Performance of metaheuristic methods for loop

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Performance of metaheuristic methods for loop

  1. 1. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 4, Issue 1, January – April (2013), © IAEME31PERFORMANCE OF METAHEURISTIC METHODS FOR LOOPLAYOUT DESIGN IN FLEXIBLE MANUFACTURING SYSTEM WITHINTEGRATED SCHEDULING1K.Mallikarjuna, 2V.Veeranna, 3K.Hemachandra Reddy,1Research Scholar, JNTU, Anantapur, India,2Dean, BITS Kurnool, India3Registrar, JNTU, Anantapur, IndiaABSTRACTFMS’s seems to be a very promising technology as they provide flexibility, which isessential for many manufacturing companies. This paper speaks about multi-objectiveoptimization related to FMS scheduling which act as a constraint in configuring the looplayout in optimum manner by various evolutionary algorithms i.e. Meta-heuristics like GA,SA etc. The first objective is concern with flexible batch scheduling problem (FBSP). Thenext objective is focus on determination of optimum machine sequence with minimum totaltransportation cost. In this paper, the various loop layout problems are tested using C++ codesfor enactment of objective function with respect to computational time and number ofproblem instances involved in GA and SA. The results of the different optimizationalgorithms (Genetic Algorithm and simulated annealing method) are compared with existingresults and conclusions are depicted.Keyword: Flexible Manufacturing systems, loop layout, Multi-objective, Genetic Algorithm,Simulated Annealing, Transportation Cost.1 INTRODUCTIONWith the advent of technology, the market for manufactured products is becomingincreasingly international. Manufacturing has thus become highly competitive and companieshave had to focus their resources, capabilities, and energies on building a sustainablecompetitive advantage. Flexible Manufacturing System[1] combines collection of machinestools which are termed as numerical control machines that can arbitrarily process a cluster ofjobs, taking automated material management and workstation control to balance resourceINTERNATIONAL JOURNAL OF PRODUCTION TECHNOLOGY ANDMANAGEMENT (IJPTM)ISSN 0976- 6383 (Print)ISSN 0976 - 6391 (Online)Volume 4, Issue 1, January - April (2013), pp. 31-38© IAEME: www.iaeme.com/ijptm.aspJournal Impact Factor (2013): 4.3285 (Calculated by GISI)www.jifactor.comIJPTM© I A E M E
  2. 2. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 4, Issue 1, January – April (2013), © IAEME32exploitation over which the system can accept automatically to variation in jobsmanufacture, amalgams and stages of yield. Material handling is important, yet sometimes itis an overlooked aspect of automation. The main function of an MHS is to supply the truematerials at the exact locations and at the right time, the cost of material handling has highpriority in total cost of production. It means handling cost is equal to 2/3 of the totalmanufacturing cost [2]. This fraction varies depending on type and quantity of production andthe degree of automation in the material handling function. Finally Material handling plays animportant role in FMS.The FMS layout involves allocating diverse reserve for attaining full competence.The arrangement has an influence on the make span and cost [3] which should be determinedin the inception of the FMS [4]. In practice most commonly used type of FMS layouts [5] are1) Line or single row layout.2) Loop layout.3) Stepladder layout.4) U-shaped layout.Among the above layouts, this paper focus on Loop layout design with integrated schedulingusing GA and SA.2 LITERATURE SURVEYDuring former epoch, FMS layout design with integrate scheduling has got extraemphasis since of its prominence from both hypothetical and real-world points of sight. Earlyinvestigation was intensed mainly on the origination and explanation of the problem as themathematical model; such as branch and bound method and dynamic programing [6], butthese approaches can only be useful for small problems. Giffler and Thompson [7] presenteda typical procedure to create all active plans related to general “n” jobs and “m” machineproblem. R.M.satish kumar and P.Ashokan [4] introduced an ACO algorithm for the layoutdesign with integrated scheduling by applying priority dispatching rules using Giffler andThompson [4] algorithm.3 PROBLEM DESCRIPTIONS3.1NotationsThe notations [21] which are used to develop a mathematical model of the design ofline layout are defined and interpreted as follows.i – part type index i=1,2,3,……,nj – Process index j= 1,2,3,…..,nik – Machine index k=1,2,3,……,mn – Number of batches / jobm – Number of machinesSmaxi – Make span of system maximumcompletion timesn,m – Make span of systemSi,j,k – Partial make span withoutpredecessors
  3. 3. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 4, Issue 1, January – April (2013), © IAEME33si,j+1,k – Enhanced make span withpredecessorsT i,j – The duration (processing time ) ofoperation j of job iT i,j+1 – The duration of operation j =1of jobiM – Total number of machines containedin themanufacturing systemMi – Machine in slot n1Mj – Machine in slot nNN – Number of slotsMHm1,m2 – Material handling cost betweenmachines m1 and m2 ( m1 m2 =1,2,3,…….,M )RDn1,n2 – Rectangular distance betweenmachinery locations n1 and n2 ( n1 n2= 1,2,3,……N )MFm1,m2 – Amount of material flow amongmachines m1 and m2 ( m1 m2 =1,2,3,….M)LOCmi – Loading cost from loading station tomachinesULOCmi – Unloading cost from unloadingstation to machinesI) Objective FunctionsMinimize Make Span F(Smaxi)Minimize F (Smaxi ) = sn,mSub toSi,j,k ≤ si,j+1,k – Ti,j+1 , j=1,2,3,…p-1Si,j,k ≥ 0, j = 1,2,3,……nMinimize Total Transportation Cost ( Z )( Z ) = ∑Mmi=1 ∑Mmj=1 ( MFm1,m2*MHm1,m2*RDn1,n2 ) + LOCmi + ULOCmjSub to∑Mmj=1 Xmi mj = 1 if machine mi is at assigned to slot N= 0 otherwise∑Mmi=1 Xmi mj = 1 if machine mi is at assigned to slot N= 0 otherwiseXmi mj ∈{0,1}, mi, mj = 1,2,…………..N
  4. 4. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 4, Issue 1, January – April (2013), © IAEME344. PROPOSED METHODOLOGYThe general explanation of the suggested procedures is shared out as follows.4.1 Genetic AlgorithmGenetic algorithms are recognized to be capable for overall optimizing. Though, theyare not sound fit to accomplish exceptionally adjusted local searches and are liable toconverge in advance earlier the best solution has been found. The genetic algorithm is avigorous technique, based on the natural selection and genetic production mechanism. Itprocesses a group or population of possible solutions within a search space.4.2. Simulated Annealing AlgorithmOne of the commonly used Trajectory based algorithms is the Simulated Annealing.SA is an optimization algorithm that is not fool by false minima and is easy to implement.For certain problems, simulated Annealing may be more effective provided when the goal isto find an acceptably good solution in fixed amount of time, rather than the best possiblesolution. It is a neighborhood search technique that has produced good results forcombinatorial 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.5. CONFIGURATION OF LOOP LAYOUTAGVLOADINGUNLOADINGS3S4S5 S7JOBS1S64units2units2unitsS2Figure 1 Loop Layout Arrangements of FMS for 7 machines6 DATA SET DETAILS FOR LOOP LAYOUT WITH FJSPA Production system with the summary and Batch sizes and the layout of FMS areshown in table1. The data set details of batch varieties and sizes are given in table 2.Let therebe parts to be processed on machine for various operations with processing times are depictedin table 3 The inter slot between machines i.e., the gap between machines measures in unitsare given in table 4 The loading/unloading distance matrix specifies distance from machinesto load/unload station are shown in table 5, unit material handling cost per unit which means;the carrying cost of parts between machines is unit cost.
  5. 5. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 4, Issue 1, January – April (2013), © IAEME35Data set details of Outline of Production systemTable 1: Outline of Production systemLayoutPatternNo. ofMachinesNo. ofbatchesNo ofoperationsLoad/ UnloadstationsNo ofAGVLoop 7 7 7 2 1Data set details of Batch varieties and sizes(VBS=Variable Batch size)Table 2: Batch varieties with batch sizes of the Loop layout with 7machines with 7 jobsBatch number B1 B2 B3 B4 B5 B6 B7BatchtypesVBS50 40 60 30 10 25 90Data 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 Loop layout with7 machines and 7 jobsBatchO1 O2 O3 O4 O5 O6 O7M T M T M T M T M T M T M TB1 2 10 4 12 6 11 5 9 7 7 1 7 3 5B2 5 4 4 2 7 4 3 6 1 6 6 5 2 3B3 3 7 5 6 1 4 6 9 7 10 2 4 4 3B4 2 9 4 2 7 9 6 1 5 9 3 4 1 3B5 7 4 6 7 5 6 4 7 2 6 1 10 3 6B6 2 9 1 3 6 4 7 3 5 6 4 6 3 6B7 4 5 2 4 7 3 6 2 5 7 1 7 3 6Data set details of inter-slot distance between machinesTable 4: inter-slot distance matrix for Loop layout with 7 machinesSlots S1 S2 S3 S4 S5 S6 S7S1 0 2 4 8 12 12 10S2 2 0 2 4 8 12 12S3 4 2 0 2 4 8 12S4 8 4 2 0 2 4 8S5 12 8 4 2 0 2 4S6 12 12 8 4 2 0 2S7 10 12 12 8 4 2 0
  6. 6. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 4, Issue 1, January – April (2013), © IAEME36Data set details of Load, Unload Matrices for Loop layoutTable 5: Load, Unload Matrices for Loop layout with 7 machinesSlots S1 S2 S3 S4 S5 S6 S7Load Station 4 6 8 12 10 8 6Unload Station 6 8 10 12 8 6 4Transportation Cost per unit distance = 1RsLoad and Unload cost per unit distance = 1Rs8 RESULTS & DISCUSSIONSIf the standard usual test problems are accessible, the performances of differentalgorithms can be compared on closely the same set of test problems. For this reason, wechose 4 benchmark problems from Kumanan et al. [5] (KMN) as the test problems of thisstudy.The table 18 shows the results of test problems for variable batch size (VBS) from KMN1- KMN 4 and is comprehend that, The test problems are solved through the proposed algorithmand the results are compared and found that performance of GA and SA for calculating totaltransportation cost (TTC) and make span (MAKSP) is varying as per the problem size. Byrelative analysis, we observed that, for KMN 1 makespan of GA is minimum than SA and KMN3 makespan of SA is minimum than GA . However,TTC is optimized for GA and found that GAaffords best TTC when compared with SA to all test problems. Further, the computational time ofGA is fluctuates as the problem size varies but the computational time of SA is zero for allproblems.The table 19 shows the results of test problems for variable batch size (VBS) fromKMN 1- KMN 4 and is comprehend that, The test problems are solved through the proposedalgorithm and the results are compared and found that performance of GA and SA for calculatingBatch waiting time(BWT) and Machine waiting time(MWT) obtained for corresponding probleminstances is varying as per the problem size and based on make span(MAKSP) value . Bysensitive analysis, we observed that, GA is best for KMN 1 whereas SA is best for KMN 3.Further, the required machine sequences (MASEQ) are depicted in the same table.Comparison ofmake span for variable batch size (VBS) by the proposed evolutionary algorithms for differentproblem sizes is depicted in Fig.2. The plot shown in Fig .2 is styled for instance KMN 1- KMN4. Comparison of total transportation cost by the proposed evolutionary algorithm for variablebatch size (VBS) is shown in Fig.3. The plot shown in Fig 3 is styled for instance KMN 1- KMN4. Comparison of Batch waiting time ( BWT ) and Machine waiting time( MWT) for constantbatch size (CBS) by the proposed evolutionary algorithms is depicted in Fig.4. The plot shown inFig.4 is styled for instance which has 7 batches/jobs.Table18: Comparison of arithmetical results of the proposed evolutionary algorithms (forVBS with number of iterations = 100)Instance -M/c x J/Bx OperationGA SAMAKSP(min)TTC(Rs)CPU(sec)MAKSP(min)TTC(Rs)CPU(sec)KMN 1-(7x7x7) 3275 4060 15 3390 4960 0KMN 2-(7x7x4) 2190 5900 14 2190 6000 0KMN 3-(7x7x5) 3080 4130 14 3040 4390 0KMN 4-(7x7x6) 5220 4100 15 5220 4940 0
  7. 7. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 4, Issue 1, January – April (2013), © IAEME37Table 19: Comparison of arithmetical results of the proposed evolutionary algorithms forVBS with number of iterations = 100)Instance(M x J/B x O)GA SABWT(min)MASEQ MIT (min) BWT (min) MASEQ MIT(min)KMN 1(7x7x7) B1: 225B2: 2075B3: 695B4: 2165B5: 2815B6: 2350B7: 2157, 5, 2, 1, 4, 3,6M1: 1550M2: 1500M3: 1495M4: 1685M5: 1195M6: 1605M7: 1510B1: 340B2: 2190B3: 810B4: 2280B5: 2930B6: 2465B7: 3307, 6, 3, 4, 5,2, 1M1: 1665M2: 1615M3: 1610M4: 1800M5: 1310M6: 1720M7: 1625KMN 2 (7x7x4) B1: 140B2: 1550B3: 690B4: 1380B5: 2020B6: 1715B7: 3904, 6, 7, 1, 3, 2,5M1: 1875M2: 975M3: 960M4: 210M5: 1040M6: 1790M7: 1035B1: 140B2: 1550B3: 690B4: 1380B5: 2020B6: 1715B7: 3904, 3, 1, 7, 6,2, 5M1: 1875M2: 975M3: 960M4: 210M5: 1040M6: 1790M7: 1035KMN 3 (7x7x5) B1: 1680B2: 1950B3: 1470B4: 2160B5: 3330B6: 2580B7: 10205, 2, 6, 3, 4, 1,7M1: 3065 M2:1780M3: 2900M4: 2780M5: 880M6: 1020M7: 1765B1: 1090B2: 1360B3: 880B4: 1570B5: 2740B6: 1990B7: 4306, 2, 3, 1, 7,4, 5M1: 2475M2: 1190M3: 2310M4: 2190M5: 290M6: 430M7: 1175KMN 4 (7x7x6) B1: 2420B2: 3420B3: 2700B4: 4380B5: 4550B6: 4620B7: 03, 4, 2, 6, 1, 5,7M1: 3580M2: 4065M3: 2950M4: 2760M5: 3745M6: 2490M7: 2500B1: 2420B2: 3420B3: 2700B4: 4380B5: 4550B6: 4620B7: 04, 5, 7, 6, 1,2, 3M1: 3580M2: 4065M3: 2950M4: 2760M5: 3745M6: 2490M7: 2500GRAPHS
  8. 8. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 4, Issue 1, January – April (2013), © IAEME38CONCLUSIONBy means of the proposed objective function, we can find the optimum sequence ofmachines in the recommended layout in the FMS. The model searches for the optimumlayout in rows and finds itself the optimum numbers of rows.From the results, we conclude that Loop layout is optimized using GA is better thanSA with constant MHD cost and frequency of trips between machines. The parameter liketransportation cost with machine sequences considering scheduling parameters as constraintssuch as make span ( MAKSP) is determined for Loop layout. The experimental results revealthat the proposed Genetic Algorithm is effective and efficient for Loop layout design. Fromthe graph, it is clear that for Loop layout, the total transportation cost is less for lower levelproblems and reaches to high value as the problem size enhanced. Further, it is conclude thatGA provides optimum transportation cost than SA, but computational time is more than SA.REFERENCES[1].William W.Luggen (1991) flexible manufacturing cells and systems. Prentice-hall, Inc. Adivision of Simon & Schustes Englewood cliffs, newjersy07632 ISBN 0-13-321738-8.[2].Tompkins ja, white ja, bozer ya, janchoco Jmn (2003) facilities planning. 3rdedn, wiley, NewYork.[3].Apple Jm (1977) plant layout and material handling. 3rdedn. The Ronald press co. New York[4].R.M. sateesh kumar, p.Ashokan, s.kumanan (2008) design of loop layout. Inflexiblemanufacturing system using non-traditional optimization technique. Int. J.Adv manufacturingtechnology (2008) 38:594-599.[5].MIKELL.P.GROOVER (1992) Automation, Production systems and computer-integratedmanufacturing. Prentice-Hall Inc. ISBN-0-87692-618-9.[6].Ruey-Mawchen+and Shin-Tang Lo++(2006) using ant colony system to solve resourceconstrained project scheduling problems. Int-J.comp sci & network secu vol.6 No-11,November 2006.[7].Giffler B.Thompson GL (1960) Algorithms for solving production scheduling problems.Int.J.Oper Res 8:487-503.[8].Hongbo Liu, Ajith Abraham, Crina Grosan, Ningning Li, a novel variable neighbourhoodparticle swarm optimization for multi-objective flexible job-shop scheduling problems.[9].J. Jayapriya, K. Thirusangu, “Petri Nets Based Theoretical Scheduling For FlexibleManufacturing Systems” Volume 2, Issue 2, 2011, and Pp: 20-24, ISSN Print: 0976- 6383,ISSN Online: 0976 – 6391

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