Journal of Engineering Research 11 (2023) 182–191
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Journal of Engineering Research
journal homepage: www.journals.elsevier.com/journal-of-engineering-research
Solution of the assembly line balancing problem using the rank positional weight method and Kilbridge and Wester heuristics method: An application in the cable industry
Miraç Tuba Çelik
a, Seher Arslankaya
b,⁎a Department of Industrial Engineering, Bursa Technical University, Bursa, Turkey
b Department of Industrial Engineering, Sakarya University, Sakarya, Turkey
A R T I C L E I N F O Keywords:
Assembly line
Assembly line balancing problem Rank positional weight method (RPWM) Kilbridge and Wester heuristics
A B S T R A C T
Today, assembly lines are frequently used in factories' production areas because they increase production pro- cesses' efficiency. Due to increased customer demands, increasing production amounts and intense competition cause severe fluctuations in production environments. This is also evident in assembly lines. Balancing problems caused by many reasons in assembly lines has become a big problem for companies. In this study, the balancing problem in the assembly line in an automotive supplier industry company that produces cables has been tried to be solved. In the solution of the problem, the Rank positional weight method, which is among the heuristics frequently used in the literature, and the Kilbridge and Wester heuristics were used. Considering the current situation, the cycle time from 170 s has been reduced to 142.25 s, and the line efficiency has been increased from 82.36% to 98.42%. There was no increase or decrease in the number of stations on the line and the number of operators working there. As a result of all these efforts, the workload was distributed equally among the stations, severely reducing waiting time. In this way, the downtimes in production were reduced, the overtime hours required to reach the required daily production amount were eliminated, and labor costs were reduced.
Introduction
Due to the increasing competition conditions, companies have started to react quickly to the market. This causes various problems in production environments. Unexpected situations that occur in manu- facturing environments cause deviations by being different from the results calculated by various methods. This is also evident in assembly lines. Deviations caused by unexpected situations cause imbalances between stations on assembly lines, causing delays, waiting times, and many more problems. There are many reasons for balance losses in assembly lines. The first of these is labor time. Labor time is a problem that is frequently encountered and has a negative impact. There can be many reasons for this problem to occur. Among these reasons are the lack of knowledge of the worker due to the lack of adequate training about the work he is doing at the station where he is assigned, the different cycle times for each product due to the appearance of various products at the same workstation, and the inefficient work of the worker while doing his job. Another problem frequently encountered in businesses that have become a big problem and cause loss of balance is
poor quality. When this problem is examined, two situations can be encountered. The first is the problem that occurs before the material arrives on the line. The second problem is the problem that the material creates when it arrives on the line. In this case, the material cannot be attached to the product, and even because there is no other material, a stop occurs. Another reason for balance losses is the failure of the machines. It will cause delays as no action can be taken until the ma- chine malfunction in the workstation is fixed. These three problems in balance losses will cause fluctuations in processing times, stoppages will occur, and even inefficiency and will cause high costs for the business [40].
Assembly line balancing
Assembly is the final production stage of manufactured products, where interchangeable parts are linked together to form final products or sub-assemblies [7]. Combining the products or semi-products that need to be produced on the production lines in the production system can also be defined as an assembly [42]. The assembly line, on the other
https://doi.org/10.1016/j.jer.2023.100082
Received 25 March 2023; Received in revised form 23 April 2023; Accepted 26 April 2023
2307-1877/© 2023 The Authors. Published by Elsevier B.V. on behalf of Kuwait University. This is an open access article under the CC BY-NC-ND license (http://
creativecommons.org/licenses/by-nc-nd/4.0/).
]]
]]]]]]]]
⁎ Corresponding author.
E-mail address: [email protected](S. Arslankaya).
hand, is a system consisting of sequential workstations where materials and operations on the part are transferred uninterruptedly along the line with the labor or material handling system [18]. In these work- stations, everything that needs to be done in the assembly process to obtain the final product is done wholly and sequentially [41]. The purpose of assembly lines is to combine the elements of the product being produced and to obtain the final product [19]. The sum of the durations of the operations performed at the stations on the assembly line cannot exceed the cycle time determined for the line. Here, the cycle time is the interval between two complete products in sequence at the last station. When calculating the cycle time, the current production time is divided by the demand [30].
Assembly lines are widely used in many manufacturing sectors, such as automotive, food, electronics, and white goods [43].Compared to other sectors, they have many advantages, such as shorter flow time and higher efficiency [26]. With the work of industrial engineers in these sectors, more value will be added to the companies, and profit- ability will increase. Industrial engineers carry out many studies on assembly lines, such as increasing the efficiency of the assembly, even distribution of the load to the workers, using lean production techni- ques, and balancing the assembly line [42]. It is essential to distribute the tasks equally to the stations on the line, as assembly lines allow for low unit price production in economies of scale. Therefore, care should be taken when designing assembly lines [9].
Classification of assembly lines by location
According to the layout of assembly lines; flat (traditional) assembly line, U-type assembly line, and parallel assembly line. Lines of work- stations lined up one after the other and where operators work in a single station are called flat (traditional) assembly lines. The product starts from the first station and leaves the last station as a finished product. The workflow is easy and fast, but the disadvantages of these lines are that they take up much space and there is a lack of commu- nication between employees [39]. The assembly line, designed in a U shape and where the two ends are close, is called a U-type assembly line. The operations here are performed on a curved line. This line is mainly preferred in modern assembly lines. In these lines, the operator can work on two different products. This is because the operator can move between the two parts of the line due to the U shape. Employee communication is more vital than a flat assembly line [36]. It was first
used in the Toyota factory [33]. In U-type assembly lines, the number of operators can be increased and decreased, thereby gaining flexibility in production volüme [39]. The same line is installed parallel to the main line in parallel assembly lines. It is preferred if the demand is in- sufficient to set up an assembly line or the capacity of a single line is insufficient. In these lines, the same products can be produced on se- parate assembly lines [39]. Shortening the line, increasing cycle times, balancing the workload thanks to resource sharing, and increasing productivity are among the advantages of parallel assembly lines [8].
Assembly line balancing problem
The most crucial problem in assembly lines is distributing the op- erations that need to be done in a balanced way between workstations, considering one or more purposes, under some constraints. This pro- blem is considered the assembly line balancing problem. Assembly line balancing problem, assuming that the processes required for the pro- duction of the product, the durations of the processes, and the priority relations between the processes are known; It is based on the re- arrangement of the assembly line in order to distribute the workload equally among the stations on the line [11]. The purpose of assembly line balancing is to distribute the workload equally to the stations on the assembly line.
Various constraints are used in simple assembly line balancing problems. These constraints can be listed as follows:
– Each job must be assigned to stations on the assembly line, – A job is assigned to only one station,
– The sum of the durations of the processes assigned to the work- stations should not exceed the cycle time,
– The antecedent of each transaction must be considered.
Assembly line balancing problems involve giving all operations on the line to other stations, paying attention to their antecedents, and satisfying other constraints. The concept of "balancing" used here means minimizing the current number of stations, giving equal workload to each station, and reducing idle times at stations [7]. In the literature, assembly line balancing problems are classified in 4 ways. The classi- fication of assembly line balancing problems is shown in Fig. 1 [42].
Assembly line balancing [6]problems have become a frequently en- countered problem in assembly line design and production companies.
Fig. 1. Classification of assembly line balancing problems [42].
Due to the balance problem in the workstations, the operator was idle, and another operator could not fulfill the assigned tasks within the specified time [40]. Some basic concepts used in assembly line balancing problems are as follows.
It is also clearly seen in the literature that the ANN or FL approaches have been used for different motivations, and satisfactory results have been obtained [2,23,1,5].
Workstation: It is the name given to the area where the work on the assembly line is done by the operator and where the tools, equipment, and machines must be mandatory to do the job is located. The product enters the first workstation, goes through various processes, and is sent to the next station [16].
Cycle Time: It is defined as the maximum time the product can stay on the workstation. The product can remain at each station only for the longest period of time [12]. The tasks in the workstations may exceed the cycle time or not reach the full cycle time. The cycle time is cal- culated as in equation 1.1 [31].
Cycle time=Total time /number of products to be made (1.1) Total work time: The total time needed for the assembly of the product to be produced. The standard times of all work items that make up the job can be found by summing [19]. Total work time is calculated as in Eq. 1.2. “ti” indicates the duration of work items.
=
=
t Total work time
i N
i
1 (1.2)
Workstation time: The sum of the standard times for work items to be completed on a Workstation [31].
Minimum Number of Workstations Required: It expresses at least how many stations the product should be processed with the calculated cycle time. If the tasks on the assembly line are assigned to each station in a way that fills the cycle time, the required minimum number of workstations is calculated as in Eq. 1.3 [31].
= = t nsmallest iC
N1 i
(1.3) Two work items with more than half the cycle time are assigned to separate workstations because their sum will exceed the cycle time. In this case, the calculation is done as in Eq. 1.4.
npossible= Number of work items with a duration greater than half the cycle time (1.4) In this case, the required number of workstations is considered the largest of Eqs. 1.3 and 1.4 [16].
nmin=biggest(nsmallest, npossible) (1.5) Average Workstation time: Average time of workstations required to produce the product on the assembly line [31].
Line efficiency: The ratio of the sum of the items assigned to the workstation durations to the total time multiplied by the cycle time [16]. Line efficiency is calculated as in Eq. 1.6. “n” indicates the number of workstations.
= ×= t × n C Line efficiency(%) i 100
N1 i
(1.6) Loss of balance: Used to indicate whether work items or operators assigned to workstations are balanced [31]. The loss of balance is cal- culated as in Eq. 1.7.
= C n = t Loss of balance(%) 100*( *n C )
*
i N1 i
(1.7) Technological priority diagram: On assembly lines, the pre- decessors of the previous job must be completed before the product can begin. The diagram showing these processes is called the technological
priority diagram. The circles in the technological priority diagram show the activities, and each activity is connected by an arrow and shows the direction of the process [16].
Priority matrix: Technological priority diagram in matrix form is called.
Literature research
The idea of assembly line balancing was first mentioned in Bryton's master's thesis published in 1954. In his study, Bryton accepted that the number of workstations was fixed, giving equal times to all work- stations and that workmen moved between workstations [10]. The first article published in the literature on assembly line balancing belongs to Salveson. Salveson tried to solve the assembly line balancing problem with the 0–1 integer linear programming model in his article published in 1955. In this study, Salveson tried to minimize the number of existing stations. However, while the number of stations decreased, it kept the cycle and processing times constant [35]. Helgeson and Birnie [15]
found a solution to the assembly line balancing problem using the po- sition weight method. Kilbridge and Wester [20], with the method they developed, created an assignment table by paying attention to the cycle time and the antecedents of the work items and assigned work items to the stations. Moodie and Young [28]performed a stochastic time as- sembly line balancing study by assuming the cycle time as a constant.
Arcus [4]developed the COMSOAL technique and performed an as- sembly line balancing study by creating solutions with specific con- straints and choosing the alternative with a minor balance loss. Suresh and Sahu [38]conducted an assembly line balancing study using the simulated annealing technique. Kim et al. [21]tried to solve the as- sembly line balancing problem using genetic algorithm. Manoria et al.
[25]conducted an assembly line balancing study by developing an expert system approach based on the position weight method. Mishra and Manoria [27], using the C+ + computer program, applied the position weight method and performed assembly line balancing work.
Aksoy et al. [3]performed a single model U-type assembly line bal- ancing study with the position weight method. Eryürük et al. [13]
conducted an assembly line balancing study for two models produced in the factory using the position-weighted balancing technique. Kumar and Gowda [22]aimed to increase the production speed to 24 machines per day by using the Rank positional weight method. At the same time, better solutions are proposed by reducing the number of workstations and cycle time. Jha and Khan [17]used three different methods such as Largest candidate rule, Kilbridge and wester column method and Rank positional weighted method, and they conducted an assembly line balancing study in an automotive manufacturing company. As a result of the study, line efficiency, balance delay, ideal time and smoothness index parameters were calculated and compared for 3 methods.
Looking at the overall performance, the Largest candidate rule tech- nique gave the best result. Nahar et al. [29]aimed to maximize bal- ancing efficiency and minimize the number of workstations by using the Ant optimization algorithm to solve the assembly line balancing problem. At the same time, Rank positional weight method was used in the study. As a result of the study, the two methods were compared and they concluded that when the cycle time is minimum, the balancing efficiency is maximum if the number of workstations does not change.
Manaye [24]conducted an assembly line balancing study in the apparel industry using Ranked positional weight and largest candidate methods. As a result of the study, it has been seen that the ranked position weight method gives better results in increasing the line effi- ciency and reducing the delay time compared to the other technique.
Kum et al. (2021) tried to increase the production line efficiency of the crimping unit. Kilbridge and wester column method, Rank positional weighted method and Largest candidate rule methods were used in the study. As a result of the study, the number of existing workstations decreased from 12 to 8 and line efficiency increased from 44% to 69%.
Among the three methods, Rank positional weight method was
determined as the best method. Salam and Liu [34]conducted an as- sembly line balancing study in an automotive industry using the Kil- bridge and Wester column approach. As a result of the study, the number of operators and workstations was reduced from 7 to 3, the idle time of the worker was reduced and the working capacity of each worker was increased up to 95.5%.
Material and method
Assembly line balancing problems have been tried to be solved by using many methods in the literature. These methods; It is possible to collect them under three headings: classification according to the pro- blem, classification according to the solution approach, and classifica- tion according to the processing time. If it is desired to consider clas- sification methods according to the solution approach, they are examined in 3 groups as heuristic methods, analytical methods and simulation techniques. Solving the problem in analytical methods takes time. Mathematical programming, branch-and-bound algorithm, dy- namic programming, position weight technique are some of these methods. In heuristic methods, a better and more valid solution can be reached quickly and with less computation. However, the disadvantage of heuristic methods is that they do not always work with the same performance and do not guarantee that the solution reached is the most accurate result. Rank positional weight method, COMSOAL method, Hoffmann heuristic and Kilbridge and Wester heuristic are some of these methods. Simulation technique, on the other hand, understands the working logic of the system, develops various strategies and imi- tates the operation of the system [16,39]. In assembly line balancing problems, as the number of transactions increases, it becomes more difficult to solve the problem and in these cases, heuristic methods are used [6]. For this reason, heuristic methods were used in the study.
Rank positional weight method (RPWM)
Developed by Helgeson and Birnie in 1961 [15]. It is a frequently used method among the heuristic methods in the literature in solving assembly line balancing problems. The position weight of each task is obtained by adding up all subsequent task times, including itself. The point to be considered here is that the task with a high position weight is selected in the first assignment process [14]. The steps applied in the rank positional weight method technique are as follows:
Step 1: A priority relationship diagram is drawn.
Step 2: Position weight (position weight) is calculated for each task.
The position weight of a task is the sum of the time required to perform that task and the duration of the tasks that follow that task.
Step 3: Tasks are sorted by position weight from largest to smallest.
Step 4: The task with the highest position weight is selected and assigned to the workstation.
Step 5: After the task with the highest position weight is assigned to the workstation, the task with the highest position weight is selected among the remaining tasks and assigned to the station considering the following constraints.
a) The reserved jobs list is checked. If tasks with no predecessor are assigned, go to b; if not, go to step 6.
b) The durations of the tasks are compared to the unused time of the station. If the duration of the task to be assigned is less than the unused time, the assignment is made and the unused time of the station is re- calculated and step 5 is repeated, if it is greater than the unused time, step 6 is passed.
Step 6: The process continues until the assignment to the station is selected, checked, and, if possible, until two conditions are met:
a) All work items are assigned.
b) There are no tasks that meet the priority requirement and the unassigned time requirement.
Step 7: The task with the highest position weight that is not assigned is assigned to the next station, and the first six steps are repeated.
Step 8: Assignment continues until all tasks are assigned to the workstations. After the implementation of all these steps, the assembly line balancing problem is solved.
Kilbridge and Wester heuristics
The Kilbridge and Wester heuristic was first used in 1961. It is used in studies in the literature because it successfully solves assembly line balancing problems that are difficult to solve [37]. In this method, among the heuristic methods, work items are assigned to workstations according to their positions in the drawn priority diagram [32]. The implementation steps of Kilbridge and Wester Heuristics are as follows:
Step 1: A priority relationship diagram is drawn.
Step 2: Tasks without predecessors are listed in the first column. When the second column is passed, the tasks followed by the tasks in the first column are listed. This process is continued until all columns are created.
Step 3: The durations of the tasks in each column are summed, and the cumulative duration is obtained.
Step 4: The cycle time is determined.
Step 5: Tasks are assigned to the station in a way that does not exceed the cycle time. If tasks exceed the cycle time when assigned to the station, that task is assigned to the next station.
Step 6: The cumulative duration of unassigned tasks is recalculated, and step 5 is repeated.
Step 7: Assignment processes continue until all tasks are assigned to the workstations.
Result
This study it is aimed to solve the assembly line balancing problem in an automotive supplier industry company that produces cables.
There are 13 processes on the line where balancing work will be done.
These processes are, respectively, airbag pre-assembly, electrical airbag test, pre-assembly, laying, waseronbou 1, waseronbou 2, taping, latch check, electrical test, final assembly, temporary taping, final observa- tion, and shipment. The targeted cycle time is 143.33 s. However, the duration of the pre-assembly six stations is 170 s, which is longer than the other stations. The reason for this problem was investigated, and it was determined that the workload of the operator working at the six pre-assembly stations was higher. This problem at the pre-assembly 6 station causes operators working at other stations to wait. The com- parison of pre-assembly 6 stations with labor times at pre-assembly 5, pre-assembly 7, and pre-assembly 8 stations is given in Fig. 2.
The Rank positional weight method and Kilbridge and Wester heuristics, which are among the heuristic methods, were used in the assembly line balancing work to be carried out between 4 stations in the factory. The duty periods of the stations belonging to the pre-assembly line to be discussed in this study were recorded with video while the workers were doing their work. When the assembly of the product started, the video was started, and when all assembly processes for that
Fig. 2. Labor times at the pre-assembly station.
product were finished, the video was stopped. In this way, operation definitions and durations were obtained. There are 39 work items in total at the stations on the pre-assembly line. Table 1shows the work items obtained from the video analysis, the duration of the work items, and the priority relationship between the items.
After determining the priority relationship between the work items, the technological priority diagram was drawn as in Fig. 3. In the given diagram, nodes show work items, and links show the priority re- lationship between work items. If work items 28 and 30 are considered, Table 1
Work items, durations, and predecessor work items.
Work items Predecessor work item or items Duration Work items Predecessor work item or items Duration
1 - 8,17 21 20 15,95
2 1 38,77 22 21 5,62
3 2 35,92 23 22 5,36
4 3 23,62 24 23 8,82
5 4 6,53 25 24 2,43
6 5 3,59 26 25 7,39
7 6 9,12 27 26 6,79
8 7 10,62 28 - 8,96
9 8 4,32 29 - 6,32
10 - 21,49 30 28 7,45
11 10 39,7 31 29 9,78
12 10 10,63 32 30,31 5,33
13 10 56,59 33 32 3,63
14 11,12,13 27,93 34 33 6,53
15 14 1,38 35 34 30,67
16 15 12,28 36 35 8,1
17 - 9,95 37 36 7,26
18 17 27,28 38 37 9,66
19 18 27,49 39 1,10,17,28,29 15,68
20 19 12,92
Fig. 3. Technological Priority Diagram.
Table 2
The current situation.
Daily production 180 pcs/day
Current cycle time on the pre-
assembly line 170 s
Target cycle time 143,33 sec
Efficiency of the line %82,36
Number of workstation 4
Total number of employees at
the station 4
Time for meals and breaks Lunch 30 min – Break time 2 × 10 = 20 min
Working time 8 h
Net working time 8 × 60–50 = 430 min
Table 3
Position Weights of Tasks.
Item Position Weights Item Position Weights
1 156,34 21 68,04
2 148,17 22 52,09
3 109,4 23 46,47
4 73,48 24 41,11
5 49,86 25 32,29
6 43,33 26 29,86
7 39,74 27 22,47
8 30,62 28 103,27
9 20 29 102,96
10 185,68 30 94,31
11 96,97 31 96,64
12 67,9 32 86,86
13 113,86 33 81,53
14 57,27 34 77,9
15 29,34 35 71,37
16 27,96 36 40,7
17 145,68 37 32,6
18 135,73 38 25,34
19 108,45 39 15,68
20 80,96
it is interpreted that task 28 must be completed before task 30. It is definitely not possible to proceed to the 30th task until the 28th task is completed. Task 28 is the predecessor of task 30, and task 30 is the successor to task 28.
After the technological priority diagram was created, the targeted cycle time was calculated to analyze the line's status and decide
whether to make any changes in the number of workstations. Table 2 gives information about the current status of the assembly line.
Cycle time = The total time / Number of products to be made.
C = (430/180) x 100 = 143,33 s
According to the calculation, the line's cycle time should be 143.33 s, while the current cycle time on the line is 170 s. The excess Table 4
Sorting position weights from smallest to largest.
Row Item Duration Position Weights Row Item Duration Position Weights
1 10 21,49 185,68 21 12 10,63 67,9
2 1 8,17 156,34 22 14 27,93 57,27
3 2 38,77 148,17 23 22 5,62 52,09
4 17 9,95 145,68 24 5 6,53 49,86
5 18 27,28 135,73 25 23 5,36 46,47
6 13 56,59 113,86 26 6 3,59 43,33
7 3 35,92 109,4 27 24 8,82 41,11
8 19 27,49 108,45 28 36 9,12 40,7
9 28 8,96 103,27 29 7 8,1 39,74
10 29 6,32 102,96 30 37 2,43 32,6
11 11 39,7 96,97 31 25 7,26 32,29
12 31 9,78 96,64 32 8 10,62 30,62
13 30 7,45 94,31 33 26 7,39 29,86
14 32 5,33 86,86 34 15 1,38 29,34
15 33 12,92 81,53 35 16 12,28 27,96
16 20 3,63 80,96 36 38 9,66 25,34
17 34 6,53 77,9 37 27 6,79 22,47
18 4 23,62 73,48 38 9 4,32 20
19 35 30,67 71,37 39 39 15,68 15,68
20 21 15,95 68,04
Table 5
Assigning tasks to stations.
Workstation Item numbers Position Weights Previous transactions Processing time Cumulative processing time
1 10 185,68 _ 21,49 21,49
1 156,34 _ 8,17 29,66
2 148,17 1 38,77 68,43
17 145,68 _ 9,95 78,38
18 135,73 17 27,28 105,66
3 109,4 2 35,92 141,58
2 13 113,86 10 56,59 56,59
19 108,45 18 27,49 84,08
28 103,27 _ 8,96 93,04
29 102,96 _ 6,32 99,36
11 96,97 10 39,7 139,06
3 31 96,64 29 9,78 9,78
30 94,31 28 7,45 17,23
32 86,86 30,31 5,33 22,56
20 80,96 19 12,92 35,48
33 81,53 32 3,63 39,11
34 77,9 33 6,53 45,64
4 73,48 3 23,62 69,26
35 71,37 34 30,67 99,93
21 68,04 20 15,95 115,88
12 67,9 10 10,63 126,51
22 52,09 21 5,62 132,13
5 49,86 4 6,53 138,66
6 43,33 5 3,59 142,25
4 14 57,27 11,12,13 27,93 27,93
23 46,47 22 5,36 33,29
24 41,11 23 8,82 42,11
7 39,74 6 9,12 51,23
36 40,7 35 8,1 59,33
25 32,29 24 2,43 61,76
37 32,6 36 7,26 69,02
8 30,62 4,6,7 10,62 79,64
26 29,86 25 7,39 87,03
15 29,34 14 1,38 88,41
16 27,96 15 12,28 100,69
38 25,34 37 9,66 110,35
27 22,47 26 6,79 117,14
9 20 8 4,32 121,46
39 15,68 1,10,17,28,29 15,68 137,14
26.67 s here is due to the excessive workload of the operator working at the six pre-assembly stations on the line.
Rank positional weight method
The steps of the Rank positional weight method are given below respectively. First of all, a technological priority diagram was drawn by paying attention to the priority relations between the work items. The type of assembly line examined is the mixed model assembly line.
Step 1: The technological priority diagram is drawn in Fig. 3.
Step 2: The position weight for each task is given in Table 3.
Step 3: After the position weights were calculated, the position weights were ordered from smallest to largest. In Table 4, the position weights are listed in order.
Step 4- Step 8: The tasks are assigned to the workstations, starting from the highest position weight, taking into account the antecedents and the cycle
time, respectively. All the processing steps from step 4 to step 8 have been performed, and the assignments to the workstations are shown in Table 5.
In Fig. 4, the tasks assigned to the station with the Rank positional weight method and the total time of each station are shown.
Minimum required number of workstations = Sum of all work items / Cycle time.
nsmallest = 560,03 / 142,25 = 3,94 ≅ 4 stations.
After the assignments were made, the efficiency of the line and the loss of balance were calculated as follows.
Line efficiency (%) =n CiN×=1ti ×100= 4 142, 25×560, 03 ×100= %98,42.
Loss of balance (%) = 100 C n* ( *n C* iN=1ti)or 1- Line efficiency = 1 – 98,42 = %1,58.
As can be seen from Fig. 4as a result of all calculations, it is seen that after all work items are assigned to the stations, the line reaches balance and thus the efficiency of the line is greatly improved. There was a 16% increase in line efficiency, which reduced the loss of balance.
Kilbridge and Wester heuristics
The steps of the Kilbridge and Wester heuristics are given below respectively. First of all, a technological priority diagram was drawn by paying attention to the priority relations between the work items.
Step 1: The technological priority diagram is drawn in Fig. 3.
Step 2: After drawing the priority diagram, all the columns (layers) were created with the tasks without antecedents in the first column. The columns created are shown in Fig. 5.
Step 3: The cumulative time was obtained by summing the dura- tions of the tasks in each column. The cumulative time is shown in Table 6.
Step 4: The cycle time is given in the current state table in Table 2.
Step 5- Step 7: The tasks are assigned to the workstations in a way that is within the cycle time and by paying attention to the antecedents.
Fig. 4. The tasks assigned to the station with the Rank positional weight method and the total duration of each statio.
Fig. 5. Layers created for Kilbridge and Wester Heuristics.
Table 6
Cumulative performance time.
Layers Each layer time Cumulative time
1 54,89 54,89
2 190,2 245,09
3 96,67 341,76
4 41,55 383,31
5 41,29 424,6
6 39,88 464,48
7 22,58 487,06
8 26,7 513,76
9 16,41 530,17
10 7,39 537,56
11 6,79 544,35
12 15,68 560,03
In addition, assigning a layer to the workstation is necessary for the other layer to pass. Table 7 shows the tasks assigned to the work- stations.
Fig. 6shows the tasks assigned to the station with Kilbridge and Wester Heuristics and the total time for each station.
Minimum required number of workstations = Sum of all work items / Cycle time.
nsmallest = 560,03 / 142,25 = 3,94 ≅ 4 stations.
After the assignments were made, the line's efficiency and the bal- ance loss were calculated as follows.
Line efficiency (%) =n CiN×=1ti ×100= 4 142, 25×560, 03 ×100= %98,42.
Table 7
Tasks assigned to workstations.
Workstation Item number Previous transactions Processing time Cumulative processing time
1 1 - 8,17 8,17
10 - 21,49 29,66
17 - 9,95 39,61
28 - 8,96 48,57
29 - 6,32 54,89
13 10 56,59 111,48
18 17 27,28 138,76
2 2 1 38,77 38,77
11 10 39,7 78,47
12 10 10,63 89,1
30 28 7,45 96,55
31 29 9,78 106,33
3 2 35,92 142,25
3 14 11,12,13 27,93 27,93
19 18 27,49 55,42
32 30,31 5,33 60,75
4 3 23,62 84,37
20 19 12,92 97,29
33 32 3,63 100,92
15 14 1,38 102,3
21 20 15,95 118,25
16 15 12,28 130,53
5 4 6,53 137,06
4 34 33 6,53 6,53
6 5 3,59 10,12
22 21 5,62 15,74
35 34 30,67 46,41
7 6 9,12 55,53
23 22 5,36 60,89
36 35 8,1 68,99
8 4,6,7 10,62 79,61
24 23 8,82 88,43
37 36 7,26 95,69
9 8 4,32 100,01
25 24 2,43 102,44
38 37 9,66 112,1
26 25 7,39 119,49
27 26 6,79 126,28
39 1,10,17,28,29 15,68 141,96
Fig. 6. Tasks assigned to the station and total time of each station with Kilbridge and Wester Heuristics.
Table 8
Comparison of the methods used in the study.
Rank positional
weight method Kilbridge and wester heuristics
Line efficiency 0,9842 0,9842
Loss of balance 0,0158 0,0158
Number of workstation 4 4
Idle time 13,29 13,29
Table 9
Station times obtained with the Rank positional weight method and Kilbridge and Wester heuristics.
Station times obtained by the Rank positional weight method
Station times obtained with Kilbridge and Wester Heuristics
Workstation 1 141,58 138,76
Workstation 2 139,06 142,25
Workstation 3 142,25 137,06
Workstation 4 137,14 141,96
Loss of balance (%) = 100 C n* ( *n C* iN=1ti) or 1- Line efficiency = 1 – 98,42 = %1,58.
As can be seen from Fig. 6as a result of all the calculations, it is seen that the line reaches balance after all work items are assigned to the stations, thus improving the efficiency of the line to a great extent.
There was a 16% increase in line efficiency, which reduced the loss of balance.
A comparison of the methods used in the study is given in Table 8.
When the table is examined, it is seen that the efficiency of the line, loss of balance, number of stations and idle time are the same for both methods. For this reason, the decision of which method to choose for the line balancing problem is left to the company manager.
Statistical analysis
In this study, the assembly line balancing problem has been solved using the Rank positional weight method and the Kilbridge and wester heuristics, and the line's efficiency has been increased. In this section, whether there is a significant difference between the results obtained by the two methods used in the solution of the problem was determined by using the SPSS Statistics program. The purpose of using the dependent t-test is to apply two different methods to the same sample group and compare them with each other. The important thing here is to compare the results of the same sample group. Each station time obtained from the two solved methods was transferred to the SPSS program. The data used in the program are shown in Table 9.
The hypotheses established for the dependent t-test are as follows:
H0: With 95% confidence interval, there is a statistically significant difference between the two methods for creating the new layout.
H1: With 95% confidence interval, there is no statistically sig- nificant difference between the two methods for creating the new layout.
Since the Sig(P) value is greater than 0.05 in the 95% confidence interval, there is no significant difference between the values obtained as a result of the two methods. Therefore, H0 hypothesis is rejected and H1 hypothesis is accepted. Tables 10–12.
Conclusion
The assembly line balancing problem has become a frequently en- countered problem in factories today. The unequal workload distribu- tion to the stations causes the resources not to be used optimally and the demand to decrease due to decreased productivity. For this reason, if this problem is solved in the factories, a significant increase in profitability will be achieved, contributing to a significant reduction in costs at the same rate.
In this study, the assembly line balancing problem has been solved using the Rank positional weight method, which is among the most frequently used heuristics in assembly line balancing problems, and Kilbridge and Wester heuristics. The fact that the cycle time in the line is more than the targeted cycle time causes an increase in the loss of balance. For this reason, the workload between stations was balanced, and the line's cycle time was reduced from 170 s to 142.25 s. This period remained below the targeted cycle time, resulting in a significant improvement. After the calculations, the number of stations was cal- culated as four, and no reduction was made. While the line's efficiency was 82.36% at the beginning, it was calculated as 98.42% after bal- ancing. Cycle time, line efficiency, and loss of balance results obtained in both methods used in the study were the same. For this reason, the decision of which method will be applied in the company is left to the manager.
When the studies in the literature in which the Rank positional weight method and Kilbridge and Wester heuristics are examined, it is seen that in some cases they give better results than other methods they are used, and sometimes their results are behind compared to other methods. However, in this study, it is clearly seen that both methods give very good results.
It has been decided to use the Rank positional weight method and Kilbridge and Wester heuristics in the study, as they reach the result quickly and easily. While making this decision, the disadvantages of both methods were taken into consideration. When the studies in the literature are examined, the fact that the methods are used in many sources shows that the methods have great contributions. It was decided to use the Rank positional weight method and Kilbridge and Wester heuristics, considering all their positive and negative features. It is thought that it will contribute to the literature due to the use of Table 10
Statistical results of methods with dependent t test.
Paired Samples Statistics
Mean N Std. Deviation Std. Error Mean
Pair 1 Rank positional weight method 140,0075 4 2,35385 1,17693
Kilbridge and Wester heuristics 140,0075 4 2,52224 1,26112
Table 11
Correlation value of methods with dependent t test.
Paired Samples Correlations
N Correlation Sig.
Pair 1 Rank positional weight method
& Kilbridge and Wester heuristics
4 -,915 ,085
Table 12
Dependent T test SPSS results.
Paired Samples Test
Paired Differences t df Sig. (2-
tailed) Mean Std. Deviation Std. Error
Mean 95% Confidence Interval of the Difference
Lower Upper
Pair 1 Rank positional weight method-
Kilbridge and Wester heuristics ,00000 4,77134 2,38567 -7,59226 7,59226 ,000 3 1000
current methods in the study and the fact that the study has been carried out in a different sector. These methods may be insufficient to solve the balancing problems of different types of assembly lines in different sectors and may give wrong results. Therefore, in future stu- dies, assembly line balancing problems can be solved for different sectors and different types of assembly lines by using different methods.
In addition, it should not be forgotten that the methods used in the study can be used in future studies.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influ- ence the work reported in this paper.
Acknowledgements
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
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