International Journal on Mechanical Engineering and Robotics (IJMER)
________________________________________________________________________________________________
Optimization of open field Layout in FMS with Scheduling as constraints – An Approach of evolutionary algorithm and Trajectory
based method
1K.Mallikarjuna, 2N. Govinda Rao, 3A. Sreekanth, 4V.Veeranna
1,2,3G. Pullaiah College of Engineering & Technology, Kurnool Andhra Pradesh, India
4Brindavan Institute of Technology & Sciences India
Abstract— In current scenario, many production companies are badly in need of advanced manufacturing systems like FMS which is very gifted technology due to its litheness. The main theme is focused on optimization concern to FMS allocation of parts as a restraint in designing the open field arrangement of machines in feasible mode by an evolutionary algorithm such as GA etc and trajectory method like SA etc. In this article the initiators of this paper put an endeavor to allocate machine allocation pattern in an optimum order with flexible batch scheduling as limitation in an FMS, based on precedence rule. The various open field layout problems are inspected to endorse the goal function in respect to problem solving time and number of engendering involved in evolutionary algorithm and Trajectory based method. The necessary programme is developed in C++ and the cipher is operate through simulation tool. Eventually in perceive of authors, the outcome of the non traditional optimization algorithms (Genetic Algorithm and simulated annealing method) are assimmilated and inferences are delineated.
Keywords— Flexible Manufacturing systems, open field layout, Genetic Algorithm, Simulated Annealing, IDE Tool.
I. INTRODUCTION
Owing to advancement in automation of industrial sectors, the merchandise for manufacturing products is enhancing globally. In order to face the challenges in the highly competitive world, the industries are to focus on available resources and energies to withstand and gain advantage of competitive market. To attain this, manufacturers has to choose the best method as an alternative such as FMS to reduce and eliminate the problems occurred in industry.
FMS is always ahead for industrial solutions; it is more lithe in solving the industrial problems to obtain best profits by decreasing the processing time and stock level in order to improve the productivity by prediction and control. To attain maximum productivity FMS has a solution through various layouts which involves supplying unlike resources. The design of these layouts leads to optimum making time and cost [1] must be
determine in the inception of FMS[2].In general the various types of FMS layouts [3] are
1) Open field layout.
2) Line or single row layout.
3) Ladder layout.
4) Loop layout.
Authors have choosen open field layout out of the above layouts which is more convenient than other. This article speaks about integrated scheduling of open field layout design
II. LITERATURE SURVEY
In view of hypothetical and real world , eminence of FMS has been highly emphasized due to its integrated scheduling in configuring optimum design of layout. In the past, researchers mainly concentrated on finding out the problem solution in mathematical model like dynamic programming and integer programming [4]
which can be useful for solving the simple problem.
Search methods are more suitable to resolve the simplel and also complex issues. The heuristic methods are commonly known for its efficiency, but quickly identify the neighbour finest solution and less assertion about obtaining global solutions. of late, metaheuristic been applied as alternative for heuristics, such as, Sheep flock and cuckoo search technique.]
Buzacott and Yao [5] presented a complete review of the analytical modes developed for the design and scheduling of FMS. Kimemla and Gershwin [6]focused on optimizing the routing of part in an FMS with the objective an optimization problem which maximizing the flow by maintaining the average in-process inventory below a fixed pointl. Chan and Pak [7]
introduced two heuristic algorithm in a statically loaded FMS for solving the scheduling problem with the goal for minimizing the total cost of tardiness. Solimanpur M, Prem and Ravi Shankar [8] have used to solve single row layout problems by considering a non –linear 0-1 programming model in which the distance between
the machines is sequence dependent in Flexible Manufacturing Systems(FMS) .”
III. PROBLEM DESCRIPTION
The problem formulation procedure adopted by Hongbo Liu and Ajith Abraham [9] has been used in this research work. We focus on design of open field batch scheduling flexible problem as constraint with the following parameters.”
- J=Jobs//batches={j1,j2,…………jn}”
- B={B1,B2,……….Bn}is a set of n jobs /n batches to be scheduled respectively. Each job Ji
consists of a predetermined sequence of operations.
Oi,j is the operation j of Ji.”
- Machines M={M1,M2,………..Mm} is a set of m Machines. ”
- Slots S={ S1,S2,S3………Sm} is a set of N fixed slots”
- Flexible FBSP usually is classified into two types as follows:”
Total FBSP {T-FBSP}; each operation can be processed on any machine of M.”
Partial FBSP {P-FBSP}; each operation can be processed on one machine of set of M.”
Authors have chosen P-FBSP integrated with facility layout problems for our research work.
A. Notations
The notations [14] which are used to develop a mathematical model of the design of line layout are defined and interpreted as follows.
i – part type index i=1,2,3,……,n j – Process index j= 1,2,3,…..,ni
k – Machine index k=1,2,3,……,m n – Number of batches / job m – Number of machines
Smaxi – Make span of system maximum completion time
sn,m – Make span of system
Si,j,k – Partial make span without
predecessors
si,j+1,k – Enhanced make span with
predecessors
Ti,j – The duration (processing time ) of operation j of job i
Ti,j+1 – The duration of operation j =1of job i
M – Total number of machines
contained in the manufacturing system Mi – Machine in slot n1 Mj – Machine in slot nN N – Number of slots
MHm1,m2 – Material handling cost between machines m1 and m2 ( m1 m2 = 1,2,3,…….,M )
RDn1,n2 – Rectangular distance between
machinery locations n1 and n2 ( n1 n2 = 1,2,3,……N )
MFm1,m2 – Amount of material flow among machines m1 and m2 ( m1 m2 = 1,2,3,….M )
LOCmi – Loading cost from loading station to machines
ULOCmi – Unloading cost from unloading station to machines
A. Objective Functions Minimize Make Span F(Smaxi) Minimize F (Smaxi ) = sn,m Sub to
Si,j,k ≤ si,j+1,k – Ti,j+1 , j=1,2,3,…p-1 Si,j,k ≥ 0, j = 1,2,3,……n Minimize Total Transportation Cost ( Z )
( Z ) = ∑Mmi=1 ∑Mmj=1 ( MFm1,m2*MHm1,m2*RDn1,n2 ) + LOCmi + ULOCmj
Sub to
∑Mmj=1Xmimj = 1 if machine mi is at assigned to slot N
= 0 otherwise
∑Mmi=1Xmimj = 1 if machine mi is at assigned to slot N = 0 otherwise
Xmimj{0,1}, mi, mj = 1,2,…………..N
IV. PROPOSED METHODOLOGY
The general explanation of the suggested procedures is shared out as follows.
A. Genetic Algorithm
Genetic algorithm is most capable for complete optimization. Though, they are not firmly suitable to accomplish local searches and are liable to converge in advance to get best solution. The genetic algorithm is a vigorous technique, based on the natural selection and
genetic production mechanism. It processes a group or population of possible solutions within a search space.
The search is probability guided and stochastic, rather than deterministic or random searching, which distinguish it from traditional methods. GAs employs the vocabulary taken from the world of genetics itself, and as a result solutions refer to organisms (genotypes) of a population. Each organism represents the code of a potential solution to a problem and the changeover of this code to a real variable is called phenotype.m
V. SIMULATED ANNEALING ALGORITHM
“One of the commonly used metaheuristic algorithms is the Simulated Annealing (SA) which falls under trajectory based methods.SA is an optimization algorithm that is not fool by false minima and is easy to implement. Simulated Annealing (SA) is a genetic probabilistic meta-heuristic for the global optimization problem of applied mathematics, locating a good approximation to the global minimum of a given function in large search space. It is used when the search space is discrete. For certain problems, simulated Annealing may be more effective provided when the goal is to find an acceptably good solution in fixed amount of time, rather than the best possible solution. It is a neighbourhood search technique that has produced good results for combinatorial problems.Simulated Annealing was first introduced by Kirkpatrick, C.D.Gelett and M.P.Beechi in 1983 and V.Cerny in 1985 to solve, optimization problem.
VI. CONFIGURATION OF OPEN FIELD LAYOUT:
FIG 1 Open field Layout Arrangements of FMS for 7 machines
VII. DATA SET DETAILS FOR OPEN FIELD LAYOUT WITH FBSP
A Production system with the summary and Batch sizes and the layout of FMS are shown in table1,. The data set details of batch varieties and sizes are given in table 2.Let there be parts to be processed on machine for various operations. Which requires the processing time and part routing with the operation sequence of parts which steers the parts on various machines are depicted in table 3 The inter slot between machines i.e the gap between machines measures in units are given in table 4 The loading/unloading distance matrix specifies distance from machines to load/unload station are shown in table 5 , unit material handling cost per unit i.e. the carrying cost of parts between machines is unit cost,. The way of part/batch moves over the machines is given in the same Table 3 as an input for FMS scheduling, where the objective is to arrive at a layout, which determines non- overlapping optimal sequence of machines such that total cost of making required movements is minimized.
A. Data set details of Production System
Table 1: Outline of Production system Layout Pattern No. of
Machines
No. of batches
No of operations
Load/Unload
stations No of AGV
Open field 7 7 7 2 1
B. Data set details of Batch varieties and sizes (CBS= Constant Batch size, VBS=Variable Batch size)
Table 2: Batch varieties with batch sizes of the Open field layout with 7machines with 7 jobs
Batch number B1 B2 B3 B4 B5 B6 B7
Batch varieties CBS 100 100 100 100 100 100 100
VBS 50 40 60 30 10 25 90
C. Data set details of processing time of parts & processing sequence of machines (O= operation, M= Machine number, T= Time in min)
Table 3: Processing time and Process routing matrices for configurations of Open field layout with 7 machines and 7 jobs
Batch O1 O2 O3 O4 O5 O6 O7
M T M T M T M T M T M T M T
B1 2 10 4 12 6 11 5 9 7 7 1 7 3 5
B2 5 4 4 2 7 4 3 6 1 6 6 5 2 3
B3 3 7 5 6 1 4 6 9 7 10 2 4 4 3
B4 2 9 4 2 7 9 6 1 5 9 3 4 1 3
B5 7 4 6 7 5 6 4 7 2 6 1 10 3 6
B6 2 9 1 3 6 4 7 3 5 6 4 6 3 6
B7 4 5 2 4 7 3 6 2 5 7 1 7 3 6
D. Data set details of inter-slot distance between machines
Table 4: inter-slot distance matrix for Open field layout with 7 machines
Slots S1 S2 S3 S4 S5 S6 S7
S1 0 2 4 8 12 12 10
S2 2 0 2 4 8 12 12
S3 4 2 0 2 4 8 12
S4 8 4 2 0 2 4 8
S5 12 8 4 2 0 2 4
S6 12 12 8 4 2 0 2
S7 10 12 12 8 4 2 0
E. Data set details of Load, Unload Matrices for Open field layout Table 5: Load, Unload Matricesfor Open field layout with 7 machines
Slots S1 S2 S3 S4 S5 S6 S7
Load Station 4 6 8 12 10 8 6
Unload Station 6 8 10 12 8 6 4
Transportation Cost per unit distance = 1Rs Load and Unload cost per unit distance = 1Rs
VIII. RESULTS & DISCUSSIONS
“An angle which has been marked by the researchers in any research is to match their views with those of other researchers. If the typical prosaic test problems are available, the working of different algorithms can be compared approximately the same set of test problems for analysis of results. For this reason, we chose 6
benchmark problems from Ashokan et al. [2] (ASK) as the test problems of this study.
Ashokan has produced a set of problems with 7 machines with 2 and 4 jobs. These benchmark problems are categorized into two groups i.e. constant batch size (CBS) problems and variable batch size(VBS) problems. There are three instances for (nxm
= 7x7)) totally, there are 6 problem instances.”
Table 16: Comparison of arithmetical results of the proposed evolutionary algorithms (for CBS=100 numbers in a batch and same quantity in all batches with number of iterations = 100)
Instan-M/c x J/B x Oper
GA SA
MAKSP (min) TTC (Rs) CPU
(sec) MAKSP (min) TTC (Rs) CPU (sec)
ASK1-(7x7x7) 6900 8100 15 7400 12862 0
ASK2-(7x6x6) 6300 7300 14 6800 10934 0
ASK3-(7x7x6) 7400 8400 14 8100 12602 0
A. Inferences
The table 16 shows the results of test problems for constant batch size (CBS) from ASK 1-ASK 3 and is comprehend that, The test problems are solved through the proposed algorithm and the results are compared and found that performance of GA and SA for calculating total transportation cost (TTC) and make span (MAKSP) is varying as per the problem size. By
relative analysis, we observed that, solutions are optimized for GA and found that GA affords best solution when compared with SA to all test problems.
Further, the computational time of GA is fluctuates as the problem size varies but the computational time of SA is zero for all problems.
Table17: Comparison of arithmetical results of the proposed evolutionary algorithms for CBS=100 numbers in a batch and same quantity in all batches.
Instance (M x J/B x O)
GA SA
BWT(min) MASEQ MWT (min) BWT (min) MASEQ MWT (min)
ASK1 (7x7x7)
B 1: 800 B 2: 3900 B 3: 2600 B 4: 3200 B 5: 2300
1, 4, 6, 3, 2, 5, 7
M 1: 2900 M 2: 2400 M 3: 2900 M 4: 3200 M 5: 2200
B 1: 1300 B 2: 4400 B 3: 3100 B 4: 3700 B 5: 2800
5, 2, 3, 4, 1, 7, 6
M 1: 3400 M 2: 2900 M 3: 3400 M 4: 3700 M 5: 2700
B 6: 3200 B 7: 3500
M 6: 3000 M 7: 2900
B 6: 3700 B 7: 4000
M 6: 3500 M 7: 3400 ASK2
(7x6x6)
B 1: 1800 B 2: 800 B 3: 2700 B 4: 2800 B 5: 1200 B 6: 2700
7, 4, 6, 2, 3, 1, 5 M 1: 1500 M 2: 3900 M 3: 3500 M 4: 3400 M 5: 1700 M 6: 1800 M 7: 2500
B 1: 2300 B 2: 1300 B 3: 3200 B 4: 3300 B 5: 1700 B 6: 3200
7, 4, 6, 3, 5, 1, 2 M 1: 2000 M 2: 4400 M 3: 4000 M 4: 3900 M 5: 2200 M 6: 2300 M 7: 3000 ASK3
(7x7x6)
B 1: 1800 B 2: 2900 B 3: 3200 B 4: 4600 B 5: 700 B 6: 5000 B 7: 1600
5, 1, 6, 2, 4, 3, 7 M 1: 3700 M 2: 4200 M 3: 1500 M 4: 2500 M 5: 3500 M 6: 3000 M 7: 1400
B 1: 2500 B 2: 3600 B 3: 3900 B 4: 5300 B 5: 1400 B 6: 5700 B 7: 2300
7, 3, 4, 2, 6, 1, 5 M 1: 4400 M 2: 4900 M 3: 2200 M 4: 3200 M 5: 4200 M 6: 3700 M 7: 2100 B. Inferences
“The table 18 shows the results of test problems for variable batch size (VBS) from ASK1-ASK3 and is understand that, the test problems are solved through the proposed algorithm and the results are compared and found that performance of GA and SA for calculating total transportation cost (TTC) and make span(MAKSP) is varying as per the problem size. By relative analysis, we observed that, solutions are optimized for GA and found that GA affords best solution when compared with SA to all test problems. Further, the computational time of GA is fluctuates as the problem size varies but the computational time of SA is zero for all problems.
The table 19 shows the results of test problems for
variable batch size (VBS) from ASK 1-ASK 3 and is figure out that, the test problems are solved through the proposed algorithm and the results are compared and found that performance of GA and SA for calculating Batch waiting time(BWT) and Machine waiting time(MWT) obtained for corresponding problem instances is varying as per the problem size and based on make span(MAKSP) value (i.e., if make span is same for both algorithm ,then waiting times will also be same, vice-versa) . By comparative analysis, we observed that, GA shows minimum waiting times when compared with SA to all test problems. Further, the required machine sequences (MASEQ) are depicted in the table.”
Table18: Comparison of arithmetical results of the proposed evolutionary algorithms (for VBS with number of iterations = 100)
Instan-M/c x J/B x Oper
GA SA
MAKSP
(min) TTC(Rs) CPU
(sec) MAKSP (min) TTC(Rs) CPU (sec)
ASK1-(7x7x7) 3380 4155 15 3440 6853.2 5
ASK2-(7x6x6) 2430 3410 14 2460 2950 3
ASK3-(7x7x6) 5220 3715 15 5220 4095 6
Table 19: Comparison of arithmetical results of the proposed evolutionary algorithms for CBS=100 numbers in a batch and same quantity in all batches
Instance (M x J/B x O)
GA SA
BWT (min) MASEQ MIT (min) BWT (min) MASEQ MIT (min)
ASK1 (7x7x7)
B 1: 330 B 2: 2180 B 3: 800 B 4: 2270 B 5: 2920 B 6: 2455 B 7: 320
7, 3, 6, 4, 1, 2, 5 M 1: 1655 M 2: 1605 M 3: 1600 M 4: 1790 M 5: 1300 M 6: 1710 M 7: 1615
B 1: 390 B 2: 2240 B 3: 860 B 4: 2330 B 5: 2980 B 6: 2515 B 7: 380
4, 1, 2, 5, 7, 3, 6 M 1: 1715 M 2: 1665 M 3: 1660 M 4: 1850 M 5: 1360 M 6: 1770 M 7: 1675 ASK2
(7x6x6)
B 1: 180 B 2: 230 B 3: 270 B 4: 1380 B 5: 1920 B 6: 1530
7, 4, 1, 5, 2, 6, 3 M 1: 805 M 2: 1730 M 3: 1305 M 4: 1375 M 5: 940 M 6: 835 M 7: 950
B 1: 210 B 2: 260 B 3: 300 B 4: 1410 B 5: 1950 B 6: 1560
2, 6, 7, 4, 3, 1, 5 M 1: 835 M 2: 1760 M 3: 1335 M 4: 1405 M 5: 970 M 6: 865 M 7: 980 ASK3
(7x7x6)
B 1: 2420 B 2: 3420
7, 3, 5, 1, 6, 2, 4 M 1: 3580 M 2: 4065
B 1: 2420 B 2: 3420
1, 6, 2, 4, 7, 3, 5 M 1: 3580 M 2: 4065
B 3: 2700 B 4: 4380 B 5: 4550 B 6: 4620 B 7: 2900
M 3: 2950 M 4: 2760 M 5: 3745 M 6: 2490 M 7: 2500
B 3: 2700 B 4: 4380 B 5: 4550 B 6: 4620 B 7: 2900
M 3: 2950 M 4: 2760 M 5: 3745 M 6: 2490 M 7: 2500 C. Inferences
The table 18 shows the results of test problems for variable batch size (VBS) from ASK1-ASK3 and is understand that, the test problems are solved through the proposed algorithm and the results are compared and found that performance of GA and SA for calculating total transportation cost (TTC) and make span(MAKSP) is varying as per the problem size. By relative analysis, we observed that, solutions are optimized for GA and found that GA affords best solution when compared with SA to all test problems. Further, the computational time of GA is fluctuates as the problem size varies but the computational time of SA is zero for all problems.
The table 19 shows the results of test problems for
variable batch size (VBS) from ASK 1-ASK 3 and is figure out that, the test problems are solved through the proposed algorithm and the results are compared and found that performance of GA and SA for calculating Batch waiting time(BWT) and Machine waiting time(MWT) obtained for corresponding problem instances is varying as per the problem size and based on make span(MAKSP) value (i.e., if make span is same for both algorithm ,then waiting times will also be same, vice-versa) . By comparative analysis, we observed that, GA shows minimum waiting times when compared with SA to all test problems. Further, the required machine sequences (MASEQ) are depicted in the table.”
IX. GRAPHS
Fig. 2 Comparison of make span for CBS=100 by Proposed algorithms
Fig. 3 Comparison of make span for VBS by Proposed algorithms
A. Inferences
Comparison of make span for constant batch size (CBS) by the proposed evolutionary algorithms for different problem sizes is depicted in Fig.2. The plot shown in Fig 2 is styled for instance ASK 1- ASK 5. It is observed that, there are moderate variations in results of MAKS Pagainst Problem instances shown in the plot for GA and SA .It is found that, MAKSP is low at small size problems and reaches to high value as problem size increases. Further, GA curve is fluctuates at lower values than SA curve.
Comparison of make span for variable batch size (VBS) by the proposed evolutionary algorithms for different problem sizes is depicted in Fig.3. The plot shown in Fig .3 is styled for instance ASK 1- ASK5. It is observed that, there are moderate variations in results of MAKSP against Problem instances shown in the plot for GA and SA .It is found that, MAKSP is low at small size problems and reaches to high value as problem size increases and also in Fig 3, MAKSP variations are
almost closer for both GA & SA. Further, GA curve is fluctuates at lower values than SA curve.
B. Inferences
“Comparison of total transportation cost by the proposed evolutionary algorithm for constant batch size(CBS) is shown in Fig.4. The plot shown in Fig 4 is styled for instance ASK1- ASK3. It is observed that, there are moderate variations in results of TTC against Problem instances shown in the plot for GA and SA .It is found that, TTC is low at small size problems and reaches to high value as problem size increases. Further, GA curve is fluctuates at lower values than SA curve. Actually GA is an effective algorithm in searching local optima when compared with SA. Further, C++ code is running in a special compiler called The C/C++ Development Toolkit (CDT).The CDT is a collection of Eclipse- based features that provides the capability to create, edit, navigate, build, and debug projects that use C++ as a programming language. Further it is more convenient to user to print and display the results and errors if any in execution.
Fig. 4 Comparison of total transportation cost for CBS=100
by Proposed algorithms Fig. 5 Comparison of total transportation cost for VBS by Proposed algorithms
C. Inferences
Comparison of total transportation cost by the proposed evolutionary algorithm for variable batch size (VBS) is shown in Fig.5. The plot shown in Fig 5 is styled for instance ASK1- ASK3. It is observed that, there are moderate variations in results of TTC against Problem instances shown in the plot for GA and SA .It is found that, TTC is low at small size problems and reaches to
high value as problem size increases. Comparison of Batch waiting time (BWT) for constant batch size (CBS) by the proposed evolutionary algorithms is depicted in Fig.6. The plot shown in Fig.6 is styled for instance which has 7 batches/jobs. It is observed that, BWT for constant batch size are less for GA when compared with SA.”
FIG 6: Comparison of proposed algorithm for batch waiting time with constant batch size for the problems with 7 batches
X. CONCLUSION
From the results, authors conclude that Open field layout is optimized using GA is better than SA with constant MHD cost and frequency of trips between machines.
The parameter like transportation cost with machine sequences considering scheduling parameters as constraints such as make span (MAKSP) is determined for Open field layout by running the C++ code on eclipse (IDE) tool for 10 test runs the performance of the proposed algorithm is tested over a number of problems selected from the literature and comparison is made between GA &SA. The experimental results reveal that the proposed Genetic Algorithm is effective and efficient for Open field layout design. From the graph, it is clear that for Open field layout, the total transportation cost is less for lower level problems and reaches to high value as the problem size enhanced.
Further, it is conclude that GA provides optimum solutions than SA, but computational time is more than SA.”
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