertainty.
Q4. What fields have comprehensively investigated the behaviour of serial production lines under variability?
The fields of Queueing Theory and Production Management have comprehensively investigated the behaviour of serial production lines under variability.
Q5. What is the effect of MTTR on Var(TH) in unbuffered balanced?
On the other hand, longer lines with lower MTTR values, by having higher TH̄ values, have lesser constraints on the possible values that the throughput can take, and therefore, lower MTTR values will result in higher Var(TH).
Q6. What did Hillier and Boling and Conway et al. show?
Hillier and Boling [64] and Conway et al. [26] showed that longer saturated lines with uniform and exponential processing times and smaller buffers reduced TH̄ in balanced saturated lines, because longer lines and smaller buffers resulted in more station blocking and starving.
Q7. Why is TH important for a company?
In Theory of Constraints terms, TH is important for a company because it is the rate at which a factory produces money per time unit.
Q8. What is the effect of the buffer size on throughput?
They demonstrated that for saturated lines with n=3, exponential processing times with a mean processing rate equal to 1 and a significantly big buffer size per station equal to 100, TH̄ of the production line was less than 1 (i.e. 0.9866), indicating that, even when the buffer size is not a significant constraint on the system, throughput is affected by the processing times’ variance.
Q9. How many buffers should be placed along the whole serial line?
When considering the amount of B placed in front of stations in balanced saturated serial lines with limited buffer capacity, Lambrecht and Segaert [57] suggested that if possible, buffers should be placedevenly along the whole serial line.
Q10. What is the significance of the arrival effects of a single-resource line?
Since it has been shown that the departure process of single-resource lines is not a renewal process [44,45] (unless the distribution of inter-arrival and service times is exponential [46]), this suggests the importance auto-correlated arrival effects.
Q11. How did Hillier and Boling show that the variance of processing times increased?
They also showed that by reducing the variance of processing times, overall TH̄ increased, without reaching TH̄ equal to 1, the value expected for deterministic serial lines.
Q12. Why is the effect not present in shorter lines?
This effect is not present in shorter lines because the throughput is not as constrained as in longer lines, due to the smaller interference among the stations.
Q13. What are the three complementary measures used to assess the performance of simple serial lines?
This subsection defines three complementary measures that have most commonly been used to assess the performance of simple serial lines: throughput, inter-departure times and flow times.
Q14. What is the widely studied factor regarding variability in saturated serial lines?
Perhaps one of the most widely studied factors regarding variability has been the topic of machine unreliability in saturated serial lines.