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CHEMICAL ENGINEERINGTRANSACTIONS 
 

VOL. 55, 2016 

A publication of 

 
The Italian Association 

of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors:Tichun Wang, Hongyang Zhang, Lei Tian
Copyright © 2016, AIDIC Servizi S.r.l., 
ISBN978-88-95608-46-4; ISSN 2283-9216 

Flexible Manufacturing Cell Formation of Processing 
Workshop based on Intelligent Computing 

Jurong Liu 
School of Mechanical Engineering, Shaanxi University of Technology, Shaanxi, China. 
124505282@qq.com 

Flexible manufacturing cell model of multiple workshops is constructed, which combines the advantages of 
physical manufacturing cell and logical manufacturing cell. A cell formation method based on adaptive inertia 
weight PSO is worked out, which considers the layout of manufacturing resources, the selection of processing 
path and the setting of processing batches. The experiment proves that the method can effectively reduce the 
total manufacturing cost. 

1. Introduction 
Design process of unit manufacturing system (cellular Manufacturing system, CMS) is called cell formation, 
and based on different environment, many scholars put forward different cell formation method. Defersha and 
Chen analysed manufacturing resources environment of multiple cycles, multiple processing routes and multi-
types, which reduced the total cost of production by optimizing the production batch, and resource quantity 
(Defersha and Chen, 2008). Manufacturing resources of the same unit is arranged in the same physical 
location to form physical manufacturing cell. Safaei and Saidi proposed a cell formation model in the similar 
dynamic environment, the objective function of which aimed to get the lowest cost of machine purchase cost, 
machine operating cost, material moving cost and cell reformation cost (Safaei and Saidi, 2008). 
Wu et al. investigated the physical manufacturing cell formation method based on machine layout under the 
condition of considering the layout of the manufacturing resources position (Wu et al., 2007). Wang and Wang 
investigated logical manufacturing cell formation under the premise of analysing additional cost of cross cell 
manufacturing, which did not change its physical location, and divided manufacturing resources into cells 
logically (Wang and Wang, 2004). Most researches on cell formation considering certain types of processed 
products, processing requirements, product type demand and environmental issues of certain available 
resources, a separate physical manufacturing unit or logical manufacturing unit was used to build cells 
respectively. Although manufacturing cells formed by these two methods have achieved good results, in the 
cloud manufacturing environment, selected manufacturing resources were not limited to this manufacturing 
cell, this workshop or this enterprise. There are still some problems and technical difficulties which have not 
been satisfactorily resolved (Wang et al, 2012; Li et al, 2011; Jozef et al, 2011; Yang et al, 2011). First of all, 
physical manufacturing cells are used to build MC, although it is in favour of transport and management 
control of processed products, some cloud manufacturing resources may not be able to be moved or moving 
costs is very high in the actual production process, which leads to the results that cell formation cannot be 
practical. If logic manufacturing unit construction method is used, physical layout of manufacturing resources 
does not need to changed, which can form manufacturing cell promptly. But it does not change the physical 
location of manufacturing resources; it may cause huge transportation costs and times. Secondly, in the cell 
formation process, a part of manufacturing resources are moved into groups to reduce transport costs and 
product time. But in the cloud manufacturing environment, manufacturing resources may be distributed in 
several different units, workshops or enterprises, so how to consider the layout of manufacturing resources in 
different workshops will inevitably become a key issue in the cell formation. In addition, there are more choices 
for products processing methods and processing path in the cloud manufacturing environment. Therefore in 
the cell formation process, how to assign multiple tasks and set batches become important factors affecting 
cell formation flexibility. In the next section, manufacturing resource layout description and mathematical 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1655037

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Liu J.R., 2016, Flexible manufacturing cell formation of processing workshop based on intelligent computing, 
Chemical Engineering Transactions, 55, 217-222  DOI:10.3303/CET1655037   

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model is investigated. In Section 3, flexible manufacturing cell formation based improved PSO (Yannis and 
Magdalene, 2010; Lin et al, 2010; Fan et al, 2004; Erwie and Hu, 2008) is proposed. In section 4, the 
proposed flexible manufacturing cell formation method is used in the cloud manufacturing environment. 
Finally, we conclude our paper in section 5. 

2. Manufacturing resource layout description and mathematical model 
Researched manufacturing environment is as follows. A certain type and number of cloud manufacturing 
resources (machines) are distributed in workshops of different companies. In order to meet different 
production tasks, physical layout can be carried out for manufacturing resources and the movement of 
manufacturing resources will produce re-layout costs. For a given set of tasks, processed products (artefacts) 
have more than one species, and at the same time, each product has more than one processing path. In the 
processing of the product, the product can be processed by a different path. Considering the above 
environment, through effective cell design, the following objectives are required to achieve. (1) For the 
corresponding tasks, assign optimal processing path, in order to improve the use efficiency of processing 
resources. (2) Layout optimization is carried out for manufacturing resources distributed in different processing 
workshops, consider the path of processing tasks, the number of processing cells and cell formation and 
adjust the machine layout to achieve the smallest manufacturing costs. 
For the above requirements, physical manufacturing cell and virtual manufacturing cell are combined. The 
processing systems (processing equipment and auxiliary equipment, etc.) of the traditional manufacturing 
enterprises in different regions, logistics systems (transportation, storage and handling equipment, etc.) and 
control systems (planning, scheduling, process control, etc.) are effectively combined to construct a flexible 
manufacturing cell for cloud manufacturing. Flexible manufacturing cell construction and task assignment 
process is shown in figure 1. 
 

 

Figure 1: Flexible manufacturing cell construction and task assignment process 

Flexible manufacturing cell construction and task assignment process is as follows. Specify the processing path 
for the processing tasks, while re-layout of manufacturing resources in different workshops is carried out. On 
this basis a new logic manufacturing cell is constructed. A single or multiple manufacturing resource (may 
belong to different processing workshop) is grouped virtually to process products with similar technology. 
The proposed flexible cell construction method based on manufacturing resources dynamical layout and 
manufacturing resources logical grouping is actually to seek an optimal compromise between physical 
manufacturing cell construction and logical manufacturing cell construction, and to achieve the purpose of 
reducing manufacturing costs. The mathematical model is as follows. p represents type of work, p=1, 2, …, P, 

218



NP represents processing number of work p. rp represents processing path serial number of work p, rp=1, 2, …, 
RP. J represents the number of workshops. m represents serial number of the manufacturing resources, which 
represents processing equipment used to complete processing tasks of work, m=1, 2, …, M. Krσ(p) represents 
the number of operation when work p adopting processing path rp. MDmj represents the initial position of the 
manufacturing resources in the system. If resource m  locates at processing workshop j, MDmj=1. On the 
contrary, MDmj=0. CCp represents additional cell processing cost when work p circulates among manufacturing 
cells. CRm represents movement cost of the manufacturing resource m. c represents serial number of the 
constructed manufacturing cell, c=1, 2, …, C, and C represents the maximum number of permitted cell. Wrp(p) 
represents resource sequence when adopting the rp-thtype of processing path to process work p. 
Wrp(p)=(W

1
rp(p), W

2
rp(p), …, W

k
rp(p)), W

k
p(p)∈(1, 2, …, M). Em represents processing ability of resource m within 

completion date. NC represents the maximum number of resources in the cell. NJ represents the maximum 
number of resources in the processing workshop. MCkrp(p) represents unit processing cost, when work p adopts 
the rp type of processing path to deal with the k-th procedure. MT

k
rp(p) represents processing time, when work p 

adopts the rp type of processing path to deal with the k-th procedure. CIp represents unit cost of transportation, 
when work p is moved in the same processing workshop. COp(i, j) represents the unit cost of transportation, 
when work p is moved between workshop i and workshop j, with COp(i, j)=0. Xrp(p) represents processed 
batches, when work p adopts path rp. Ymc represents whether resource m locates in the processing cell c. If it is 
in the cell, Ymc=1. Otherwise Ymc=0. Zmj represents whether resource m locates in the processing cell j. If it is in 
the cell, Zmj=1. Otherwise Zmj=0. 
The objective functions are shown from (1) to (6). 

( )

1 1 1

( ( ) ( ) ( ))
rp p

p r rp p
p

K pRP
k k

job r
p r k

C X p MC p MT p
= = =

= ⋅ ⋅    (1) 

1

( ) 1

( ) ( )
1 1 1 1 1

( ( ) ( , ) )
rp p

k k
p r rp p

p

K pRP J J

lo r p w p j w p j
p r k i j

C X p CO i j Z Z +
−

= = = = =

= ⋅ ⋅ ⋅     (2) 

1

( ) 1

( ) ( )
1 1 1 1

( ( ) )
rp p

k k
p r rp p

p

K pRP J

li r P w p j w p j
p r k j

C X p CI Z Z +
−

= = = =

= ⋅ ⋅ ⋅     (3) 

1 1

1
( )

2

M J

m m mj mj
m j

C CR MD Z
= =

= ⋅ −    (4) 

1

( ) 1

( ) ( )
1 1 1 1

1
( ( ) | |)

2

rp p

k k
p r rp p

p

K pRP J

e r P w p c w p c
p r k c

C X p CC Y Y +
−

= = = =

= ⋅ ⋅ −     (5) 

job lo li m eC C C C C C= + + + +   (6)  

The constraint is as follows: 

( , , )| ( )
( ) ( ) , 1, 2, ,k p p

rp

k
r r mp r k w p m

MT p X p E m M
∀ =

⋅ ≤ =    (7) 

1

1, 1, 2, ,
C

mc
c

Y m M
=

= =     (8) 

1
1, 1, 2, ,

J

mj
j

Z m M
=

= =     (9) 

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1

, 1, 2, ,
M

mc c
m

Y N c C
=

≤ =  .   (10) 

1
, 1, 2, ,

M

mj j
m

Z N j J
=

≤ =  .   (11) 

1
( ) , 1, 2, ,

p

p
p

R

r p
r

X p N p P
=

≤ =  .   (12) 

3. Flexible manufacturing cellformation based improved PSO 
PSO algorithm has many advantages, but also has disadvantage of precocity (Hu and Eberhart, 2002).In 
order to avoid falling into local optimum, adaptive inertia weight method is used to get rid of attract of local 
optimum point. Adaptive particle swarm optimization algorithmmakes a balance between global search and 
local search capability by means of adaptive inertia weight factor w, and determinesmutation probability based 
on convergence degree to escape from local optimum. A periodical attenuation adaptive strategy is proposed 
based on damping motion. 

max max

1
ln

max min( ) cos( )
A

t
T ww t w e t w

T
π

= +   
(13) 

wmax is the maximum value of w and wmin is the minimum value of w. Usually wmin=0.1, wmax=0.9. Tmax 
represents the maximum iteration number. A represents amplitude of w, when t=Tmax. T represents amplitude 
change cycle of inertia weight factor. A and T are determined according to test. Particle swarm optimization 
algorithm is always chasing individual extreme value pbest and global extreme value gbest in the iteration 
process and is easy to fall into local optimal solution. The proposed adaptive mutation is based on population 
average fitness variance, when the algorithm meeting the case of premature convergence, it can jump out of 
local optimum. Population average fitness variance is 

2

2

1

1
max

n
i avg

i i avg

f f
n f f

σ
=

 −
 =
 − 

  

 (14) 

1

1 n
avg i

i
f f

n =
=   

 (15) σ2represents population average fitness variance, n represents the number of particles in the particle swarm, fi 
represents fitness of particle i, and favg represents average fitness of particle swarm at present. σ2reflect the 
convergence degree of particle swarm. The small	σ2 means that particle swarm tends to converge. On the 
contrary, the particle swarm is in a random 
Search phase. The mutation probability is shown in (16), where k∈[0.3, 0.6], σ2d=0.05.. 

2 2,

0,

d
m

k
p

otherwise

σ σ
σ
 <= 


 

 (16) 

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The particle encoding is divided into three parts. Four works are processed by six of equipment. Work 1 has 
one processing path, and work 2, 3, 4 has two processing paths respectively. Decoding formula is  

1

, 1, 2, , , 1, 2, ,p
p

p
p

r
rp p p pR

r
r

w
N ROUND N p P r R

w
=

 
 
 = ⋅ ∀ = = 
 
 
 


 

. 

Prepresents the serial number of work; Rp represents the number of processing path of work p. wrσ	represents 
the proportion of processing number at path rp to the total number of works. 
The process of improved particle swarm optimization is as follows.  
Step 1. Generate particle swarm randomly, the initial speed of particle is 0, the local optimum is equal to the 
value of variable and calculate value of objective function according to variable value. 
Step 2. Calculate inertia weight factor and calculate fitness of all particles. If the current fitness value of particle 
is better than individual extreme, pbest is set as position of current particle. Set gbest according to global 
optimal value update strategy. 
Step 3. Determine whether σ2< 2d is set up. If σ2< 2d is not set up, turn to step 4. Otherwise calculate 
mutation probability pm and carry out mutation operation for the particle. 
Step 4. Determine whether it achieves the maximum iteration number and output external swarm. Otherwise 
the maximum iteration number is increased by 1 and the algorithm turns to step 2. 

4. Model testing 
Some company needs to make six kinds of work, P1, P2, P3, P4, P5, P6. The number of work is N1=30, N2=40, 
N3=30, N4=60, N5=50, N6=40. There are ten machine tools, which are divided into three sets {M1, M2, M3}, {M4, 
M5, M6, M7}, {M8, M9, M10}. These machine tools are distributed in three workshops, J1, J2, J3. Processing ability 
Em is {2000, 2500, 4000, 3000, 2000, 4500, 3500, 4500, 3000, 5000}.  
CCp={30, 40, 50, 40, 30, 40}, CRm={2000, 2500, 1500, 2000, 1000, 1500, 2000, 2500, 1000, 2000}, NJ=4, C=3, 
NC=4. Cost comparison of three algorithms is shown in table 1. Total cost of proposed algorithm is 272650, 
which is less than the other two algorithms. 

Table 1: Cost comparison of three algorithms 

 Flexible cell Physical cell Logic cell 

Processing cost 258150 258150 258150 

Cross workshop transportation cost 8100 8200 10800 

Transportation cost within the workshop 750 786 656 

Movement cost of the resources 1200 1500 0 

Cross cell processing cost 4450 5410 4450 

Total cost 272650 274046 274056 

5. Conclusions 
On the basis of physical manufacturing cell and logical manufacturing cell, the flexible manufacturing cell 
formation of cloud manufacturing resources is investigated. A method based on improved PSO is used to 
construct flexible manufacturing cell and the experiment proves that the method can effectively reduce the 
total manufacturing cost. 
 
 
 

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Acknowledgements  

This work is supported by Shaanxi Provincial Education Department Key Scientific Research Project of Key 
Laboratory (12JS033), Shaanxi University of Technology Fund Project (SLGKY14-02). 

References 

Defersha M.F., Chen M.Y, 2008, A linear programming embedded genetic algorithm for an integrated cell 
formation and lot sizing considering product quality, European Journal of Operational Research, 187, 46-
49, DOI: 10.1016/j.ejor.2007.02.040. 

Erwie Z., Hu C.H., 2008, Solving constrained optimization problems with hybrid particle swarm optimization, 
Engineering Optimization, 40(11), 1031-1049. 

Fan S.K., Liang Y.C., Zahara E., 2004, Hybrid simplex search and particle swarm optimization for the global 
optimization of multimodal functions, Engineering Optimization, 36, 401-418. 

Hu X., Eberhart R.C, 2002, Multi-objective Optimization Using Dynamic Neighborhood Particle Swarm 
Optimization, Proceedings of the IEEE Congress on Evolutionary Computation, 1677-1681. 

Jozef B., Lewoc A.I., Slawomir S., Antonina K., Peter K., 2011, An Integrated Manufacturing and Management 
System for Manufacturing Enterprises, Journal of Computational Information Systems, 1, 1, 1-10. 

Li C.Q., Shang Y.L., Hu C.Y., Zhu P.F., 2011, Research on Cloud Manufacturing Multi-granular Resource 
Access Control based on Capacity Constraint, Advances in Information Sciences and Service Sciences, 3, 
5, 79-86. 

Lin T.L., Horng S.J., Kao T.W., 2010, An efficient job-shop scheduling algorithm based on particle swarm 
optimization, Expert Systems with Applications, 37, 3, 2629-2636. 

Safaei N.M., Saidi M.S., Jabal M.A., 2008, A hybrid simulated annealing for solving an extended model of 
dynamic cellular manufacturing system, European Journal of Operational Research, 185, 563-592, DOI: 
10.1016/j.ejor.2006.12.058. 

Wang S.L., Chen G.S., Kang L., Li Q., 2012, Information Model of Cloud Manufacturing Resource Based on 
Semantic Web, International Journal of Digital Content Technology and its Applications, 6, 19, 339-346. 

Wang Z.L., Wang H.F., 2004, Manufacturing cell reconstruction technology research under agile 
manufacturing mode, Journal of computer integrated manufacturing system, 10, 7, 727-731. 

Wu X.D., Chu C.H., Wang Y.F., 2007, A genetic algorithm for cellular manufacturing design and lay put, 
European Journal of Operational Research, 181, 156-167. 

Yang Q., Li L., He G.Z., 2011, An Improved Particle Swarm Optimization for Constrained Optimization 
Problems, International Journal of Advancements in Computing Technology, 3, 10, 216-223. 

Yannis M., Magdalene M., 2010, A Hybrid Multi-Swarm Particle Swarm Optimization algorithm for the 
Probabilistic Traveling Salesman Problem, Computers and Operations Research, 37, 3, 432-442. 

 

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