https://doi.org/10.31449/inf.v43i1.2676 Informatica 43 (2019) 39 –43 39 
Improving Flow Lines by Unbalancing 
Zsolt Mihály 
Optasoft Kft., 1051 Budapest, Hungary 
E-mail: zsolt.mihaly@optasoft.hu, www.optasoft.hu 
 
Zoltán Lelkes 
Department of Information Technology, Pallasz Athéné University, 6000 Kecskemét, Hungary 
E-mail: lelkes.zoltan@gamf.kefo.hu, www.uni-pae.hu 
 
Keywords: flow line, throughput, cycle time, work-in-process  
Received: October 30, 2018 
The paper's aim is to show how the performance of a balanced manufacturing flow line can be improved 
on the critical WIP level by making it unbalanced to some extent. The explanation and a quantitative 
example are presented. There is a trade-off between system balance and stability, and it can be handled 
as an optimization problem. Data are gathered using a physical simulation system. The analysis is carried 
out with a discrete time simulation program which applies next-event time advance mechanism. The model 
has been implemented in AIMMS modelling language. 
Povzetek: V prispevku je prikazana uporaba rahle neuravnoteženosti pri kritičnih opravilih na sicer 
uravnoteženih opravilih tekočega traku. Model je bil implementiran v jeziku AIMMS in rezultat 
ovrednoten s pomočjo diskretne simulacije. 
1 Introduction 
The world makes great efforts to diminish the ecological 
footprint of humanity. For this reason, companies have to 
meet more and more regulations; corporations are forced 
to be more efficient. Thus, researches on environmentally 
benign business practices receive more and more attention 
[12]. One of the main interests is to improve production 
systems, like production of cars, pharmaceutical 
ingredients or electrical goods. It not only diminishes the 
ecological footprint, but also increases the profitability of 
the company by higher productivity, lower response time 
or lower inventory level. 
Discrete manufacturing systems can be classified by 
several disciplines. Following Govil and Fu [4], the 
manufacturing systems can be  
• job shops,  
• flow lines,  
• flexible manufacturing systems, 
• assembly systems.  
Manufacturing systems consist of stations. They are 
atomic processes, that is to say, they cannot be divided 
further. The main characteristic of a station is its process 
time. This is the time needed to process an entity. It is a 
scalar in a deterministic model, and a random variable in 
a stochastic model. In the latter case, process time has a 
mean, a variance, and a type of probability distribution 
function. 
The research of manufacturing systems uses diverse 
modelling techniques, e.g., simulation models [13], 
queueing theory and Petri nets [9].  In this paper, flow 
lines are investigated using physical experiments and a 
discrete time simulation model. In flow lines, stations are 
connected in a linear way (see Figure 1). Some examples 
from the literature contain investigations into flow line 
with common buffer [16], complex optimization problems 
where the flow line is only one element in the model [8] 
or more complicated systems. Huang and Li examined a 
two-stage hybrid flow shop with multiple product families 
[7]. Simulation modelling has a wide range of applications 
in engineering-aided manufacturing regarding system 
performance. Modelling apparel assembly cells [1], a 
Mercedes-Benz production facility [10], or analysing the 
performance of a Korean motor factory [2] are only some 
of the examples. 
Hopp and Spearman [6] investigated flow lines in 
which there is only one machine per station, one job class, 
no capacity constraint, and the queueing principle is first 
in, first out (FIFO). Three main modelling measures are 
proposed by them: 
 
Figure 1: The general structure of a flow line (B: buffer, P: process). 

40 Informatica 43 (2019) 39 –43 Z. Mihály et al.  
 
• Throughput (TH): the number of entities (cars, 
apples, people, etc...) coming out from the system 
during a given time 
• Cycle time (CT): the time an entity spends in the 
system 
• Work-in-process (WIP): the number of entities 
residing in the system at the same time 
The system performs better if it has a higher TH or a lower 
CT. These parameters are not independent from each 
other. Little's law makes a connection among them: 
𝑊𝐼𝑃 = 𝑇𝐻 × 𝐶𝑇 
According to the previous equation, the optimal value 
of WIP in a deterministic system is 
𝑊 0
= 𝑇 0
× 𝑟 𝑏 
Where 
• Bottleneck rate (𝑟 𝑏 ): the rate of the station that has the 
highest utilization 
• Raw process time (𝑇 0
): the sum of the average 
process times in the flow line 
• 𝑊 0
 is called the critical WIP level ([6]). 
 
The variability of procedures is measured with the 
coefficient of variation (CV): 
𝐶𝑉 =
𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑚𝑒𝑎𝑛 
Hopp and Spearman use two so called characteristic 
functions to analyse the performance. The dependent 
variables are the TH and the CT, while the independent 
variable is the WIP level both times. The flow line is 
modelled as a closed network. It means that the level of 
WIP is a model parameter [14]. Regarding performance 
analysis, three important concepts were introduced [6]: 
Best case performance: the best possible performance 
for a line. It is balanced, and there is no batching.  
Worst case performance: the worst possible 
performance for a line. All the entities move in one batch. 
Practical worst case (PWC): as the worst case 
performance is so bad that it is far from practical instances, 
PWC was introduced to define a realistic worst case. 
The paper's aim is to show how the performance of a 
balanced manufacturing flow line can be improved on the 
critical WIP level by making it unbalanced to some extent. 
The explanation and a quantitative example are presented. 
There is a trade-off between balance and stability, and it 
can be handled as an optimization problem.  
2 Method of examination 
In this research, the same characteristics are used to 
evaluate the performance as in [5]. Both physical and 
simulation model experiments are performed to gather 
data. Both models are flow lines with FIFO queueing 
discipline containing single machine stations, one job 
class and using constant work-in-process (CONWIP) 
control. It means that a new entity arrives into the system 
only when another one leaves it. 
In the physical model experiment, a toy car factory 
has been realized with the assumption of infinite raw 
material stock. The entire process to build a small car takes 
4 minutes. In an arbitrary way, the operations could be 
distributed among 4 production processes where one-one 
person works with different abilities. Beside the four 
production processes, there is a transport process as well. 
Altogether there are 5 stations. 
Building a simulation model consists of three levels. 
There is a superstructure which can represent all the 
possible flow lines. Beside this, there is a mathematical 
model and an algorithm. Based on the algorithm, a discrete 
time simulation program with next-event time advance 
mechanism is worked out. Comparing with fixed-
increment time advance method, it is more complicated, 
but more efficient regarding computational need [15]. 
The simulation program is implemented in AIMMS 
modelling language [11]. It has already been used in other 
studies with success. E.g., [3] used it on supply chain 
optimization with homogenous product transport 
constraints. The simulation program can be easily 
extended in this environment. AIMMS is linked to the 
most modern solvers, which are easily integratable. 
Furthermore, it has an advanced graphical user interface, 
which can be used for creating simply usable and 
ergonomic softwares. 
3 Results 
3.1 The explanation of the trade-off 
Regarding a given raw process time (𝑇 0
), a deterministic 
balanced line performs better than a deterministic 
unbalanced line. On the other hand, the balanced line has 
a worse stability regarding variability [6] . 
Let us investigate a balanced system whose raw 
process time is 𝑇 0
, and has n stations. It is true in this case 
that 
∀𝑖     𝑇 𝑖 =
𝑇 0
𝑛 
(𝑇 𝑖 denotes the average process time of the i-th 
station) That is to say, all the process times are the same. 
So the bottleneck rate: 
𝑟 𝑏 =
𝑛 𝑇 0
 
If the system with the raw process time 𝑇 0
 is 
unbalanced then 
∃𝑖     𝑇 𝑖 >
𝑇 0
𝑛 
From this, it can be concluded that for the unbalanced 
system 
𝑟 𝑏 <
𝑛 𝑇 0
 
The TH of a deterministic system is calculated in the 
following way: 
𝑇𝐻 = min {
𝑊𝐼𝑃 𝑇 0
, 𝑟 𝑏 } 

Improving Flow Lines by Unbalancing Informatica 43 (2019) 39 –43 41 
The two systems have the same performance until  
𝑊𝐼𝑃 ≤ 𝑟 𝑏 𝑇 0
 
After that the balanced system works better because it 
has a higher 𝑟 𝑏 . This proves that a balanced line has a 
better performance in this case 
It is harder to prove mathematically that a balanced 
line is less stable. Nonetheless, this effect could be seen 
when investigating the physical model. In this section, an 
example is shown. Two flow lines are compared. For both 
of them, 𝑇 0
= 8ℎ, and each of them contains four stations. 
In the balanced line 
∀𝑖     𝑇 𝑖 = 2ℎ 
In the unbalanced line, the first station is the 
bottleneck, its process time is 5h, and 1h regarding the rest 
of them. In the stochastic case for both systems 
∀𝑖     𝐶𝑉
𝑖 = 1 
The characteristics of the flow lines are summed up in 
Table 1. 
The results of the experiment can be seen in Figure 2. 
Relative changes are displayed on the ordinate, which 
shows the deteriorating effect of variability from a 
different aspect as usual characteristic functions. The 
reason for applying it is that it is easier to see the 
difference in the drop of performance regarding WIP. 
These characteristics are calculated in the following way.  
𝑇𝐻
𝑟𝑒𝑙 =
𝑎𝑏𝑠 (𝑇𝐻
𝑠𝑡𝑜𝑐 ℎ
− 𝑇𝐻
𝑟𝑒𝑙 )
𝑇𝐻
𝑠𝑡𝑜𝑐 ℎ
 
𝐶𝑇
𝑟𝑒𝑙 =
𝑎𝑏𝑠 (𝐶𝑇
𝑠𝑡𝑜𝑐 ℎ
− 𝐶𝑇
𝑟𝑒𝑙 )
𝐶𝑇
𝑠𝑡𝑜𝑐 ℎ
 
 Balanced Unbalanced 
𝑇 1
 2h 5h 
𝑇 2
 2h 1h 
𝑇 3
 2h 1h 
𝑇 4
 2h 1h 
𝐶𝑉
1
 1 1 
𝐶𝑉
2
 1 1 
𝐶𝑉
3
 1 1 
𝐶𝑉
4
 1 1 
Table 1: The characteristics of the investigated flow lines 
Both of the diagrams show that the extent of 
deterioration is bigger when the line is balanced. In this 
case, the maximal TH decrease is 42% in the balanced 
system, and 18% in the unbalanced one. The maximal CT 
increase is 73% when the flow line is balanced; 22% when 
it is unbalanced. It means that the maximal deterioration 
of TH is twice as high in balanced lines as in unbalanced 
lines, and the maximum of CT deterioration is three times 
as high. That is, evidence is shown that balanced line has 
less stability regarding variability. The same phenomena 
could be observed in each physical experiments. The loss 
of TH and the growth of CT increase until the critical WIP 
value is reached. After the peak, both functions begin to 
decrease. At high WIP levels, they will converge into 0. 
Table 2 sums up the results regarding the peaks. 
 
a) Decrease of TH 
 
b) Increase of CT 
Figure 2: The stability of flow lines regarding variability 
 Balanced Unbalanced 
TH 42% 18% 
CT 173% 122% 
Table 2: Comparison of the maximal deteriorations 
3.2 A quantitative example for system 
unbalancing 
In this section, a quantitative example is shown in which 
the unbalanced system has a better performance on the 
critical WIP level. Three systems are compared: a 
balanced and two unbalanced. The balanced system has 
uniform process times of 1 hour. The CV of the first three 
stations are equal to 0.1, and the last station's CV is 1. In 
the unbalanced systems, the process times of three 
operations are 1.15 hour, and there is one with 0.55 hour. 
That is, they differ in the position of the non-bottleneck 
process. The station with the process time of 0.55 hour has 
CV = 1. The CV of the bottlenecks are 0.1. The 
characteristics of the investigated systems can be seen on 
Table 3. 
 
0
5
10
15
20
25
30
35
40
45
1 3 5 7 9
Relative TH decrease [%]
WIP [-]
Balanced Unbalanced
0
10
20
30
40
50
60
70
80
1 3 5 7 9
Relative CT increase [%]
WIP [-]
Balanced Unbalanced

42 Informatica 43 (2019) 39 –43 Z. Mihály et al.  
 
 
Balanced 
Unbalanced 
(first three are 
bottlenecks) 
Unbalanced 
(last three are 
bottlenecks) 
𝑇 1
 1h 1.15h 0.55h 
𝑇 2
 1h 1.15h 1.15h 
𝑇 3
 1h 1.15h 1.15h 
𝑇 4
 1h 0.55h 1.15h 
𝐶𝑉
1
 0.1 0.1 1 
𝐶𝑉
2
 0.1 0.1 0.1 
𝐶𝑉
3
 0.1 0.1 0.1 
𝐶𝑉
4
 1 1 0.1 
Table 3: The characteristics of the investigated flow lines. 
The critical WIP level of the flow line can be 
calculated in the following way: 
𝑊 0
= 𝑟 𝑏 × 𝑇 0
= 1
1
ℎ
× 4ℎ = 4 
The positions of the bottleneck procedures have no 
effect in the unbalanced systems (Figure 3/b, 3/c). In the 
deterministic case, the balanced system performs better, as 
expected. On the other hand, when there is variability, the 
unbalanced flow line has a better output on the critical 
WIP level (see Table 4, 5). According to the experiments, 
the TH of the unbalanced system can be 9-11% higher 
compared with the balanced line, the CT is 8-9% lower. 
The results confirm the assumption that there is a trade-off 
between balance and stability, and it can be handled as an 
optimization problem. 
 
 Balanced Unbalanced 
TH [1/h] 1 0.87 
CT [h] 4 4.6 
Table 4: the performance of the investigated system on the 
critical WIP level in the deterministic case 
 Balanced Unbalanced Improvement 
TH  0.74 1/h 0.82 1/h 11% 
CT 5.38 h 4.90 h 9% 
Table 5: the performance of the investigated system on the 
critical WIP level in the stochastic case 
4 Conclusion 
Endeavours are generally made to balance flow lines. This 
is an intuitive idea, and earlier researches showed 
examples where unbalanced systems had worse 
performance. In this paper, it has been shown that 
unbalancing the flow line in a small extent achieves better 
performance on the critical WIP level, that is to say, higher 
TH and lower CT. In the examined case, the TH was 9-
11% higher and the CT 8-9% lower on the critical WIP 
level. 
This result is important in flow lines as well where the 
manufacturing is precise, but there are several products. 
Each of them might have a low variability, but the 
variability of the stations ’ process times can be high if the 
average process times of products are different. 
 
 
a) Deterministic 
 
b) Stochastic (First three processes are bottlenecks) 
 
c) Stochastic (Last three processes are bottlenecks) 
Figure 3: Comparison of the performance of a balanced 
and two unbalanced systems. 
 
 
0
5
10
15
20
25
30
0
0,2
0,4
0,6
0,8
1
1,2
1 3 5 7 9
CT [h]
TH [1/h]
WIP [-]
Balanced TH Unbalanced TH
Balanced CT Unbalanced CT
0
5
10
15
20
25
30
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
1 3 5 7 9
CT [h]
TH [1/h]
WIP [-]
Balanced TH Unbalanced TH
Balanced CT Unbalanced CT
0
5
10
15
20
25
30
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
1 3 5 7 9
CT [h]
TH [1/h]
WIP [-]
Balanced TH Unbalanced TH
Balanced CT Unbalanced CT

Improving Flow Lines by Unbalancing Informatica 43 (2019) 39 –43 43 
List of symbols 
CT Cycle time 
TH Throughput 
WIP Work-in-process 
𝑇 0
 Raw process time 
𝑟 𝑏 Bottleneck rate 
𝑊 0
 Critical WIP level 
𝑇 𝑖 Average process time at station i 
𝐶𝑉
𝑖 Coefficient of variability at station i 
n Number of stations 
References 
[1]  J. T. Black and B. J. Schroer. Simulation of an 
apparel assembly cell with walking workers and 
decouplers. Journal of Manufacturing Systems, 
12(2):170-180, 1993. 
https://doi.org/10.1016/0278-6125(93)90016-M 
[2]  K. Cho, I. Moon, and W. Yun. System analysis of a 
multi-product, small-lot-sized production by 
simulation: A Korean motor factory case. Computers 
& Industrial Engineering, 30(3):347-356, July 1996. 
https://doi.org/10.1016/0360-8352(96)00003-4 
[3]  T. Farkas, Z. Valentinyi, E. Rév, and Z. Lelkes. 
Supply chain optimization with homogenous product 
transport constraints. In Computer Aided Chemical 
Engineering, volume 25, pages 205-210, 2008. 
https://doi.org/10.1016/S1570-7946(08)80039-9 
[4]  M. Govil and M.C.Fu. Queueing theory in 
manufacturing: A survey. Journal of Manufacturing 
Systems, 18(3):214-240, 1999. 
https://doi.org/10.1016/S0278-6125(99)80033-8 
[5]  W. J. Hopp. Supply Chain Science. Waveland Pr Inc, 
Long Grove, Illinois, 2011. 
[6]  W. J. Hopp and M. L. Spearman. Factory Physics. 
McGraw-Hill Education, New York, New York, 
2000.  https://doi.org/10.1036/0256247951 
[7]  W. Huang and S. Li. A two-stage hybrid flowshop 
with uniform machines and setup times. 
Mathematical and Computer Modelling, 27(2):27-
45, January 1998. 
https://doi.org/10.1016/S0895-7177(97)00258-6 
[8]  J. Olhager and B. Rapp. Balancing capacity and lot 
sizes. European Journal of Operational Research, 
19(3):337-344, March 1985. 
https://doi.org/10.1016/0377-2217(85)90130-4 
[9]  H. T. Papadopoulos and C. Heavey. Queueing theory 
in manufacturing systems analysis and design: A 
classification of models for production and transfer 
lines. European Journal of Operational Research, 
92(1):1-27, July 1996. 
https://doi.org/10.1016/0377-2217(95)00378-9 
[10]  Y. H. Park, J. E. Matson, and D. M. Miller. 
Simulation and analysis of the Mercedes-Benz all 
activity vehicle (aav) production facility. In 
Proceedings of the 1998 Winter Simulation 
Conference, pages 921-926, December 1998. 
https://doi.org/10.1109/WSC.1998.745790 
[11]  M. Roelofs and J. Bisschop. AIMMS The user's 
guide. AIMMS B.V., AP Haarlem, The Netherlands, 
2016. 
[12]  J. Sarkis. A strategic decision framework for green 
supply chain management. Journal of Cleaner 
Production, 11(4):397-409, June 2003. 
https://doi.org/10.1016/S0959-6526(02)00062-8 
[13]  J. S. Smith. Survey on the use of simulation for 
manufacturing system design and operation. Journal 
of Manufacturing Systems, 22(2):157-171, 2003. 
https://doi.org/10.1016/S0278-6125(03)90013-6 
[14]  W. Whitt. Open and closed models for networks of 
queues. AT&T Bell Laboratories Technical Journal, 
63(9):1911-1979, November 1984. 
https://doi.org/10.1002/j.1538-7305.1984.tb00084.x 
[15]  W. L. Winston. Operations Research: Applications 
and Algorithms. Cengage Learning, Boston, 
Massachusetts, 2003. 
[16]  H. Yamashita and S. Suzuki. An approximation 
method for line production rate of a serial production 
line with a common buffer. Computers & Operations 
Research, 15(5):395-402, 1988. 
https://doi.org/10.1016/0305-0548(88)90056-1 
  

44 Informatica 43 (2019) 39 –43 Z. Mihály et al.