Modeling of assembly line balancing for optimized number of stations and time

INTERNATIONALMechanical Engineering and Technology (IJMET), ISSN 0976 –
International Journal of JOURNAL OF MECHANICAL ENGINEERING
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME
AND TECHNOLOGY (IJMET)

ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online) IJMET
Volume 4, Issue 2, March - April (2013), pp. 152-161
© IAEME: www.iaeme.com/ijmet.asp
Journal Impact Factor (2013): 5.7731 (Calculated by GISI) ©IAEME
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MODELING OF ASSEMBLY LINE BALANCING FOR OPTIMIZED
NUMBER OF STATIONS AND TIME

Anoop Kumar Elia1, Dr. D.Choudhary2
1,2
Guru Nanak Dev Engg.College, Bidar.585401

ABSTRACT

In this work, the Buxey 29 tasks problem is solved for minimum number of stations
and cycle time. The precedence matrix is presented for the 29 tasks. The classification of
ALB problem and their solution procedure are presented. Single model ALB and equivalent
multi model ALB are treated as similar model and common solution procedure is presented.
The number of stations required for the feasible solutions are varied and cycle time are
computed. The algorithm used in the derivation of the feasible solutions is presented. The
advantages of using a certain number of stations are discussed. Finally important conclusions
are drawn and future work is defined.

Keywords: Number of stations, Number of feasible solutions, Cycle Time, Optimum
Stations and Time.

INTRODUCTION

An assembly line is formed of a finite set of work elements which are also referred to
as tasks. Each task is identified by a processing time for the operation it represents and a set
of relationships for precedence, which specifies the allowable ordering of the tasks. Assembly
line balancing (ALB) is defined as a process in which a group of tasks to be performed are
allocated on an ordered sequence of assembly line. Systematic design of assembly lines is not
a simple and easy task for the designers. Manufacturers and Designers have to deal with their
existing factory layout in the initial phase. The Cost associated and reliability of the system,
complexities involved in tasks, selection of equipment, operating criteria of assembly line,
multiple constraints, scheduling methodologies, allocation of stations, control of inventory,
buffer allocation are the most important area of concern.

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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –

The parameters that include in ALB is: (l) precedence relationships; (2) number
of workstations; (3) cycle time. The number of stations cannot be less than the number
of tasks. The cycle time must be greater than or equal to the maximum of time of any
workstation and the time of any task. In other words, the workstation time should not
have the time higher than the cycle time.
Tendencies in the design and orientation of assembly lines in the
manufacturing are linked to line evolution. Information need to be collected by
designers in this step about the tendencies of the line which need to be implemented.
Balancing as well as sequencing problems depends on the types of assembly lines. For
example, single model line delivers a single product on the line. Layout of the facility,
changes required in tools, workstation indexes remains almost constant. Batch model
lines deliver small number of different products over the line but in batches. In mixed-
model case, different variations of a generic product are delivered at the same time but
in a mixed scenario.
Consideration of the problems associated with work transport system is also a
design requirement. In addition to manual work transport over the line, continuous
transfer also exists with three types of mechanized work transport systems, namely,
synchronous transfer, intermittent transfer, and asynchronous transfer [1]. Different
orientations of the line need to be studied by the designer since it varies widely
according to the floor layout of the production unit. Generally, straight, parallel, U-
shaped [2] are applied. Several design factors are important to assess and consider
with the assembly line design and balancing. The solution variations which are to be
decided depend on the factors like production approaches, objective functions and
constraints. A few of the design constraints related to assembly line balancing are
precedence constraints, zoning constraints and capacity constraints [3].
Efficient formulation of line design problem depends on the database
enrichment. To collect assembly line data, knowledge related to several performance
indices and workstation indices are essential for a line designer. Assembly line design
model and methodology for solution combine the model stage. Design tools are
formulated and modeled once the input data is collected and verified. Modeling of
design tools includes the output data, interaction between different modules and
methods required for solution.
Wide range of heuristic as Branch and Bound search, Positional weight
method, Kilbridge and Wester Heuristic, Moodie-Young Method, Immediate Update
First-Fit (IUFF), Hoffman Precedence Matrix [4] and meta-heuristic based solution
strategies as Genetic Algorithm GA [5], Tabu Search TS, Ant Colony Optimization
ACO [3], Simulated Annealing SA [6] for assembly line problems are taken for study
in industrial and research level. Verification of the developed models is a result of
performance towards the objectives defined for that particular line. Line performances
of assembly line design are a measure of multi-objective characteristics.

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Figure 1: Classification of ALB Solution Procedures.

Several solution procedures that are available in the literature are presented in Fig. 1.
Variable objective functions are taken into account for assembly line [7]. Goal of the designer
is to design a line for higher efficiency, lesser delay in balance, smoother production, and
optimized time for processing, cost effectiveness, overall labor efficiency and just in time
production. The aim is to develop a line by considering the best of the design methods which
may deal in actual fact with user preferences. Design evaluation refers to a user friendly
developed interface where all necessary assembly data is accessible extracted from different
database. Most of the solutions for assembly line balancing problems explore one final
optimized solution. However, it is important to look for the alternative solutions [8].
Validation and verification of several algorithms and methods is combined and incorporated
into different design packages [9].
In this work, the Buxey 29 tasks problem is solved for minimum number of stations
and cycle time. The precedence matrix and solutions are presented for the 29 tasks. The
classification of ALB problem and their solution procedure are also presented.

2.0 CLASSIFICATION OF ALB PROBLEMS

Assembly Line Balancing problem can be classified into two categories, namely,

• Problem based on objective functions.
• Problem based on problem structure.

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Figure 2: Classification of ALB problems.

Problem based on objective functions:
• Type 1: Cycle time is known, and objective is to minimize number of stations.
• Type 2: Number of stations are known, and objective is to minimize cycle time.
• Type 3: Objective is maximization of workload smoothness.
• Type 4: Objective is maximization of work relatedness.
• Type 5: Objective is maximization of multiple objectives with type 3 and 4.
• Type E: Objective is maximization of line efficiency by minimizing both cycle time
and number of stations.
• Type F: Objective is feasibility of line balance for a given combination of number of
stations and cycle.
Problem based on problem structure:
• SMALB: Single model ALB problems, where only single product is produced.
• MuMALBP: Multi model ALB problems, where multiple products are produced in
batches.
• MMALBP: Mixed model ALB problems, where generic products are produced on the
line in a mixed situation.
• SALBP: Simple ALB balancing problems, where the objective is to minimize the
cycle time for a fixed number of workstation and vice versa.
• GALBP: A general ALB problem includes those problems which are not included in
SALBP.

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3.0 EQUIVALENT SINGLE MODEL

Tasks of several models are combined into an equivalent single model. Combined
precedence diagram need to be derived from all the single model diagram along with the
average task times. The objective of balancing is to optimize the number of workstations with
a pre-decided fixed cycle time. The fixed cycle time is treated as the solution lower bound,
for determining desired station numbers, is increased by 1 sec per iteration. Solution lower
bound is found with minimum cycle time [10] as:

For equivalent single models, the algorithm is defined below. The algorithm delivers
number of feasible solutions.

• Assign a new station STATION[1] with a cycle time T = MINCYCLETIME
• Determine all the tasks that do not have the predecessor TASKSWOPRED = { i, j,….,
n}
• Assign one task in TASKSWOPRED to STATION[1]
• Remove the taks that is assigned to STATION[1] from the graph and update it as
TASKSWOPRED = { j,k,….,n }.
• Update the station cycle time as T = MINCYCLETIME - ti
• Repeat steps 3 to 5, until T is positive and update the T and TASKSWOPRED each
time.
• When T turns negative, look for any other tasks in TASKSWOPRED to fit in
STATION[1], but the T should remain positive.
• When T turns zero or negative for all the tasks in TASKSWOPRED, create a new
station as STATION[2].
• Repeat steps 3 to 8.
• Repeat step 3 to 9 for all feasible solutions.
• Try the solutions for a pre-decided number of stations. If the solutions derived are not
feasible, repeat 3 to 9 after update the T as MINCYCLETIME+1.
• When all the feasible solutions are obtained, store the updated T.

4.0 SIMULATION RESULTS

For experimental; purpose, Buxey 29 tasks Problem [11] is chosen. The precedence
diagram for the Buxey is presented in Fig. 3. In case of multiple models, the equivalent task
diagram can be derived in the form shown in Fig. 3. For the sake of simplicity, a single model
precedence diagram is shown and solved in this work. The Buxey problem has a total of 29
tasks and the associated tasks are shown above each task in Fig. 3.

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Figure 3: Buxey 29 tasks precedence diagram.

Table 1 shows the precedence matrix for the Buxey 29 tasks problem. In the matrix, the
columns and rows represent the task number. It shows the precedence relation between the
tasks. For example, in row 2 and column 6, it is indicated as 1 in the matrix, which means the
task 6 is preceded by task 2. If the value is zero, it means there is no precedence relationship
in the diagram. The last row of the Table 1 shows the time associated with each task.

Table 1: Precedence matrix for the Buxey 29 Tasks problem

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There are different parameters in this problem which can vary to derive a best
possible solutions using design of experiments. However, in this case on one parameter is
varied to find out the feasible solutions. The parameter that is varies in the work is number of
stations.
The number of solutions is varied from 8 to 9 and 10. For each case, the number
feasible solutions are computed and the cycle time is determined. Also, the total time
consumed by each station is also computed.

Table 2: Feasible solutions for 8 stations for the Buxey 29 Tasks problem

By running the algorithm mention Sec.3, nine feasible solutions are obtained. The
Table 2 shows the assigned stations for each task under each solution. For example, in
solution 2, task 1 is assigned to station 2, task 2 is assigned to station 1 etc. Table 2 can be
modified into different for all the tasks that is assigned to each station under each feasible
solution, which is not presented here.

Table 3: Total time taken by each station for the Buxey 29 Tasks problem

Table 3 shows the total time taken by each station under each solution. Of all the
solutions, Solution 1 and 2 provides the best cycle time of 324 sec. depending upon the
complexity of tasks and ease of operation, either Solution 1 or Solution 2 can be chosen. The
cycle time for both these solutions is 41 sec.

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Table 4: Feasible solutions for 9 stations for the Buxey 29 Tasks problem.

Again, the number of stations are varied from 8 to 9 and the algorithm as mentioned
in Sec. 3 is run. In this case, there are 16 feasible solutions are obtained as shown in Table 4.
By increasing the number stations, there is a significant increase in the number of solutions.
However, the best solution for practical implementation to be chosen based on the minimum
cycle time and the complexity involved in transportation and assignment of tasks to these
stations. The cost of other resources also should be considered when choosing the best
feasible solution.

Table 5: Total time taken by each station for the Buxey 29 Tasks problem.

Here again, the solution 1 yields the best possible solution since the cycle time is
minimum of all. Solution 1 takes a total time of 324 sec which is same as in the case of 8
station model. The cycle time in this case is 38 sec. If the cost of installation of the stations is
given priority, it is the 8 station model, which suits best for this problem over 9 station model.

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Table 6: Feasible solutions for 10 stations for the Buxey 29 Tasks Problem.

Again, by increasing the number of stations from 9 to 10, 16 feasible solutions are
obtained. From Table7 the best solution yields 324 sec of total time and a cycle time of 34
sec. By increasing the number of stations, there in change in the number of feasible solutions
and the same kind behavior is noticed when the number of stations further increased to 11, 12
and so on. Although the cost of installation of stations increases when the number of stations
is increased, it provides the best flexibility in maintenance of the stations.

Table 7: Total time taken by each station for the Buxey 29 Tasks problem

CONCLUSIONS

In this work, the single model assembly line problem or equivalent model of multi
model assembly line problem are solved for minimum number of stations and minimum cycle
time. The number of stations are varied from 8 to 10 and the feasible solutions for each case
are derived. By increasing the number of stations from 8 to 10, the total time remain as 324
sec for solution 1 and the cycle time has decreased from 41 sec to 34 sec. The number of
feasible solutions increased from 9 to 16 when the number stations are changed from 8 to 9,
but there is no improvement after that. Depending up the resources available, one can choose

160


the number of stations as 8 or 9. Eight stations model yield less installation and maintenance
cost, whereas the 9 station model provides best ease maintenance and operation. As future
work, the models can be tried with multi models as an extension and optimization of cycle
time and smoothening of the task assignment can be tried.

REFERNCES

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Volume 3, Issue 1, 2012, pp. 58 - 66, ISSN Online: 0976 - 6979, ISSN Print: 0976 – 6987.

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