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*Tu Chuanqing (1968~), Corresponding author, Associate professor, doctor.

Excel-Based Simulation on Problems of Two-Stage Assembly Line

Queuing

Qiao xianxia Tu Chuanqing*

College of Computer and Information EngineeringJiangxi Agricultural University

Nanchang Jiangxi China

E_main: Qiao Xianxia@163.com chuanqingtu@yahoo.com.cn

Abstract: It is difficult to design mathematic

models for the problems of assembly line

queuing in the workshop, and simulation is

usually made in the computer. But it requires

that the researchers have high level of computer

proficiency to build up a simulation model with

a computer language. Taking Excel as a tool, we

have established a simulation model for the

problems of two-stage assembly line queuing.

With this model, we can not only easily examine

the production efficiency of this assembly line,

but also examine whether enlarging the space

between the two workstations could impose

some influences upon the productivity of

assembly lines and the waiting time.

Keywords: assembly line; queuing problems;

simulation model

0 Preface

It is often impossible to construct a

mathematic model because the problems of

assembly line queuing occur continuously and in

parallel. However, it is often no problem to

simulate these queuing problems. Presently,

there are plenty of literatures related to

simulation on problems of two-stage assembly

line queuing. But it requires that the researchers

have high level of computer proficiency to buildup a simulation model with the computer

language, which, to some extent, hinders the

application and popularity of such a model. In

this paper, taking Excel as a tool, we introduce a

method of setting up a simulation model on

problems of two-stage assembly line queuing.

1 Problems of Two-Stage Assembly Line

Queuing

Figure 1 represents two workstations on an

assembly line in which A is operating

Workstation 1 and B Workstation 2 respectively.

The products finished by A at Workstation 1 will

be passed to Workstations 2 at which B

continues to process. The volume of products is

an important factor for consideration in the

design and analysis of such an assembly line,

because the product storage of each workstation

will have effects on the workers efficiency. On

the assembly line in Figure 1, suppose that the

two workstations are connected and that there is

no place for the semi-finished products, two

possible cases will take place as follows: If Aworks more slowly than B, B is forced to wait;

but if A is faster than B on the contrary, then A

has to wait.

In the simulation of this problem, suppose

A is the first worker on the assembly line, then

he can work on the semi-finished products at any

time. Therefore, we focus our analysis on the

mutual influences between A and B.

Figure 1Two Workstations on an Assembly

Line

2011 International Conference on Business Computing and Global Informatization

978-0-7695-4464-9/11 $26.00 2011 IEEE

DOI 10.1109/BCGIn.2011.130

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1.1 Research Targets

About the assembly line, we hope that this

research will help solve the following problems:

i) how much is the average time for each worker

to complete the work? ii) what is the

productivity of this assembly line? iii) how longwill A wait for B? iv) how long will B wait for

A? v) how will it affect the productivity, the

waiting time and other factors that the space

between the two workstations are enlarged to

deposit semi-products and that workers

independence is increased subsequently?

1.2 Data Collection

For a systematic simulation, we need the

data about As and Bs processing time. To

collect the data, a feasible method is to divide

the total processing time into short periods, ineach of which each worker is observed

individually. In this example, we divide the

processing time, 10 seconds a period. A is

observed at work 100 times, but B only 50 times.

The times for the observation of the two at work

are different. We know that the more times for

the observation and the smaller division of the

time intervals, the more accurate the research

result. We make a table about the processing

time as shown in Table 1 below.

Table 1 The Data of Observation on the Two

Workers

In Table 2, we show the random intervals

distributed by the ratio of the data collected from

the actual observation. For example, four out of

one hundred times A has completed his

operations within 10 seconds. If one hundred

numbers are allocated, we should allocate four of

them to those operations completed within 10

seconds. These four numbers can be random,

such as 42, 18, 12 and 93, which though will

make our search very complicated. For a

convenient search, we allocate them with such

consecutive numbers as 00, 01, 02, 03. For the

fifty observed data of B, we can use two

methods to allocate the random numbers. In the

first method, we use fifty numbers like 00 to 49

for distribution and omit in the simulation all

those numbers larger than 49. However, this is a

great waste that we will discard half of the

numbers in the random sequence. In the secondmethod, we duplicate the frequency number. For

example, we distribute 00 through 07 to eight

out of one hundred observed data whose

processing time is within 10 seconds instead of

distributing 00 through 03 to four out of fifty

times whose processing time is within 10

seconds. In this way, the times for observation

are doubled while the ratio remains the same.

Table 2 The Random Intervals of A and B

2 Simulation Model on Two-Stage Assembly

Problems

2.1 Manual Simulation

Table 3 shows the results of manual

simulation of A and B processing 10 products.

The random numbers come from the Table of

Random Numbers, from the first column of

double-digit, the numbers are selected

downwards.

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If we count the time from zero and measure

it by the second, the first random number 56 is

corresponding to 50 seconds in which A

completes the first processing task. Then this

taskpiece is transmitted to B who starts at 50

seconds. The next random number is 83, and

according to Table 2, it takes B 70 seconds to

complete the taskpiece. Simultaneously, A is

processing a second taskpiece, starting from at

50 seconds and ending at 100 seconds (the

corresponding random number is 55). However,

A cannot start processing a third taskpiece

immediately afterwards as B completes the first

taskpiece at the 120th second. Consequently, A

has to wait 20 seconds before processing a

fourth one. With the same method of counting

above, we can calculate the rest data in the table:with a random number and the corresponding

processing time, we can figure out the waiting

time and the completing time. Then we can find

that the waiting time for both A and B is very

long because there is no storage place between

the two workstations.

Table 3: A and BSimulation of

Two-Stage Assembly Line

Now, we can answer some questions and make

some comments on the system. For example,

The average processing time of each

workpiece: 610/10=61 second;

The average processing time of worker A:

470/10=47 second;

The average processing time of worker B:

440/10=44 second;

The utilization of worker A: 470/540=87%;

The utilization of worker B:

440/560=78.6% (the initial 50 seconds for

waiting is removed)

Although we have explained how to build a

simple manual simulation on this problem, the

sample of 10 drawings is too small to warrant

the result reliability. A more reliable result could

be attained only through thousands of repeated

calculations on the computer.

2.2 Simulated by Excel

Figure 2 shows the partial results of the

simulation by Excel on the two-stage assembly

lines, which is in the same format as that of the

manual simulation in Table 2. This time, we

have used Excel to simulate 1, 000 times,

namely we suppose that A and B have processed

1,000 workpieces in total. Its specific operating

procedure is as follows:

Step one, generating random numbers by

the function RANDBETWEEN ()A fundamental step for any method of

simulation is to generate random variables

related to the distribution function. In this

example, the distribution function is about the

time for A and B to complete each taskpiece.

The function RANDBETWEEN () can generate

a random number for any pair of specified values.

What we need now is to generate the random

numbers between 0 through 99, which can be

attained by the function RANDBETWEEN (). In

Table 4, the 2nd

and 7th

columns are randomseries generated by =RANDBETWEEN(0,99),

representing the random numbers corresponding

to the time for A and B to complete each

taskpiece.

Step two, establishing the relation between

the random numbers and the processing time by

the function VLOOKUP

According to the distribution rules of

random numbers specified in Table 2 above, we

can establish the relation between the processing

time and the random number by the function

VLOOKUP. The method is to input 0 ~ 99

sequentially in the cell A3~A102, and then

according to the distribution rule of random

numbers to input in the cells B3~B102 and

C3~C102 separately the corresponding time for

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A and B to complete their processing work.

Figure 2 A and Bthe Simulation of

Two-Stage Assembly Lines by Excel

Table 4 Excel Cell Formula in Figure 2

The simulation technology being an

analysis tool, its dynamic characteristics

determine its advantages in quantitative analyses.

But an analytical method is different, which

indicates the average result of the long-term

operation of a system. As is shown in Figures 3

and 4, we can find a visible start-up. Figure 3

exhibits the average time for A and B to

complete 100 processing taskpieces. These data

are accumulative, i.e., the first datum is

generated randomly corresponding to thecompleting time for the first taskpiece. The

average completing time for two taskpieces is

the average value of the time to complete the

first taskpiece plus that to complete the second

one. By analogy, the average completing time

for three taskpieces is the average value of the

time to complete the first one plus those for the

second and the third ones respectively, and so

forth.

Note that the curve can be in different

shapes rather than exactly what is shown in thefigures below because the initial part of the

curve is determined by the flow of the generated

random numbers. What we are sure of is that

within a short period of time after the start-up of

the system, the average processing time is

fluctuant and then tends to be stable slowly.

Figure 3 Average Processing Time for Each

Workpiece

Figure 4 shows the average stay time in the

system, which includes the processing time and

the waiting time for each taskpiece. For

examplein Figure 2 the stay time for the first

taskpiece is 90 seconds in the system, which is

the sum of the cells G3, I4 and L3. And the stay

time for the 2nd

taskpiece is 120 secondsthesum of the cells G4, I4 and L4. And by analogy,

we can attain the stay time for the 1, 000 th

taskpiece in the system. At the start-up stage, we

can see in the curve trend of gradual increase,

because the system is started up from the idle

state when there is no interval in the process of

transferring the taskpieces from A to B.

However, as the 2nd taskpiece enters the system,

there is possibly a wait between two procedures

because of the inconsistent speed of A and B and

of no storage place between the two

workstations, which forces the taskpieces

entering afterwards to delay. As the time goes by,

the taskpieces transmission will tend towards

stability unless the working capacity in the 2nd

procedure is weaker than that in the 1st one.

Figure 4 Average Stay Time of Products in the

System

According to the simulation data in Figure

2, we can also produce some indices to

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investigate the system efficiency as is shown in

Table 5 below:

Comparatively, the result of the manual

simulation of 10 taskpieces is not too bad. The

average working time for A and B is 46.13 and

46.31 seconds respectively, which is very close

to the expected average value from the long-term

operations. The expected working time for A is

104+206+3010+/100=45.9 seconds,

and that for B is10 4+20 5+30 6+

/50=46.4 seconds.3 Research on the Storage Space Between Two

Workstations

A research on the storage space between of

two workstations is also very significant. We can

solve this problem by comparing the data of

productivity and utility in different storage

places. In the previous sections, we have built up

a simulation on the situation where there is no

storage space between two workstations. In a

second simulation, we create a storage space and

record some possible changes about the related

data. And then we set up other simulations on

the second, third, and so on, storage spaces.

With these data generated, decision makers can

calculate the cost increased to build more storage

spaces and the benefits brought about by the

improved productivity, and then make a

comparison of the cost and the benefits. More

storage spaces between two workstations

probably means a larger workshop, more

materials and taskpieces in the system, more

material handling equipment, transmission

equipment, and more use of heat and electricity,

as well as more maintenance of the workshop,

etc.

References

[1] Richard B. Chase, etc. Operations

Management for Competitive Advantage

[M].Beijing: Machinery Industry Press,2003.

[2]Hu Yunquan. Operations Research Tutorial

2nd edition [M]. Beijing: Tsinghua

University Press, 2003.

[3]Zhou Dehui Zuo Qi Li Changwen,

Application on Excel in Modern

Management [M]. BeijingPublishing House

of Electronics Industry1997.

[4]Chen Xuesong, Fang Rengcun, Cao Ju,

Research on Statistics Calculation of

Simulation Queuing System [J]. ComputerSimulation, 2003, (7).

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