MINIMIZATION OF EXPECTED MAKESPAN IN …...Scheduling in manufacturing systems is classically associated with scheduling a set of jobs on a set of machines in order to maximize the

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International Journal of Mechanical Engineering and Technology (IJMET)

Volume 10, Issue 08, August 2019, pp. 232-243, Article ID: IJMET_10_08_020

Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=8

ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication

MINIMIZATION OF EXPECTED MAKESPAN IN

FLOWSHOP USING CBM

D. Sanjeeva Rao

Part time research scholar, Department of Mechanical Engineering, College of

Engineering(A), Andhra University, Visakhapatnam, India

M. Srinivasa Rao

DGM (Maintenance), Department of MMSM, Visakhapatnam Steel Plant, India

V.V.S. Kesavarao

Professor, Department of Mechanical Engineering, College of Engineering(A),

Andhra University, Visakhapatnam, India

ABSTRACT

Manufacturing units have to meet concurrently several requirements such as:

quick reaction to market demand, high product quality, justifiable manufacturing costs

and well-timed deliveries, etc. Generally, the shop floor level personnel treat

maintenance and processing times in segregation for the purpose of scheduling, joint

consideration of equipment maintenance and scheduling on the performance of the

manufacturing system is taken into consideration in this paper. In practice machines

may be temporarily not available for many reasons, such as unforeseen scheduled

preventive and breakdown maintenance, operator non availability, spare parts

damage, etc. An effort is made to schedule a flowshop problem with time deterioration

under “Condition Based Maintenance” (CBM) constraints to minimize the expected

makespan. The randomness of the problem is tackled by simulation. Genetic and tabu

search algorithms applied to tackle such hard problem. Experimental studies

conducted and the results are promising in nature.

Key words: Scheduling, simulation, condition based maintenance, time deterioration

Cite this Article: D. Sanjeeva Rao, M. Srinivasa Rao and V.V.S. Kesavarao,

Minimization of Expected Makespan in Flowshop Using CBM. International Journal

of Mechanical Engineering and Technology 10(8), 2019, pp. 232-243.

http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=8

1. INTRODUCTION

Due to cut throat competition difficult challenges are being faced by manufacturing

organizations. Automation and modernization of equipment is the path chosen by different

manufacturing companies to increase the product-variety and for better product quality

resulting into raise of the cost of manufacturing processes. To achieve operational excellence

in this new environment, companies need to focus on shop floor efficiency and effectiveness.

Minimization of Expected Makespan in Flowshop Using CBM


Appropriate maintenance of production systems and machinery, adoption of proper

production scheduling programs, and implementation of quality techniques will yield

effective and efficient shop floor operation. As a practice the scheduler prepares schedule for

set of orders on a number of machines in such a way the timing, order sequence, and machine

assignment of these orders are optimal with respect to one or more objectives. A large number

of performance measures for evaluating scheduling objectives/performance have been in

vogue at present. Such measures are job flow time, machine utilization, makespan, tardiness,

job handling cost, labor utilization, etc.

More overscheduling has become vital in order to meet customer requirements as

promptly as possible while maximizing the profits to stay in the world of global competition.

Scheduling in manufacturing systems is classically associated with scheduling a set of jobs on

a set of machines in order to maximize the profit. Manufacturing system is classified as job

shop, flow shop and open shop. A common job shop problem consists of n jobs {j1, j2,

j3,…,jn} to be processed through m machine {m1, m2, m3, …, mm}. Technological

constraints demand that each job should be processed through the machines in a particular

order and gives a significant special case named as flow shop. For a general job shop

problem, the number of possible sequences are (n!)m, where n is number of jobs and m is the

number of machines. With the technological constraints in case of flow shop, number of

different sequences reduces to (n!). This reduced number is quite large for even temperate size

problems and recognized to be NP hard problems (Pinedo, 2012).

In classical scheduling problems, machines are assumed to be available through the whole

planning horizon, on the contrary in reality machines may not be available during certain

periods of planning horizon, due to breakdown or for attending preventive maintenance jobs.

Preventive maintenance is the main cause of unavailability of machines. Some researches

addressed this problem by machine scheduling with availability constraints where the number

of preventive maintenance periods and their intervals are fixed and known in advance,

without change in the performance measure. In fact, the constraints are formulated in a way to

plan the jobs in the available periods of time. Apart from scheduled preventive maintenance,

there are many uncertainties in process industry such as machine breakdown, operator-stock

condition, changes in availability date and latest completion times; we must consider them to

ensure the production running successfully.

A condition based on preventive and corrective maintenance policy is a technique adopted

in amass production units. The condition of the system/machinery is assumed to deteriorate

with time. The proposed model in this paper incorporates both deterioration as well as random

common cause failures. The deterioration stages are modeled as discrete state processes. The

system is put to random inspection to know the condition. The mean times between

inspections are exponentially distributed. If the observed condition at an inspection exceeds

the threshold value due to deterioration, the system calls immediate attention for maintenance.

Maintenance costs are included operational cost in firms hence are to be minimized without

compromising life of machine. Hence preventive maintenance, inspections, and predictive

maintenance are done properly to reduce maintenance expenses. Collection failure data and

optimizing maintenance schedules will reduce maintenance expenses.

Machine gets stopped because of maintenance. If the job continues processing

immediately where it was left earlier i.e., before stoppage of machine when once the machine

becomes operable after maintenance, the problem was called “resumable”. On the other hand,

the problem was called “non-resumable” if the job has to start afresh from the beginning after

maintenance of machine.

Scheduling of maintenance operations and production sequencing are normally treated

separately. In most of these researches, it is assumed that job processing times are fixed and

D. Sanjeeva Rao, M. Srinivasa Rao and V.V.S. Kesavarao


known in advance while deteriorating jobs exists in practice. Such deterioration appears in,

e.g., scheduling of maintaining job in case of fire fighting, cleaning assignments, issues

involving worker forgetfulness, tool wear, etc. In order to model these practical problems,

processing time of each job is considered as a function of its starting time. In other words, the

jobs processed later consume more time than the jobs processed earlier. The scheduling

problem with deteriorating jobs is mostly found in a metallurgical units.

2. LITERATURE SURVEY

Extensive research has been under progress starting from Johnson to current researchers for

optimization of flow shops scheduling. Their approaches are broadly two types; optimization

algorithms and heuristic algorithms. Constructive techniques are proposed for solving

flowshop problems (Nawaz et al., 1983) or improvement techniques are proposed for solving

flowshop problems (Kirkpatrik, 1983, Taillard, 1990, 1993, Ishibuchi et al. 1995). Cost-

discounted Markov decision process formulated for single machine problem by Glazebrook,

(1984). Birge et al., (1990) considered more general breakdown processes. Allahverdi et al.,

(1994) presented that a problem with parallel machines subject to random breakdowns could

be converted into parallel-machine problem with modified processing time. Constructive

scheduling generates a schedule from beginning. Improvement methods start from a initial

feasible solution improves this solution in the process of reaching global solution.

Improvement methods are generally based on meta-heuristic approaches such as, tabu search,

Genetic Algorithms (GA), Artificial Bee Algorithm (ABA), ant colony algorithm, etc.

The concept of preventive maintenance in scheduling was treated by several researchers:

two heuristic algorithms of time complexity O (n log n) are proposed by Lee, (1994),

considering preventive e maintenance, and provided their error bound analysis. Schmidt,

(2000) described scheduling problems with limited machine availability for one flowshops.

Further analyzed some results from heuristics. The problem with some periods of preventive

maintenance on two machines in resumable case was considered by Blazewicz et al., (2001)

local search based heuristic algorithms are analysed by them. Allaoui et al., (2004) solved

flow shop scheduling problem with maintenance constraints applying simulation and

optimization methods and compared the results with NEH heuristics. Ruiz et al., (2006)

considered two popular preventive maintenance methods in flow shop scheduling problem.

Antonio and Maria,(2008) has described system failures are assumed to occur at the first

instant in which a random constant threshold is reached by (a) the sum of received shocks, (b)

the minimum of shocks, (c) the maximum of shocks. Safariet al., (2009) have considered

condition based maintenance in flow shop scheduling and proposed model by integrating

heuristics and simulation for fixed processing times. Cheng, (2011) illustrated usage of

simulation for finding the Near-Optimal Preventive Maintenance Policies for a Repairable

System. Many of the scheduling problems are NP-hard in nature (Pinedo, 2012).Simulation

study of dispatching rules in stochastic job shop dynamic scheduling was proposed by Edna,

B.S. et al., (2014).

It is clear from the literature review presented in the preceding section that the joint

consideration of scheduling, and maintenance is gaining increasing attention from the

researchers in recent years. While available approaches are mostly limited to simple problems

like single machine, single product, single quality characteristic, etc. Multiple machines and

multiple products, each having multiple quality characteristics are quite often are more

relevant in actual production system. Further, nature and extent of integration required in case

of flow shop need to be optimal. Further, the demand of the jobs/tasks, variety of products,

and availability of resources, production rates, etc. may vary with time. All these factors make



the actual production systems are dynamic in nature and in turn increase the complexity of

mathematical modeling.

Considering the literature an effort is made to develop a model incorporating the

preventive maintenance and break down maintenance activities in the flow shop scheduling

problem which is solved by integrating simulation as well as heuristics.

The reminder of this paper is organized as follows: A study of maintenance techniques

problem assumptions are described in section-3. Section-4 describes the heuristics that are

applied in this paper. In section-5, simulation algorithm is described. Further model is

presented combining simulation and heuristics in section-6 along with analysis of results and

finally, conclusions are drawn in section-7.

3. STUDY OF MAINTENANCE TECHNIQUES

In a continuous growing global market productivity is playing a key role to stay competitive,

for any manufacturing company. Productivity can be achieved through availability of

machines and availability can be increased through adopting the efficient maintenance

practices, by focusing on different types of maintenance and strategies. In his seminal book

reliability centered maintenance, John Moubry suggested that three distinct generation of

maintenance. In the first generation i.e., upto Second World War the expectation of

maintenance is to fix when machine fails. In second generation maintenance i.e., upto 1970

the expectation of maintenance is high equipment life follow bath tub curve. In third

generation maintenance after 1970 the expectation of maintenance is high and reliability level

is high. Six failure patterns are observed. Condition monitoring is one technique that is

practiced.

Condition Based Maintenance (CBM) or predictive maintenance, uses primarily

nondestructive testing techniques, visual inspection, and performance data to assess

machinery condition. It replaces arbitrarily timed maintenance tasks with appropriate

maintenance task at only when warranted by equipment condition. CBM includes improved

knowledge of failure mechanisms, advancements in failure forecasting techniques,

advancements in monitoring and sensor devices, advancements in diagnostic and prognostic

software, computer networking technologies.

In The time based preventive maintenance, maintenance are performed at fixed periodic

intervals regardless of the dynamic health status of machinery machine breakdown is one of

the disorder commonly found on the production floor. This problem decreases the profit

margin of the due to production loss and maintenance cost. Single component or multiple

failures are the reasons for the machine breakdown. Hence the tendency is to do more

preventive maintenance. This makes the cost of PM keeps on increasing. Where as CBM

recommends maintenance actions based on the information collected through condition

monitoring. So that unnecessary maintenance can be avoided. Depending on the health

condition of machinery, maintenance can be done which ultimately minimizes maintenance

cost.

In condition-based maintenance framework, a deterioration indicator that correctly

describes the dynamic of the failure process is to be defined first. Usually this efficient

metrics can be constructed from collected information on various deterioration-related

monitoring parameters, such as vibration, temperature, lubricating oil contamination, and

noise levels. Deterioration models are suggested by many people considering deterioration

processes in dynamic environments with stochastic approaches. It is assumed that condition

based maintenance in which each machine suffers degradation due to shocks. When total

degradation for such machines reaches to a threshold value maintenance has to be carried out.

Upon the inspection of the system and its condition, inspectors need to decide whether to take



an action such as Nominal Preventive Maintenance (NPM) and Essential Preventive

Maintenance (EPM) or no action is needed. In spite of practicing CBM, some times machines

will cease to perform because of unforeseen breakdowns, which are called random break

down. It is assumed that a machine keeps processing the jobs sequentially until it break down

or it has finished all the jobs, and machine breakdowns may arise at any time in working

periods because of unforeseen situations. Reactive maintenance has to be carried out to bring

back the machine into workable condition. Maintenance policies, which are commonly

considered by simulation are reactive/corrective maintenance and preventive maintenance are

addressed in this paper. Maintenance policies address as the components of the framework for

reactive maintenance follows Weibull chance failures and the shape of function is greater than

1.

4. ASSUMPTIONS

A job consists of several operations, each one has to be performed on a particular machine at

any instant job can be processed on one machine only.

At the start time, all jobs are available for processing. One has to choose the start job among

many. No preference among the jobs. Preemption of jobs is not allowed.

Setup times between operations are included in the processing times.

Two jobs cannot be processed simultaneously on any particular machine.

Jobs are always processed without any defect. Basic job processing times and constant

deterioration rate known in advance.

There is only one type of machine and no restrictions on buffering between machines.

Machines are not available at all times due to NPM and EPM operations.

Machine inspections are planned at periodic times nTn(n = 1, 2, …).

All machines have the same mean values shocks, degradation for each shocks, maintenance

times, recovery value and the maintenance threshold values and inspection will not interrupt

machine production.

Random break downs are considered in this paper using Weibull distribution. This paper

adopts the CBM policy for a cumulative degradation model where a machine suffers

degradation due to shocks, and does EPM when the total amount of additive degradation

exceeds a level called k. The inspections occur in a pre-specified intervals nTI (n = 1, 2, …) to

prevent failures, where TI (> 0) is the inspection interval time. If the total degradation exceeds

a threshold level Z(0 < Z ≤ K) at time nT, the NPM is performed. Otherwise, no PM is

performed.

Shocks are the main reason of degradation for each machine. The number of shocks

occurrence injth

inspection interval Nj has Poisson distribution. In additional, random

variables {Wj} (j = 1, 2, …) denotes the amount of degradation due to jth

shock and is

considered to have an exponential distribution. Degradation of each machine in a period dp is

also considered as:

pN

p jj 1d W

Recovery value (Decreasing the degradation value after PM operations) Δdeg when

operation maintenance is executed, has lognormal distribution. Also degradation values after

NPM and EPM operations d0 are equal to d−Δdeg and 0, respectively. The amount of time

needed for NPM and EPM operations are Tm, Tb respectively, have lognormal distribution,



where time needed for operations of NPM are more than BPM and we have dt = d0 + dp.

Where d0 is identified at the end of each period for the next period as follows:

deg0 = dt – deg for Z dt < K

deg0 = dt for 0 dt K

deg0 = 0 for dt K

When random shocks occur the degradation process may receive two types of impacts

where the first type is a sudden increment jump and the second one is degradation rate

acceleration. Cha and Finkelstein (2009,18) extended the brown-proschan model by assuming

that random shocks will result in an immediate system failure with a probability of p(t) but

accelerate the system aging process by a certain increment with a probability.

5. SIMULATION ALGORITHM

5.1. Notations

n : number of jobs

d : degradation value when machine is inspected

m : number of machines

Finishi,j : finish time of job j on machine i

Sequence of jobs:

k : kth

job of sequence

W : degradation value of each level

tij : processing time of job j on machine i

bij : basic processing time of j on machine i

aij : linear deterioration coefficient

tij : iij i, ij(a *start ) b

rmni : remaining time to next inspection

N : number of shock in each inspection period

starti,j : start time of job j on machine i

wran = Weibull random number

cwran = Weibull random number value

The permutation flowshop scheduling problem consists of scheduling n independent and

non preemptive jobs gathered in setj = {1,2,3,…,n} and mmachines = {1,2,3,…,m} all jobs

should follow a fixed route of machines to be completed and due to the assumption sequence

of jobs on all machine are identical. We assume processing time tij is of job j on machine i is

given linear function of its starting time t, i.e., tij = (aij * starti,j) + bij where aij 0 denotes the

deterioration rate of job j on machine i and bij 0 is the fixed process time of job j on

machine i.

Degradation value related to each shocks and cumulative value of degradation are calculated

at each inspection interval after determining the number of shocks for each machine.

In each inspection, it is needed to compare degradation value with thresholds.

Based on maintenance strategy, PM or essential repair time are calculated.

After preventive maintenance operation, recovery value is subtracted from degradation value.

When random shocks occur, the degradation process may receive two types of impacts where

the first type is a sudden increment jump and the second one is degradation rate acceleration.



Some times random shocks will result in an immediate system failure with a probability of

p(t) and calls for maintenance immediately and some times accelerate the system aging

process by a certain increment with a probability.

After basic repair, degradation value set to zero.

It is necessary to note where inspection is occurred i.e. in middle or end time of particular

processing job.

Because of the fact that the problem has probabilistic nature, it is necessary to replicate the

computation of simulator several times for each sequence when all the features of the problem

remain constant. After that all replication is done, mean of obtained makespan is considered as

expected makespan.

It is also necessary to note that in some cases in spite of following conditioned base

maintenance inspections, certain surprises happen due to sudden failures and unforeseen

technological disruptions before inspection interval, generally the trend of such failures follow

Weibull distribution where shape of curve is greater than 1. Such conditions are incorporated

in this model.

The simulator algorithms employed in heuristics has the following steps for each

sequence.

Step-0: Initialize i = 1, ii,start = 0, finish0,j = 0, deg0 = 0.

Step-1: If i m {go to step-2}; else {finish the simulator procedure}.

Step-2: Setdeg0 = 0, j = 1; Run degradation algorithm with initial degradation deg0.

Step-3: If j n {go to step-4}; else (go step-14}.

Step-4: Set g = σj, rmni = rmni – tig, starti,g = max(finishi–1g starti,g).

Step-5: If rmni > 0 {go step-6}; else {go step-7}.

Step-6: Setfinishi,g = starti,g + ti,g, j,1i,start = finishi,g and go step-13.

Step-7: If d k {if rmni < 0 {set nmni = rmni + tig; go to step-8}; else {go to step-11}}; else

if d Z {if rmni < 0 {set rmni = rmni + tig; go to step-9}; else {go to step-12}} else {go to

step-10}.

Setrmni = rmni + TI, j 1i,start = finishi,g; Go to step-13.

Step-9: (a) Generate two log normal random numbers as MPM time Tm, recovery value

_deg; Setfinishi,g = starti,g + Tm +tig; deg0 = d – deg;

(b) Run degradation algorithm with initial degradation d0;

Set rmni + TI, j 1i,start = finishi,g; Go to step-13.

5.1.1. Degradation algorithm with initial degradation deg0

The degradation algorithm is used in simulator algorithm which has the following steps:

Step-1: Generate a Poisson random number as degradation level N.

Step-2: d = deg0.

Step-3: for k = 1 to N.

a) Generate an exponential random number as degradation for degradation level k,W.

b) d = d + W

End for (k)

Step-4: Generate Weibull random number wran with shape of curve > 1 and cdf // to address

random shocks because of unforeseen situations.



If wran cwran

{//sudden failure; d = K + l; goto step-8(a) of simulated algorithm

else goto simulated algorithm}

6. COMBINATION OF SIMULATION AND HEURISTICS

The majority optimization problems are too difficult to be solved by mathematical

programming. Combining optimization and simulation is one kind of approach to solve such

problems. The concept of intelligent agents to simulate the manufacturing process was

adopted by Nadoli et al. (1993). Programming techniques of object-oriented approach,

constraints programming, and simulation techniques were integrated by A.D. Talbi et al.

(1995). Since the problem considered in this paper is strongly NP-hard, Heuristics along with

simulation technique (called simulator) is adopted to obviate the complexity of the problem at

hand. The flow chart Fig.1 is depicted below.

Figure 1 Flow chart

6.1. Analysis of Results

The computational results obtained from our proposed algorithms employed in this paper are

tabulated. The empirical data is collected from a local industry. The CBM parameters are

determined first. In practice the parameter related to stochastic distribution of the number of

shocks in inspection period, EPM and NPM operation times, recovery value and degradation

value for each shock are specified according to the information collected through condition

monitoring devices i.e., shock pulse meters. Also threshold values are determined according

to life distribution of machines based on empirical data.

The number of shocks in each inspection period and degradation value for each shock

have Poisson and exponential distribution with 25 and 0.6 mean values, respectively. Also

recovery value after NPM operations is fixed using lognormal distribution with mean 3 and

variance value of 0.2. This parameter is selected such that the generated random number from

this distribution is less than NPM threshold and more than zero. Shape of Weibull distribution

curve is 2 and scale of curve is taken as 100 based on empirical data. Cumulative distribution

value of survival is taken as 0.02.

Since, the lengths of both periods of inspection and preventive maintenance might

influence the algorithm performance, different levels of these parameters are considered.

Number of jobs n{20, 30, 40} and machines = {20, 30}, therefore there are 6 combinations of

n and m where the processing times bij is distributed as a U[1, 99] and deterioration constant



aij as U[0, 3]. For each combination of jobs and machines, different values of inspection

interval and necessary times of operations of minimal and basic preventive maintenance are

considered. Operation times of minimal and basic maintenance with lognormal distribution

have means 3.0 and 3.65 and variances of 0.1. Inspection period is set {150.250, 350}.

Once the expected makespan of each instance has been obtained for each algorithm, the

best solution obtained for each instance of same size is selected and it is calledbest value of

instance. With this, calculated the relative percentage deviation (RPD) with respect to this

best solution with the following expression:

RPD = (average value of instance – best value of instance)/average value*100 where

average value of instance is average of all expected makespan attained for considered

instances. RPD help us to compare algorithms because the RPD values denote relative

distance of average algorithm solution from best solution obtained for special instance,

clearly, lower values of RPD are preferred.

The worst percentage deviation (WPD) with respect to this best solution with the

following expression is also calculated:

WPD = (maximum value of instance – best value of instance)/

average value*100

where maximum value of instance is maximum (worst)of all expected makespan attained

for considered instances. WPD help us to compare algorithms because the WPD values

denote relative distance of worst algorithm solution from best solution obtained for special

instance, clearly, lower values of WPD are preferred. Statistical analysis performed on the

results for both resumable and non resumable cases.

Multi factor ANOVA performed in which factors such as number of jobs, number of

machines, inspection intervals and response variable of relative percentage deviation are taken

into consideration. Preliminary experiments shown that ANOVA’s hypothesis of

homogeneity of variance not true and hence Box-cox transformation is applied to all RPD.

Mean plot and least significant difference for the algorithms at 95% confidence have shown

us that there is no statistically significant difference.

7. CONCLUSION

The problem is run in C++ and on a PC with 1.5 GHz Intel Core 2 Duo and 2 GB of RAM

memory. In this paper, we had studied the problem of scheduling a flowshop to minimize

expected makespan based on condition based maintenance constraints and sudden unexpected

failure because of breakdown maintenance. In fact many real life industry problems represent

the double complexity (algorithmic and structural-functional). We have illustrated the

approach of combining the simulation and the optimization to deal with this problem. Tabu

and GA and a simulator were used to construct this approach. The obtained results strongly

manifest the superiority of GA over others in both cases resumable and nonresumable. GA

achieved better results with respect to other algorithms in terms of CPU time, RPD and WPD

values. Further to this we investigated the problem of scheduling deteriorating jobs in a flow

shop environment. The job deterioration is a very promising issue and extensions of the same

to other flow-shops, including hybrid and flexible flow-shops, job-shops and open-shops can

be explored as well. Moreover, using more than one objective and developing other meta-

heuristic algorithms, especially population-based meta-heuristics can be regarded as some of

the other future research directions.



Average RPD values are shown in the table.

Table 1 Average RPD values in non-resumable cases

Instance GA Tabu

20*20 0.62 0.65

20*30 0.6 0.65

20*40 0.48 0.5

Average 0.558 0.576

Table 2 Average RPD values in resumable cases

Instance GA Tabu

20*20 0.72 0.75

20*30 0.7 0.8

20*40 0.64 0.7

30*20 0.8 0.8

30*30 0.62 0.7

30*40 0.65 0.62

Average 0.68 0.72

WPD values are shown in the table.

Table 3 Average WPD values in non-resumable cases

Instance GA Tabu

20*20 0.72 0.75

20*30 0.65 0.76

20*40 0.5 0.65

30*40 0.65 0.67

Table 4 Average WPD values in resumable cases

Instance GA Tabu

20*20 0.76 0.78

20*30 0.72 0.82

20*40 0.66 0.73

30*20 0.81 0.82

Average 0.71 0.75

Table 5 Time in minutes

Instance GA Tabu

20*20 16.5 17.5

20*30 18 18.3

20*40 20.2 21.2

30*20 27.5 28.7

30*30 39.3 39.8

30*40 40 45.1



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