Establishment of AGVs fleet size in FMS Using Petri-Net

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1 Interntionl Journl of Science, Engineering nd Technology Reserch (IJSETR) Estlishment of AGVs fleet size in FMS Using Petri-Net S.C. Srivstv & R.K.Singh* Abstrct Automted guided vehicles re widely used mteril hndling devices in Flexible Mnufcturing Systems (FMS) environment. The efficient opertions of FMS require creful nd detiled study for estimtion of optiml fleet size of AGVs. In this rticle, n nlyticl model considering witing / blocking time, empty trvel time nd lod hndling time, for determintion of minimum number of AGVs, without impiring the efficiency of FMS is developed. In this reserch, Petri-Net model is lso presented to highlight the pth followed by AGVs through vrious mchines. Index Terms Petri Net, Trnsition Probility Mtrix, Automted Guided Vehicles, Flexible Mnufcturing system (FMS). I. INTRODUCTION The min components of FMS re mchine tools, nd mteril hndling system which re connected by network of computers nd controller for controlling the system. Necessities in present mrket scenrio hve generted much interest in development of both simultion nd nlyticl techniques for designing mteril hndling systems like Automted Guided Vehicles (AGVs). Automted Guided Vehicles (AGVs) re one of the most importnt mteril hndling system components tht ffects the performnce nd efficiency of FMS. The control system long with its hrdwre / softwre decides the criticl route of AGVs, mong the sttions. In spite of vrious problems ssocited with AGVs, prticulrly in deling with multi vehicle system, AGV bsed mteril hndling systems find wide rnging pplictions in ssembly, wrehousing nd trnsfer of tools / prts. In this pper, n nlyticl model for estimting the mximum number of AGVs hs been proposed. In the proposed nlyticl model, number of times n AGV moves to vrious mchines per unit flow is represented by flow mtrix nd the probility of ech route undertken by AGV is determined, dopting the trnsition probility mtrix. Besides this, n ttempt hs been mde in this reserch to Mnuscript received Oct 15, S.C. Srivstv, Deprtment of Production Engineering, BIT Mesr, Rnchi , Indi,. * R K Singh(Corresponding Author), Deprtment of Production Engineering, BIT Mesr, Rnchi , Indi, cpture the grphicl power of Petri net to model AGVs in FMS. The pper is further orgnized s follows. The following section focuses on the efforts of vrious reserchers in the re pertining to modeling of FMS. Section 3 discusses the design problems of AGVs bsed Mteril Hndling System (MHS). The system is described long with the nlyticl model in section 4. Section 5 illustrtes the solution methodology. An illustrtive exmple is detiled in section 6. Section 7 describes the Petri net modeling methodology. The pper is concluded in section 8. II. LITERATURE REVIEW. Mhdeven nd Nrendrn [5] presented mthemticl model to design n utomted guided vehicle bsed system for n FMS. But, their model ws simplified one without considering scrp rte, demnd of prts etc. Rjoti et l.[7] presented simultion bsed nlysis to determine optiml fleet size of AGVs. But there re some drwbcks in using simultion bsed models. These re too time consuming nd provide solution for specific problem. Moreover, Simultion models cn not be used for dynmic problems. Yim nd Linn [12] delt with the sme topic nd lso used Petri-Net bsed simultion to investigte effect of different push nd pull disptching rules on system performnce. Petri-Net bsed models hve lso been used to obtin production rtes, throughputs delys, resource utiliztion, cpcity, reliility mesures nd ded lock voidnce for FMS. The detiled informtion out these pplictions cn be found in [2], [8], [3], [6], [10]. The detils of Petri-Net cn be found in vrious other litertures [9], [10]. III. DESIGN PROBLEMS OF AN AGVS BASED MHS The chievement of high performnce from AGVs is ffected by severl design nd control issues tht re required to be solved before the instlltion of system. Some of these issues long with their effects hve been discussed here. First of ll, type nd number of vehicles put into service should be specified. It is desirle to keep number of vehicles s less s possible becuse of the fct tht increse in number of AGVs [16] clls for sophisticted softwre requirements for controlling purpose nd thus mking the system instlltion expensive. An pproprite guide pth configurtion long with the proper loctions of lod nd trnsfer sttion, nd buffer spces re lso mjor decision vriles tht govern the resolution of ded lock [17], bottlenecks nd ccidents etc. Rules for vehicle disptching need to be specified in order to 1092

2 Interntionl Journl of Science, Engineering nd Technology Reserch (IJSETR) mximize the throughput from the system. Unit lod sizes, centrl nd / or locl work in process storge cpcity etc. re lso to be known in dvnce. In order to chieve n optiml system performnce in terms of mximum throughput nd system efficiency, it is essentil tht the system is to be dministered by judicious mix of forementioned prmeters. IV. SYSTEM DESCRIPTION AND ANALYTICAL MODEL The configurtion nd lyout of n FMS considered for this study is digrmed in Fig. 1. The proposed FMS consists of four mchines, one centrl buffer, one input (I/P) nd output (O/P) buffers nd four sfe zones. B 5 M1 M C.B. 9 M Figure 1: A typicl FMS tken under considertion The proposed FMS configurtion is modified version of the configurtion discussed erlier by Rjoti et l. [7], Bozer nd Shrinivsn [1] nd Yim nd Linn [12]. Components of system considered in this study re: Mchines M1, M2, M3 nd M4 (numbered 1 to 4) 5 C.B Buffers Centrl Buffer (C. B., Numbered 5), nd I/P nd O/P buffer (B., numbered 10). Sfe zones (s shown by numbers 6, 7, 8 nd 9). These re provided by decrese the trffic problems. Only one job cn enter in the control zone t time nd control zones re lso provided with buffers for queuing of the vehicles. Some of the AGV trcks provided bi-directionl movement, shown by double sided rrows. AGV lwys choose shortest pth between two loctions. It tkes two minutes to pss through ny AGV trct nd one minute to pss through control zone. It tkes hlf minute to lod or unlod prt. Ech mchine is provided with suitle sensor to show the completion of job processing. 8 M3 V. SOLUTION METHODOLOGY Determintion of number of AGVs in FMS hs become significnt s well s complicted tsk. This decision is lrgely ffected by other design nd control prmeters s discussed in previous sections. In ddition to these prmeters, the ove decisions lso depend on the operting behviour of the systems, becuse the operting dynmics re influenced by the rndomness in prt rrivls, vilility of lterntive processing units, disptching strtegies reltive to prts nd vehicles, vilility of lterntive vehicles routes, trffic congestion etc.. void the exhustive computtion nlysis in determintion of individul impct of ech prmeters on system, probility bsed pproximte nlysis is dvocted in this reserch to ddress the problem. In the proposed model, percentge of time n AGV moves to vrious mchines for unit flow is denoted by flow mtrix nd ide bsed on trnsition probility mtrix employed to determine probility for ech route to be under tken by the AGV Nottions D i : Demnd for job i (%) L M ij : Numbers of lods removed for mchine to nother loction. : Number of mchines, job i hs to visit to complete processing in the j th sequence [NAGV] : Number of AGVs P ij : Probility tht the job i is processed using j th sequence. R i : Net requirement for job i. Seq i S i : Number of sequence in job i cn be processed. : Scrp rte for job i T : Men processing rte for mchine. T T v : Time tken by AGV to trvel between two loctions nd b. : tl ville time of AGV per shift. T ij : Processing time of job i in the th mchine when undergoing processing using j th sequence. T totl : tl AGV time required per shift. X : Number of prts processed simultneously. Here [NAGV] refers to lest integer greter tht NAGV. Complete solution pproch is discussed in following steps: Step 1: Clculte the net requirement of jobs (in percentge) R i = D i / (1 - S i ) (1) Step 2 : Define nd clculte the element of flow mtrix 1093

3 Interntionl Journl of Science, Engineering nd Technology Reserch (IJSETR) Considering I/P nd O/P buffer s (m + 1) th mchine the element of flow mtrix, f two mchines nd b is given by :- X Seq i R ipij * i1 j1 f (2) Here, b = 1, 2,..., (m + 1) 1 And, = On simplifiction eqution (ii) cn be rewritten s- f = R 1 (P 11 * + P 12 * + P 13 * P 1Seqi * ) + R 2 (P 21 * + P 22 * + P 23 * P 2Seqi * ) R X (P X1 * + P X2 * + P X3 * P XSeqi * ) (3) Here, (ij) = 1; if b th mchine is visited immeditely fter th mchine in the j th sequence of job I. 0; else 1; if mchine is visited in j th sequence of job i. 0; else T totl Where, m1 1 L m1 1 m1 b1 L TP m1 b1 m1 TP u t u m1 t t t t I u 1 L TP u t I b 1 b1 bb w Bb b B I i : Loding time t sttion i. u i : Unloding time t sttion i. t w : Witing time. t ij : Trvel time between sttions i nd j. Step 6 : Clculte number of AGVs required. I B I b..(5) Finlly knowing the totl time ville per AGV, per shift, the number of AGVs is obtined by dividing totl required time from totl ville time. So, N AGV = T totl / T AGV But this comes out to be rel vlue generlly, hence smllest integer greter thn N AGV i.e. [N AGV ] is tken. Step 7 : Clculte the men utilistion of AGVS U m = ( [N AGV ] / N AGV ) * 100 Here, U m denotes men utiliztion of AGV system. Step 3 : Define the element of trnsition probility mtrix Trnsition Probility Mtrix TP = [TP ] is obtined by normlizing the flow mtrix F = [f ] Step 4 : Clcultion of men processing rte of ech mchine X i ij i1 Seq j1 M b1 X i1 R ipij(ij) (4) Seq i R ipij (ij) j1 Step 5 : Clculte totl time required by the AGV to complete the given tsk on ech mchine. In this step different possibilities for routing of prt from one mchine to nother fter processing re tken under considertion. First of ll due to limited buffer storge cpcity in front of the mchines, it my be required to put the semi finished prts t the centrl buffer in cse AGV finds mchine busy. Let is the proportion of time in which this hppens. Secondly it my lso be possible tht the time required to move from mchine to centrl buffer nd centrl buffer to mchine is more thn tht the time required to complete in process prt loded on mchine. In this cse AGV will prefer to wit t mchine centre insted of going to centrl buffer. Let is proportion for this possibility. Hence equipped with these possibilities eqution for totl time cn be expressed s - VI. AN ILLUSTRATIVE EXAMPLE The configurtion of FMS described in figure 1 is gin referred to determine the AGVs requirement for the system. Dt pertining to the processing time of jobs on the mchines re listed in tle 1. Detils out vehicle trvel time between vrious pirs of sttions re presented in tle 2. The relevnt informtion relted to job flow, demnd mix, scrp rte, sequence probility etc. re given in tle 3. The vlues of t w, nd re tken 11 minutes, 0.4 nd 0.25 respectively. After executing step 1, step 2 nd step 3 outlined in section 4, the flow mtrix nd trnsition probility mtrix re constructed nd shown in tle 4 nd tle 5. Men processing rte nd number of lods from the mchine re clculted for the given dt fter execution of step 4. For mchine 1 clcultion of men processing rte is given in tle 6. Clcultion of number of lods for sme mchine is done s L 1 = 480 / 1 22 (Tking 8 hours shift.) The corresponding vlues for mchine 2, 3 nd 4 is given in tle 7. There fter the totl time required by the AGV, so tht tsk on ech mchine could be completed within the given time horizon is clculted bsed on the step 5. For instnce the procedure to enumerte the totl time required by AGV for mchine 1 is illustrted s : Putting the vlues of prmeters t w, nd in eqution 5, t totl comes out to be 1094

4 Interntionl Journl of Science, Engineering nd Technology Reserch (IJSETR) (T totl ) 1 = 0.4 [22 {0.417 ( ) ( ) }] [22 {0.417 (6+11+1) ( ) } ] [22 {0.417 (6+1) (12+1) } ] = min The corresponding vlues for mchines 2, 3 nd 4 re given in tle 7. The vlue of totl time for the proposed problem is minutes. Now, let totl AGV time ville per shift is 420 minutes (due to time elpsed in the initil setting of AGVs.). Finlly, totl number of AGVs is clculted ccording to step 6 nd this comes out to be 4. Job no. Tle 1. Processing Time of Prts Trvel Time (min) B C. B B C. B Tle 2. Trvel Time between Two Sttions B tl B Demnd D1% S1% Tle 3. Other Relted Input Dt Description of Job Mchine Visited Probility Seq 1 Seq 2 Seq 1 Seq Tle 4. Flow Mtrix No. of m/c B tl Net req. Ri % Tle 5. Trnsition Probility Mtrix B B Tle 6. Tle to Clculte Men Processing Rte of Mchine 1 Job no. i R i P ij R ij * P ij * Col 1 (ij) R ij * P ij/ Sum Col 2 T ij Col 1 * Col Sum = Tle 7. Vrious Clculted Vlues for Mchines 2, 3, nd 4. Prmeter Mchine (i) Men Processing rte ( 1) Number of Lods tl Time Sum T totl = Tle 8. Detils of Plces Plce Number Description 1. M1 is free 2. M2 is free 3. M3 is free 4. M4 is free 5. Pllet sttion is free 6. Loded pllet for PR1 is ville 7. AGV is ville 8. PR1 in M1 s in buffer 9. PR1 in M1 s out buffer 10. PR1 in M3 s in buffer 11. PR1 in M3 s out buffer 12. PR1 in M2 s in buffer 13. PR1 in M2 s out buffer 14. PR1 in M4 s in buffer 15. PR1 in M4 s out buffer 16. Counter for PR B VII. PETRI NET MODELING METHODOLOGY Petri nets [13], [14] re well suited to model the dynmics of flexible mnufcturing systems [15]. These concisely 1095

5 Interntionl Journl of Science, Engineering nd Technology Reserch (IJSETR) represent the ctivities resources nd constrints of the system in single coherent formultion. Formlly Petri-Net is represented s set of form: N = (P, T, F, H, 0 ) Here, P : Finite non-empty set of positions or plces T : Finite non-empty set of trnsitions. F : P * T {1, 2...} nd H : T * P {0, 1, 2...} 0 : Function, representing initil mrking of plces Grphiclly, Petri-Net work is bi-prtiet grph with two types of vertices. Vertices p P re drwn s circles nd vertices t T re represented s brs or brriers. In Petri-Net plces re represented by smll circles (0) nd mrkers re represented by smll dots (.), decides the sttus of the plces. Trnsitions re represented by smll brs these my be either simple or timed. In this rticle, mchine trnsitions represent event (strt or finish), hence tken s simple trnsitions ( - ), while AGV trnsitions represents ctivities, therefore tken s time trnsitions ( ). The rcs, generlly tken s stright lines, from trnsition to plces nd plces to trnsitions, defines the vlue of net function. In this rticle Petri-Net, cple of representing of flow of jobs through vrious mchines is lso presented. VIII. CONCLUSIONS A probility bsed nlyticl model is developed by utilizing the ville informtion pertining to trget production plnt nd prt routing. The problem is nlysed under sttic condition, however some llownce for initil instlltion of system is considered. Determintion of optimum fleet size for AGVS is n importnt design fctor. It is very difficult to crry out simultion nlysis due to presence of multiple decision vriles nd high computtionl time. Therefore, present model is very useful to mke resonly good estimte of vehicle requirement in resonly good time. Production rtes of ech mchine in the FMS cn be lso be known using this probility bsed model. A simple Petri-Net model to represent flow of jobs through vrious mchines without considering time element is lso presented in figure 2. The ssocited plce nd trnsition nottions re displyed in tle 8, tle 9 nd 9b. Tle 9b. Detils of Simple Trnsitions Trnsition Number Description 21. M1 processing PR1 22. M2 processing PR1 23. M3 processing PR1 24. M4 processing PR1 25. Unloding nd Loding of Pllet for PR AGV Trnsitions Simple Trnsitions Plces kens Figure 2: Petri Net model to represent movements for Product Tle 9. Detils of AGV Trnsition Trnsition Number Description 11. AGV trnsports PR1 from I/P nd O/P buffer to M1 12. AGV trnsports PR1 from M1 to M3 13. AGV trnsports PR1 from M3 to M2 14. AGV trnsports PR1 from M2 to M4 15. AGV trnsports PR1 from M4 to pllet sttion IX. REFERENCES [1] BOZER, Y. A., nd SHRINIVASAN, M. M., Tndem configurtions for utomted guided vehicle system nd nlysis of single vehicle loops, IIE Trnsctions, 23 (1), p 72 82, [2] D SOUZA, K. A. nd KHATOR, S. K., A survey of Petri-Net pplictions in modeling controls for utomted mnufcturing systems, Computers in Industry, 24, p 5 16, [3] LIN, J. T., nd LEE, C. C., ACTPN bsed scheduler for flexible mnufcturing cell, Journl of the Chinese Institute of Engineers, 18 (5), p , [4] MAHADEVEN, B., nd NARENDRAN, T. T., Design of n utomted guided vehicle-bsed mteril hndling system for 1096

6 Interntionl Journl of Science, Engineering nd Technology Reserch (IJSETR) flexible mnufcturing system, Interntionl Journl of Production Reserch, 28 (9), p , [5] MAHADEVEN, B., nd NARENDRAN, T. T., Estimtion of number of AGVs for n FMS : n nlyticl model, Interntionl Journl of Production Reserch, 31 (7), p , [6] MENG, J., SOH, Y. C., nd WANG, Y., A TCPN model nd dedlock voidnce for FMS jobshop scheduling nd control system, IEEE Interntionl Workshop on Emerging Technologies nd Fctory Automtion, Pris, Frnce, p , [7] RAJOTIA, S., SHANKER, K., nd BATRA, J. L., Determintion of optiml AGV fleet size for n FMS, Interntionl Journl of Production Reserch, 36 (5), p , [8] SHUKLA, C. S., nd CHEM, F. F., The stte of the rt in intelligent rel time FMS control; comprehensive survey, Journl of Intelligent Mnufcturing, 7 (6), p , [9] VISHWANDHAM, N., nd NARHARI, Y., Stochstic Petri-Nets for performnce evlution of utomted mnufcturing systems, Informtion Decision Technology, 14, p , [10] VISHWANDHAM, N., NARHARI, Y., nd JHONSON, T. L., Dedlock prevention nd dedlock voidnce in FMS using Petri-Net moldes, IEEE Trnsctions on Robotics, 6 (6), p , [11] VISHWANDHAM, N., nd NARHARI, Y., Performnce modeling of utomted mnufcturing systems, Prentice Hll of Indi, New Delhi, [12] YIM, D., nd LINN, R. J., Push nd pull rules for disptching utomted guided vehicles in flexible mnufcturing system, Interntionl Journl of Production Reserch, 31 (1), p 43 57, [13] Zhou, M. C. nd DiCessr, F., Petri net Synthesis for Discrete Event Control of Mnufcturing Systems, Kluwer, [14] Jung, M. D., A Petri net synthesis theory for modeling flexible mnufcturing systems, IEEE Trns. On System Mn nd Cybernetics, Prt A, 27(2), [15] Silv, M. nd Vlette, R., Petri net nd Flexible Mnufcturing System, LNCS: Advnces in Petri nets, p , [16] Co, G. C. nd Tnchoco, J. M. A., A review of reserch on AGVS vehicle mngement. Engineering Costs nd Production Economics, 21, 35-42, [17] Lee, C. C. nd Lin, J. T., Dedlock prediction nd voidnce bsed on Petri nets for zone-control utomted guided vehicle systems. Interntionl Journl of Production Reserch, 33, , Ritesh Kumr Singh is Associte Professor in the Deprtment of Production Engineering, BIT, Mesr, Rnchi, Indi. He hs 14 yers of teching nd reserch experience. His reserch interests include continues improvement philosophies such s len mnufcturing, TOC, Six Sigm, Reconfigurle Mnufcturing Systems (RMS), supply chin mngement nd e-sourcing etc. He hs uthored nerly 40 technicl ppers in peer-reviewed journls, nd t vrious interntionl conferences. His contributions hve ppered in vrious reputle journls such s Advnce Engineering Informtics, Engineering Appliction of Artificil Intelligence, IJPR, IJAMT, PPC, JEM, etc. Shrd Chndr Srivstv is Associte Professor in the Deprtment of Production Engineering, BIT, Mesr, Rnchi, Indi. He hs 14 yers of teching nd reserch experience. His reserch Interest includes, FMS, Mnufcturing Automtion etc. He hs uthored nerly 25 technicl ppers in peer-reviewed journls nd conference proceedings. 1097