Performance of Unreliable Merging Lines with Uneven Buffer Capacity

CIO2018, 009, v1: ’Performance of Unreliable Merging Lines with Uneven Buffer Capacity . . .

12th International Conference on Industrial Engineering and Industrial Management XXII Congreso de Ingeniería de Organización Girona, Spain, July 12-13, 2018

Performance of Unreliable Merging Lines with Uneven Buffer Capacity Allocation Abstract The purpose of this study is to investigate the impact that unevenly allocating buffer capacity has on throughput and average buffer level regarding unreliable lines to better understand the relevant factors in supply chain design. Results show that the best patterns for unreliable merging lines in terms of generating higher throughput rates (TR), as compared to a balanced merging line counterpart, are those where total available buffer capacity is allocated between workstations in either an inverted bowl pattern (i.e. concentrating buffer capacity towards the centre of the line), or a balanced line pattern. In contrast, when considering the trade-off between generating revenue resulting from TR and reducing cost created by average buffer levels (ABL), we found that the balanced pattern was not the best pattern. The best pattern was dependent on the length of the line and on the total buffer capacity as shorter lines with very constrained buffers were best served with an inverted bowl pattern while longer lines had the best results when applying an ascending buffer allocation pattern. Longer lines, in contrast, had the best results regarding the trade-off between TR and ABL, on average, by allocating buffer capacity evenly in one of the parallel lines while applying any other pattern in the remaining parallel line.

Keywords: Unreliable merging lines; uneven buffer allocation; average buffer level; throughput; simulation.

1 Introduction Parallel merging lines with no mechanical pacing are probabilistic mass production queueing systems in series. Stocks of partially finished items are usually transferred to a buffer storage location. Merging lines that are unbalanced with respect to their buffer capacities are an important research and practice topic. Often, technical considerations restrict the amount of space available in the line, thereby making it difficult to allocate total buffer capacity evenly amongst individual buffers.

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Taking into account the fact that significant production is taking place in developing economies, as well as the immense growth in remanufacturing and reverse logistics, this emphasizes the importance of research work on unreliable assembly lines with uneven buffer capacity across industries. In addition, queueing networks with parallel, merging stages are common in a variety of manufacturing systems, as well as in computer networks and supply chains. Furthermore, all merging lines are likely to suffer from adverse performance disturbances in the form of downtime resulting from machine failure. This article, therefore, deals with the twin issues of merging line’s uneven buffer allocation and unreliability. How best to allocate buffer space in order to meet the desired performance objectives contributes value to both research and industry practice, and is a burgeoning area of investigation. It has long been a general belief that balancing an unpaced serial production line so that each workstation completes its task at the same rate as the preceding and subsequent stations and where buffer space is allocated evenly, gives the best performance (Lambrecht and Segaert, 1990). Some research (see for instance Conway et al., 1988), however, indicated that that in view of the fact that real life unpaced assembly lines can never be truly balanced and will certainly suffer breakdown failures, it is of interest to incorporate the facts of uneven buffer size allocation and machine breakdowns into the line design to investigate how best to obtain good performance. It is the aim of this article to present the results of the impact of unbalancing buffer capacity on performance, by simulating unreliable merging lines where buffers of unequal sizes are placed between workstations in a variety of patterns, line lengths and total buffer capacities. The structure of the remainder of this paper is as follows. Following a brief review of the relevant literature, we present the methodology of the study. Subsequent sections discuss the results and the conclusions of this investigation.

2 Literature Review The vast majority of studies on parallel (also known as fork-join, u-shaped, or twosided) merging assembly lines have focused on line balancing (see for example, Akpınar and Bayhan, 2011; Barron, 2015; Purnomo et al., 2013; Sönmez et al., 2017). For a comprehensive literature review of merging line balancing methods, see Battaïa and Dolgui (2013) and Sivasankaran and Shahabudeen (2014). Just a few studies, on the other hand, were done on merging lines with uneven buffer capacities. They 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 (1998) presented general strategies on the efficient placement of buffers in unbalanced assembly systems with random processing times.

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Futamura (2000) studied optimal server allocation to tandem queueing networks with uneven allocation of buffer capacities (BCs), unbalanced mean service times (MTs) and coefficients of variation (CVs). He showed that optimal configurations can be predicted and that there is a general interaction between the CV of the service time distribution and the number of servers at the stations. Most recently, Shaaban et al. (2017) 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. On the other hand, Gershwin (1991) analyzed a class of assembly/disassembly network systems in which machines are unreliable, buffers are finite, and machines perform operations whenever none of their upstream buffers are empty and none of their downstream buffers are full, and the network structure is a tree. An approximate decomposition method to estimate TR was presented. Focusing on three-station assembly systems, Bhatnagar and Chandra (1994) used simulation to study the effect of variability due to unreliable stations and imperfect yields on these systems. Greater TR improvements were found from increasing the production rate of individual stations than from increasing the size of buffers. Jeong and Kim (2000) investigated buffered production systems with feeder stations merging into an assembly station. They developed heuristics to determine the line configuration which would bring about a desired TR at a minimal cost. They assumed exponential times to failure & repair and processing times with finite buffer sizes. Yuan and Liu (2005) studied an unreliable assembly system in which different types of components are processed by two separate work centers before merging to an assembly station with random breakdown. They developed formulas for the probabilities of system state, blocking, starvation, stock-out, and system availability in the steady state. They also obtained the distributions of blocking and failure times. Recently, Jia et al. (2016) studied the transient behavior of assembly systems with merging serial lines, comprised of Bernoulli machines (subject to failure) with finite buffers. Formulas were derived to efficiently measure TR, work-in-process levels, and probability that any one station will be blocked or starved. They developed an analytical method for dealing with larger and more complex assembly systems, with multiple feeder lines and merge stations. We can see from the above review that the focus of merging line research was on the development of line balancing and mathematical optimization methods. To our knowledge, there are no studies on the influence of uneven buffer allocation patterns on TR and ABL in unreliable merging lines.

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The performance of merging lines with uneven buffer sizes is studied here to bridge some of the gaps in this research area. To assess if uneven buffer size allocation can generate better results than those obtained from having a constant buffer capacity level all along the line, this study applies simulation and statistical analysis. In addition, the effect of various design variables (line length, mean buffer capacity and buffer imbalance configuration) is evaluated.

3 Methodology Discrete-Event simulation was viewed as the most appropriate tool for this study because of the severe limitations of mathematical approaches in dealing with more realistic and complex merging lines, typically reported with positively skewed operation times. The Simio 9.147 simulation software (Kelton, Smith and Sturrock, 2014) was used to study the behavior of the unreliable, unbalanced merging line. The merging line’s dependent performance measures used are TR and ABL. Furthermore, we used a representation of the trade-off between TR revenue and ABL cost. As previous authors have shown that ABL costs could be up to 25% of the total cost of the product (Azzi et al., 2014), we then considered a combined factor of 1TR - 0.25ABL. To generate representative simulation data, a suitable warm-up/transient period is needed to ensure that observations are very close to normal operating conditions. Law (2014) suggested running a preliminary system simulation, selecting one output variable for observation. A trial procedure has found that after an initial simulation run of 20,000 minutes, acceptable steady-state behavior was established. So, all data gathered during the first 20,000 minutes were discarded, and 100 independent runs of 120,000 minutes each were carried out excluding the first 20,000 minutes of non-steady state data. Typically, manufacturing equipment on the factory floor is unreliable. In unreliable merging lines, the stations are subject to random breakdown and repair events. In this study, the failure rate used is 0.001 breakdowns per minute and the repair rate is 0.010 repairs per minute, i.e. MTBF = 1000 minutes and MTTR = 100 minutes. Therefore, line efficiency = 91% [MTBF 1,000 / (MTBF 1,000 + MTTR 100)], which is the same efficiency figure used by Altiok and Stidham (1983) and Hopp and Simon (1993). For each station, the processing time was modelled as a Weibull distribution with mean of 10 time units, whereas the CV was fixed at 0.274, in line with Slack’s (1982) recommendations. The independent variables and their levels (for parallel lines 1 and 2) were: • Line length: N = 5 and N = 8 (i.e. odd and even numbers). • Mean Buffer Capacity (BC) per station: These values were selected such that BC ≠ 0, while taking into account that over a certain level of buffer space, the

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law of diminishing returns sets in, leading to negligible improvement in efficiency as buffer size increases. BC = 2 and BC = 6. Thus, total buffer capacity of the complete line remained constant and only buffer capacity per individual station varied. Six different uneven buffer capacity allocation pattern (Pi) for both lines 1 and 2 were considered (Table 1). Table 1. Buffer allocation patterns Line Length (N) Mean Buffer Capacity (BC) Ascending (/) A Descending (\) B C1 Bowl shape (V) C2 D1 inverted bowl shape (Λ) D2 E1 General E2 Balanced

5 2 1,1,1,5 5,1,1,1 3,2,1,2 4,1,1,2 1,2,3,2 1,2,4,1 2,2,3,1 2,3,2,1 2,2,2,2

6 3,3,3,15 15,3,3,3 9,6,3,6 12,3,3,6 3,6,9,6 3,6,12,3 6,6,9,3 6,9,6,3 6,6,6,6

8 2 1,1,1,1,1,1,8 8,1,1,1,1,1,1 4,3,1,1,1,1,3 4,2,1,1,1,1,4 1,1,3,4,3,1,1 1,2,2,4,2,2,1 2,2,2,3,3,1,1 2,2,3,3,2,1,1 2,2,2,2,2,2,2

6 3,3,3,3,3,3,24 24,3,3,3,3,3,3 12,9,3,3,3,3,9 12,6,3,3,3,3,12 3,3,9,12,9,3,3 3,6,6,12,6,6,3 6,6,6,9,9,3,3 6,6,9,9,6,3,3 6,6,6,6,6,6,6

The patterns used in this study correspond to those used in some previous publications on reliable unbalanced production lines, such as McNamara et al. (2013) and Shaaban et al.(2015). Overall, the total number of cells simulated is 324 (2 line lengths x 2 MB levels x 9 uneven buffer allocation patterns for line 1 x 9 buffer allocation patterns for line 2).

4 Results Due to space limitations, Table 2 shows a summary of the simulation experiments by presenting the average TR, ABL and TR-0.25ABL results for all the combined experiments. Considering Table 2, “Blcd+Blcd” represents a merging line where the two parallel lines are balanced, while the results of a “Balanced” pattern for Parallel line 1 (L1), for example, show the average response value when applying a “Balanced” pattern only in L1 and every other pattern for Parallel line 2 (L2). Similarly, results of an “A” pattern regarding L2 show the average response value when applying the “A” pattern in L2 and every other pattern in L1. Grey cells in Table 2 show the best pattern found for the average results per response. For instance, it can be seen that TR is maximized with a Balanced + Balanced pattern, overall, with the exception of applying an inverted bowl pattern (“D1” pattern) when BC=2 and N=5. However, caution should be exercised with this result, as we didn’t find statistically significant differences for this particular configuration.

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Furthermore, we found that both ABL and TR-0.25ABL had their best performance when N=8 by applying a “Balanced” pattern in combination with any other rule. In addition, Table 1 shows that when N=5, an ascending order pattern (“A” pattern) resulted in the best performance. The exception is again found in a line where BC=2 and N=5, since applying a D1 pattern in either parallel line will produce the best TR-0.25ABL results. Table 2. Average response results for different experimental settings depending on buffer patterns TR

ABL

N=5 BC

Pattern Blcd+Blcd

2

L2

L1

0,56

TR-0.25ABL

N=5 L2

L1

0,51

N=8 L2

L1

1,31

N=5 L2

L1

1,41

N=8 L2

L1

0,23

L2 0,16

Balanced

0,56

0,56

0,51

0,51

1,32

1,32

1,15

1,15

0,23

0,23

0,22

0,22

A

0,56

0,56

0,49

0,49

1,24

1,24

1,84

1,84

0,25

0,25

0,03

0,03

B

0,55

0,55

0,51

0,51

1,41

1,40

1,47

1,47

0,20

0,20

0,14

0,14

C1

0,56

0,56

0,50

0,50

1,35

1,35

1,62

1,62

0,22

0,22

0,09

0,10

C2

0,55

0,55

0,50

0,50

1,36

1,36

1,53

1,53

0,21

0,21

0,12

0,12

D1

0,56

0,56

0,51

0,51

1,30

1,30

1,51

1,51

0,24

0,24

0,13

0,13

D2

0,56

0,56

0,51

0,51

1,31

1,31

1,52

1,52

0,23

0,23

0,13

0,13

E1

0,56

0,56

0,50

0,50

1,34

1,34

1,55

1,55

0,22

0,22

0,12

0,12

E2

0,56

0,56

0,50

0,50

1,35

1,35

1,63

1,63

0,22

0,22

0,09

0,09

Blcd+Blcd

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L1

N=8

0,66

0,63

3,80

4,01

-0,29

-0,38

Balanced

0,66

0,66

0,61

0,61

3,83

3,83

3,30

3,31

-0,30

-0,30

-0,21

-0,22

A

0,66

0,66

0,59

0,59

3,54

3,55

5,44

5,43

-0,23

-0,23

-0,77

-0,77

B

0,64

0,64

0,62

0,62

4,13

4,12

4,24

4,24

-0,39

-0,39

-0,44

-0,44

C1

0,65

0,65

0,61

0,61

3,92

3,91

4,73

4,72

-0,33

-0,33

-0,58

-0,57

C2

0,65

0,65

0,61

0,61

3,97

3,96

4,44

4,44

-0,34

-0,34

-0,50

-0,50

D1

0,66

0,66

0,61

0,61

3,73

3,74

4,35

4,36

-0,28

-0,28

-0,47

-0,47

D2

0,66

0,65

0,62

0,62

3,79

3,80

4,37

4,37

-0,29

-0,29

-0,47

-0,48

E1

0,65

0,65

0,61

0,61

3,88

3,89

4,47

4,47

-0,32

-0,32

-0,50

-0,50

E2

0,65

0,65

0,61

0,61

3,93

3,93

4,75

4,76

-0,33

-0,33

-0,58

-0,58

5 Discussion and conclusions Results from this study show that a balanced buffer allocation pattern in both parallel lines, when considering the combined result of TR as a revenue generating

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variable and ABL as a cost-related variable, is not always the best pattern to increase performance in merging, unreliable production lines, because an inverted bowl pattern of buffer allocation works best for lines with 5 stations and a mean buffer capacity per station of 2, while an ascending pattern of buffer allocation is the best pattern for lines with 5 stations and a mean buffer capacity of 6. Otherwise, the best pattern, on average, regarding a combined result of TR and ABL is to assign a “Balanced” pattern to one of the parallel lines while assigning any other pattern to the other parallel line. However, our results show that the best pattern regarding Throughput performance, by itself, is in fact the “Balanced + Balanced” buffer allocation pattern, even though the inverted bowl pattern provides very similar throughput performance for a short line with limited mean buffer capacity. More research is needed to understand why either an inverted bowl or an ascending pattern produce the best trade-off between TR and ABL in shorter lines. Furthermore, an analysis of the difference between reliable and unreliable merging lines is needed.

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