The Operation Data Analysis Research Based on the Queuing Theory of the D
Cigarette Factory Product Warehouse System
Xiao-he Sheng 1, Wei-ping Yang2, Tian-min Liao3, Yao Liang3 ,Wen-xia Xu3,Xing-zhao Yi3
1,2
Industrial Engineering, KunMing university of science and technology, KunMing, China
New Trend International logistics technology limited liability company, ShenZhen, China
3
City college, KunMing university of science and technology, KunMing, China
3
congestion because of random factors' influence [4]. The
Abstract- Queuing theory is a regularity discipline
longer the line up, the more time to waste, at the
based on the influence of random factors which fostering
meanwhile, the lower efficiency of system, shown as
the phenomenon of queuing in line or congestion of the
Fig 1. With the fast growth of Queuing Theory,
[1]
system . After a deep research on the basic ideology of
logistics systems has been widely used in wide fields,
queuing theory, this paper establishes the automated
as medical treatment process system,
2
warehouse mathematic
modelofofIndustrial
the systemEngineering,
and has givenDifferent such
Department
University of Hobbiton,
City,
Country cashier, AGV
transportation,
distribution,
supermarket
the flabby condition constraints of the warehouse model
(e-mail address)
dolly, and have made remarkable effect. But in the
with its application. According to this model, people can
automatic warehouse system, the application is still
work out the parameters such as equipment utilization
efficiency of automatic warehouse system, the number of
relatively rare. With a in-depth research of a cigarette
goods waiting for service, the average waiting time and the
factory product warehouse system, basing on the basis
average captain operation in system, etc. Finally with the
of Queuing Theory, the author designs a scheme of the
system analysis, the paper provides the basis for
model mathematically, and works out the operation of
optimization design or evaluation of the status of the
the system parameters, so to optimize and improve the
warehouse system.
system.
Keywords- Queuing theory, automated warehouse,
mathematical modeling, cigarette factory warehouse
system
customer
Customer
coming
I.INTRODUCTION
With the increasing progress of globalization of
economy and the rapid development of science and
technology, the modern logistics has been paid more
and more attention. It is also regarded as the "third
profits source" except the function of reducing
consumption of resources and improving labor
productivity[2]. As the typical representative in the
modern logistics field, with a higher demand of
automation degree, automated warehouse has been
extensively used and has achieved significant results. It
reduces the tobacco logistics costs greatly and so to
obviously improve the circulation of tobacco production
efficiency[3].
II. THE QURUING THEORY
Queuing theory is said to be a theory of stochastic
service system, which is to study a discipline of
regularity, a phenomenon of queuing in line or
C
A
B
D
E
Queuing
structure
Queuing
discipline
Service
discipline
Service
structure
Customer
leaving
Fig 1 Queuing system block diagram
III.QUEUING MODEL OF AUTOMATED
WAREHOUSE
Automated warehouse refers to a storage system
that to save goods by top shelves, and put in or
outbound goods with roadway stacker automatically
[5]. The product warehouse system in a cigarette
factory mainly includes finishing warehousing
subsystem, empty tray group supply subsystem,
finished product outbound subsystem, empty tray
group return library subsystem, exception handling
and checking subsystem and scattered dish smoke
process subsystem, etc[6].
A. Overview of D cigarette factory products warehouse
system
The basic composition of cigarette factory
products warehouse system as Fig 2:
G
F
I
Fig.2. The basic composition of cigarette factory products warehouse system
Ｈ
Description of working process as follows:
(I) Warehousing System
Finished products ars transported from upstream, via
the link smoke transmission system and are passed to
Treasury product warehouse platform, waiting in A
place and cached by B palletizing robot (according to
A smoke every tray 28). The procedure includes
empty tray group (each group of 10), passing the C
conveying system (including ring shuttle car and
chain, roller conveyor, etc), then to be completed by
stacker Treasury.
(II) Storage System
The whole finished products tray and empty smoke
tray group are saved in E place, including sampling
inspection, returning-back process of unqualified
outbound products during the period.
(III) Outbound System
The whole tray products are sent to the platform in F
by stacker smoke, transported by conveying system
(including ring shuttle car and chain, roller conveyor,
etc) to G place, after being removed by robots,
finally to finish the outbound homework by artificial
with telescopic chain conveyors.
B. The establishment of product warehouse queuing
model
(I) The establishment of the constraints and
relaxation conditions of warehouse model
(i) The warehouse is limited to unit format automated
warehouse;
(ii) Shelves for closed roadway shelves, only four
sets of roadway in a stacker, there are four service
windows within the system, accessing to goods
service:
(iii) The arrival time of the goods obeys to random
position distribution[7], for product warehouse
stackers service, the time depends on distribution[8],
and when all warehouse locations are parked, the
following goods will be in a waiting state;
(iv) The whole warehouse is one end income, and the
other output;
(v) There is no waiting loss in the system.
(II) The establishment of warehouse queuing model
It is known from the constraint and relaxation
conditions that the warehouse system obeys to the
Multiple Service Windows Waiting System M/M/n
queuing model[9]. Suppose the system has n service
windows, each window operate independently; the
finished products arrives according to Poisson flow,
the strength for  ; The service time of every
window tends to distribution, then average service
rate for  ; the stable distribution of theory proving
=
system is
Fig3:


 1 1 
 . The model is shown as
n
,
1
XXXX…XXXX
The arrival of pallets of
finished cigarette product
2
…
3
The leaving of pallets of
finished cigarette product
4
Fig.3. Multiple Service Windows Waiting System M/M/n
Queuing Model
Refer to the Queuing M/M/n Model calculation
method, several computation formulas of related
parameters is as follows [10]:
(i) The probability of 0 service desk in system:
n 1
P0  (
k 0
k
1
k!

n
1 1
)
n! 1  
1
(ii) Since there is no waiting loss existing, the
relative through ability of the system: Q=1;
(iii) The absolute through capability of system:
A  Q  
(iv) The average length of waiting queue:
Lq 
1n 1
(n  1)!(n  1 ) 2
p0
(v) Average number of windows in service:

 n (n )k 1
nn  k 1 
LP  n 
p0  
p0   n  1
n!
k  n 1
 k 1 (k  1)!

(vi) The line length in system:
1n1
p0  1
(n  1)!(n  1 ) 2
(vii) The average waiting time of goods:
L
1n p0
Wq  q 
  n  n !(1   )2
(viii) The probability of time-waiting of goods in
system:
Ls  Lq  LP 


npn
nn k
 p0 
n  1
k n n !
C (n, 1 )   pk  
k n
IV. THE CALCULATION and ANALYZATION of
RELATIVE PARAMETERS of D CIGARETTE
FACTORY PRODUCT WAREHOUSE SYSTEM
A. The calculation of related parameters in the
system
D cigarette factory is a plant which has a production
capacity of 446000 big box of cigarettes, on the basis of
each tray with 28 smoke cold salvers, working 250 days
a year, seven hours a day, the loading and unloading
keep balance. Then the calculation is as below:
446000 boxes/year by 5 ÷ 250 days ÷ 28 a/tray ÷ 7 =
46 PL/h;
According to the peak of 1.3, the storage capacity is: 46
PL/h x 1.3 = 60 PL/h
According to each group is 10 trays, the flow of empty
tray group is: 60 PL/h ÷ 10 / group = 6 group/h.
Suppose the loading and unloading is balanced in this
system, the outbound traffic is: 60 PL/h + 6 group/h =
66 PL/h. The total flow of the system is: 66PL/h×
= 1 3 2 P L / h
2=132PL/h. That is:
The capacity of single stacker is 67PL/h, since in the
actual operation, stacker operational efficiency cannot
be higher 85％ than its real ability, so we set = 67 x
85% = 57 PL/h; then can come:
 132

 2.3
 57
1 
=

132

 0.58  1
n 4  57
So the queuing system is stable. With the actual date
into the above formula, the numeral value of other
parameters can be calculated as follows:
(i) The probability of 0 service desk in system:
k
4 1
P0  (
1
k!
k 0

4
1
) 1  0.103
4! 1  0.58
1
(ii) The relative through ability of the system: Q=1
(iii) The absolute through capability of system:
A= =132
(iv) The average length of waiting queue:
1n1
2.35
Lq 
p0 
 0.103  0.382
2
(n  1)!(n  1 )
3!(4  2.3) 2
(
v) Average number of windows in service:
LP  n  1  2.3
(vi) The line length in system:
Ls  Lq  LP  0.382  2.3  2.682
(vii) The average waiting time of goods:
Wq 
Lq


0.382
 0.0029h  0.174 min
132
(viii) The probability of time-waiting of goods in
system:
C (n, 1 ) 
npn
4  0.124

 0.293
n  1
4  2.3
(ix) Efficiency of stacking machine operation:
Lp
2.3
 0.575
n
4
B .System analysis results


After systematically analysis, we can find that the
queuing model is relatively stable. With satisfaction of
the balance between loading and unloading, it has the
shorter waiting time of goods, and belongs to be a
reasonable and fluent automatic system. So it is quite fit
the operation status of D cigarette factory warehouse
system. Though the model is excellent, it also has some
shortages. There are only 2 to 3 stackers in work on
average, it is not high of the equipment efficiency,
existing resources wasting problem. Faced with this
condition, we can consider to increase the capacity of
the storage and improve production efficiency by
increasing the subsequent equipments.
V.
CONCLUSION
Based on the systematically analysis of the D cigarette
factory warehouse system, combining with the queuing
relating theory, this paper has made a calculation and
consideration to the product warehouse system
parameters. So to provide accurate data support for
optimization design and system evaluation. The author
aims to discover the deficiency in time and adjust
design or manufacturing strategy. Finally the paper
would have great influences of automatic warehouse
system on the design, optimization, plan evaluation and
strategy adjustments positively.
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