ࡱ> ,.+~kG (bjbjَ vD$%]&&&&&&&$JJJJP<,J(4VL h V! Lm$L($*t,(&x x x (B &&B B B x H&&JJ&&&&x B $B f && n@JJ The 14th INTERNATIONAL DAAAM SYMPOSIUM Intelligent Manufacturing & Automation: Focus on Reconstruction and Development 22-25th October 2003 AGV SYSTEM CONTROL IN A GROUP TECHNOLOGY Bilic, B.; Bajic, D. & Veza, I. Abstract: The article deals with algorithm that optimizes load routing in tandem AGV systems. The algorithm takes care about temporary conditions of production system and predetermined task schedules. Also it reserves times and defines vehicles for transport tasks performing. Key words: AGV tandem system, group technology, branch and bound method 1. INTRODUCTION There are two types of AGV systems: a conventional network and tandem configuration AGV systems. In a conventional network system each vehicle is allowed to serve any station in the system. A tandem AGV was first proposed by Bozer and Srinivasan (1989, 1991, and 1992). It is based on partitioning all the stations into non-overlapping single-vehicle closed loop with an additional transit area (bidirectional transit station) provided as an interface between adjacent loops. Each loop contains only one vehicle. Each work station belongs to only one loop. Tandem AGV systems support the effective implementation of group technology since each loop (or a subset of loops) may be viewed as a cell. 2. A LOAD-ROUTING PROBLEM IN A AGV TANDEM SYSTEM When a load (material) arrives to output buffer of station in production system, it is necessary to determine the transport route of load to destination. If the load has to be transported to the station that is situated in another loop, it is necessary to use two or more vehicles. In that case the transport time between stations change dynamically. Route with shortest travel time, as well as material quantity that will be transported is determined by solving the load routing problem. The empty vehicle dispatching rule is one of the factors that influence the load routing problem. Different empty vehicle dispatching rules exist. Among them, the most usable is FEFS (first-encountered-first-served) rule. Under this rule, a vehicle which has just delivered a load will travel empty to inspect the output buffer of each workstation and transit station in that loop in order to locate next move request. 3. LOAD-ROUTING ALGORITHM This algorithm (Fig.1) optimizes load routing in the unidirectio-nal and bidirectional AGV tandem systems. The algorithm takes care about temporary conditions of production system and predetermined task schedules. Also it reserves time and defines vehicles for transport tasks performing. It bases on branch and bound method. Past experiences of this method were in optimization of transport path in traditional AGV systems (Kaspi & Tanchocco, 1990). Algorithm uses FIFO (first-in-first-out) rule of empty vehicle control. According to FIFO rule transport tasks are performed in order of appearing in the system. Assumption and constraints in algorithm application are: 1. Input material quantity in process station is equal to output material quantity. 2. At the same time vehicle transports only one transport unit. 3. The buffer size of all workstations and transit stations are infinite. 4. Intrastation travel time of vehicle is ignored. 5. The effects of acceleration and deceleration on the vehicle velocity are insignificant. Condition in the production system is described by the transport tasks schedule. Transport task schedule contains tasks for every vehicle arranged according to perform sequence. In task list following data have to be defined: transport task description (e.g. start and destination station), starting ta and finishing tb time of reserved time intervals for performing transport tasks in the loop k.  EMBED Equation.2  - concluding time of the last traveling on the currently task schedule of vehicle k,  EMBED Equation.2  - the destination station of the last traveling on the currently task schedule of vehicle in the loop k. Every vehicle must start and finish transport task within predetermined time interval EMBED Equation.2 :  EMBED Equation.2 . (1) tin - loaded-vehicle travel time from station i to j on the same loop, tl - time taken by vehicle to pick up a load at every station i, tu - time taken by vehicle to drop off a load at every station j. The load routing problem is a problem of finding the basic nodes m. Basic nodes represent transit stations with the minimal time needed for the load, which has started from the starting station, to arrive at the basic node. The load that has to be transported is currently in the station P. In the beginning the station P represents the basic node ( EMBED Equation.2 ). The load arrival time  EMBED Equation.2  on the station P is defined. Station O is destination to which the load has to be transported. Following notations in defining the algorithm are used: ttr - load transport time in a transit area, (j - label of node which directly precedes to node j,  EMBED Equation.2  - the earliest planned time of arrival load in a station j. Set ( is defined which includes all transit stations and the destination station O. The load arrival time at the station j (tj), is calculated for every station from the set (, which is connected with the basic node m. The calculated tj is compared with the previously determined  EMBED Equation.2 . If  EMBED Equation.2 , then  EMBED Equation.2  is replaced with the tj ( EMBED Equation.2 ). The basic node is a transit station from the set ( for which the earliest load arrival time from the station P is found. From the set ( the node m with the earliest arrival time EMBED Equation.2  ( EMBED Equation.2 ;  EMBED Equation.2 ) needs to be chosen. After that the node m is removed from the set (. If the basic node m is not the node O, then searching and branching from the node m is continued with the calculation of the time tj for rest of the stations, from the set (, that are connected with the node m. If  EMBED Equation.2 , then the optimum solution is found. The optimal material flow from the station P to station O is determined with the use of backtracking. After that the time intervals are calculated and reserved, and the transport task is added to a list of transport tasks for all vehicles. The load arrival time at the station j (tj), depends upon the mutual position of the stations i and j. Two basic cases can be distinguished: 1) Transport inside the loop  EMBED Equation.2 . (2) a) If  EMBED Equation.2  vehicle in the loop k is still busy when a load (material) arrives at station i at time ti. b) If  EMBED Equation.2  the task schedule of vehicle in the loop k is empty 2) Transport inside transit area  EMBED Equation.2 . (3)  EMBED CorelDRAW.Graphic.10  Fig. 1. The load routing algorithm 4. EXAMPLE The algorithm is applied to the example that is solved by the static linear programming model. Author of that was Lin et al. (1994). Optimal load routing procedure from station 26 to station 16 in the bidirectional material flow is presented by the Fig. 2.  EMBED CorelDRAW.Graphic.9  Fig. 2. Search tree for example 5. CONCLUSION In the article algorithm for solving the load routing problem in tandem AGV systems is presented. The algorithm simultaneously enables: the optimal load routing in production system, time and vehicles reservation for transport task performing. The algorithm can only be used in automated production systems in which the transport is integrated with production process. It is intended for on-line control of transport systems. It also can achieve material flow optimization in production systems which do not use vehicles of the same kinematics. 6. REFERENCES Bozer, Y. A. & Srinivasan, M. M. (1989). Tandem configurations for AGV systems offer simplicity and flexibility, Industrial Engineering, Vol. 21., No. 2, pp. 23-28. Bozer, Y. A. & Srinivasan, M. M. (1991). Tandem configurations for automated guided vehicle systems and the analysis of single vehicle loops, IIE Transactions, Vol. 23., No. 1, 1991., pp. 72-82, ISSN 0740-817X Bozer, Y. A. & Srinivasan, M. M. (1992). Tandem AGV systems: A partitioning algorithm and performance comparison with conventional AGV systems, European Journal of Operational Research, 63, pp. 173-191, ISSN 0377-2217 Kaspi, M. & Tanchocco, J. M. A. (1990). Optimal flow path design of unidirectional AGV systems, International Journal of Production Research, Vol. 28., No. 6, pp. 1023-1030, ISSN 0020-7543 Lin, J. T.; Chang, C. C. K. & Liu, W.-C. (1994). A load-routeing problem in a tandem-configuration automated guided vehicle system, International Journal of Production Research, Vol. 32., No. 2, pp. 411-427, ISSN 0020-7543 Authors: DSc. Bozenko BILIC, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture (FESB), R. Boskovica bb, 21000 Split, Croatia, Phone: 00385 21 305 851, Fax: 00385 21 463 877, e-mail:  HYPERLINK mailto:iveza@fesb.hr bbilic@fesb.hr DSc. Drazen BAJIC, FESB, R. Boskovica bb, 21000 Split, Croatia, Phone: 00385 21 305 852, Fax: 00385 21 463 877, e-mail:  HYPERLINK mailto:iveza@fesb.hr dbajic@fesb.hr Prof. DSc. Ivica VEZA, FESB, R. Boskovica bb, 21000 Split, Croatia, Phone: 00385 21 305 854, Fax: 00385 21 463 877, e-mail:  HYPERLINK mailto:iveza@fesb.hr iveza@fesb.hr PAGE  PAGE 2 PAGE1 '~:;K 7 '()uvxycdзЦКЦj?CJEHUmH jB CJUVmH  6CJmH jCJEHUmH jAB CJUVmH jCJUmH 6H*CJmH  * CJOJQJ6565CJ55CJOJQJCJH*CJ CJOJQJ5'y:;KL  7 8 $1$$$1$1$$1$$1$$$1$1$$1$9V"C`  %"&"4"5""#$C%"&#&+''(((((   ' ~\ xf8y$ 1$s  1$s  1$s  1$  1$  & F 1$ 1$1$1$ $%89:vwyz{|,-./HI\]^_#$%&Wںںںںڦڏ jz6jM CJEHUmH j AB CJUVmH j3 CJEHUmH jAB CJUVmH 6CJH*mH  6CJmH 6H*6 jEHUj&P P. A!n"n#n$n%SS@ 0 000>&P P. 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Embedding 176_lZR6o$hъftil0??LIST\trfltrfdPPPŹ'}?n X'}?h0olelLIST\obj flgs bboxpCEobbx pCE+hE?usdnWLISTlgobloda$@X\`dl (d.ط;wpFLIST\trfltrfdPPPŹQi;?Pi;޿LXRt?wYRt?) 0LISTJobj flgs bbox " x$obbx  " x$- !7x$usdnXLISTlgoblodavv$<PTX\rv d.yD}LIST\trfltrfdPPPŹf1w/?'I(7LISTLobj flgs bboxHr?fK?LEm2LISTobj flgsbboxAv+obbx Av+Av+usdn^LISTplgobloda$H hlp~ d.hEmbedding 178xJfJ$NZLswm$hъftil0??LIST\trfltrfdPPPŹ'}?Qz'}?O\(olelLISTobj flgsbboxhobbx hhusdn_LISTplgobloda$H hlp~ d.Embedding 180xqxG{2G^$hъftil0??LIST\trfltrfdPPPŹ'}?'}?q.-olelLISTobj spnd:flgs bbox!yMobbx !yM!yMusdn`LIST(lgobloda$D`dhlpx| d.>pChъftil0??LIST\trfltrfdPPPŹ'}?g'}?iPb&txsm:'}?g'}?iPb&UKSelection of basic node m:txtjLISTLobj flgs bbox1pobbx 1pԆe7LusdnbLISTlgoblodaxx$<PTX\tx d.x' =pFLIST\trfltrfdPPPŹː}Z?5e@s?77H+LISTLobj flgs bboxSrpb(obbx Srpb(Ԇ/xL"usdncLISTlgoblodaxx$<PTX\tx d.xH' =pFLIST\trfltrfdPPPŹː}Z?5e@k ?7qZ%LISTobj flgsbboxTzZYobbx TzZYTzZYusdndLISTplgobloda$H hlp~ d.Embedding 182l ޏ6$o $hъftil0??LIST\trfltrfdPPPŹ'}?a6A'}?@* olelLISTobj flgsbboxzYobbx zYzYusdneLISTplgobloda$H hlp~ d.xEmbedding 184 ޏ$oXׁ$hъftil0??LIST\trfltrfdPPPŹ'}?@'}?@* olelLISTobj flgsbbox<obbx <<usdnfLISTplgobloda$H hlp~ d.Embedding 186 #ޏD$oG^$hъftil0??LIST\trfltrfdPPPŹ'}?FL'}?qp5olelLISTTobj flgs bbox67%8vobbx 67%8v67= _usdngLISTlgobloda$<PTX\{ d.NJ((DDLIST\trfltrfdPPPŹ'}?a6A'}? 4"LISTTobj flgs bbox4Yvobbx 4Yv4Y_usdnhLISTlgobloda$<PTX\{ d.ԇ((DDLIST\trfltrfdPPPŹ'}?|n7'}? 4"LISTTobj flgs bboxvdobbx vdXiusdniLISTlgobloda$<PTX\{ d.P.o`/o`/DDʈLIST\trfltrfdPPPŹ'}?e-xg '}?(LISTTobj flgs bboxCDvd%8obbx CDvd%8CDXi&OusdnjLISTlgobloda$<PTX\{ d.lo`No`NDDʈLIST\trfltrfdPPPŹ'}?kE*pm@'}?(LISTobj flgs bboxI 2Wbobbx I 2WbQ6_^usdnkLISTlgoblodatt$<PTX\ptd.&Nftil0??LIST\trfltrfdPPPŹ'}?<v'}?l "LIST8obj spnd6flgs bboxmobbx mmusdnlLIST(lgobloda$D`dhlpx| d.>0Chъftil0??LIST\trfltrfdPPPŹ'}?~e:@'}?{rtxsm6'}?~e:@'}?{r0UKNtxtjLIST8obj spnd6flgs bboxJ"IQobbx J"IQJ"IQusdnmLIST(lgobloda$D`dhlpx| d.>0мXChъftil0??LIST\trfltrfdPPPŹ'}?=؎'}?+txsm6'}?=؎'}?+0UKYtxtjLIST\obj flgs bbox;pCobbx ;pC AEuusdnnLISTlgobloda$@X\`dl (d.ϐ;wpFLIST\trfltrfdPPPŹg;?g;޿d ?c ?BmLISTJobj flgs bboxa_etobbx a_etp_d6tusdnoLISTlgoblodavv$<PTX\rv d.ѐyD}LIST\trfltrfdPPPŹs1w/? A#LISTLobj flgs bboxvQ^9obbx vQ^9Kʞ#3usdnpLISTlgoblodaxx$<PTX\tx d.hҐ' =pFLIST\trfltrfdPPPŹ|D?1pjAs?0HLISTLobj flgs bboxr^9obbx r^96ʞN3usdnqLISTlgoblodaxx$<PTX\tx d.@Ԑ' =pFLIST\trfltrfdPPPŹ|D?ރ\#s?0HLISTobj flgsbbox][ 7V obbx ][ 7V ][ 7V usdnsLISTplgobloda$H hlp~ d.֐Embedding 190xH֐}>hъftil0??LIST\trfltrfdPPPŹ'}?*w'}?$ %AolelLISTnobj spnd4flgs bboxg@3vobbx g@3vg@3vusdntLIST(lgobloda$D`dhlpx| d.>xِ>0ڐChъftil0??LIST\trfltrfdPPPŹ'}?T@'}?Ztxsm4'}?T@'}?Zx UK TRANSIT AREAtxtjLISTobj spnd04flgs bbox)N fobbx )N f)N fusdnuLIST(lgobloda$D`dhlpx| d.>x Chъftil0??LIST\trfltrfdPPPŹ'}?(\'}?hъftil0??LIST\trfltrfdPPP'}?MGbc'}?[*8@olelLISTTobj flgs bboxN8%8nBobbx N8%8nBN8=m+usdnxLISTlgobloda$<PTX\{ d.x ) DDʈLIST\trfltrfdPPPŹ'}?a6A'}?6JLISTTobj flgs bbox nBobbx  nB {+usdnyLISTlgobloda$<PTX\{ d.xK  DDʈLIST\trfltrfdPPPŹ'}?|n7'}?6JLISTTobj flgs bbox qobbx  q݉ qusdnzLISTlgobloda$<PTX\{ d.x(LLDDʈLIST\trfltrfdPPPŹ'}?$'`q'}?^r>LISTTobj flgs bbox<4%8qobbx <4%8q<4݉&Oqusdn{LISTlgobloda$<PTX\{ d.xxDDʈLIST\trfltrfdPPPŹ'}?$'`q'}?^r>LISTobj flgs bboxp;U"5.obbx p;U"5.x 3Y9*usdn|LISTlgoblodatt$<PTX\ptd.xP &Nhهftil0??LIST\trfltrfdPPPŹ'}?2'}?('V LISTobj flgs bboxc љ4sobbx c љ4sk ɝ 8'ousdn}LISTlgoblodatt$<PTX\ptd.x &Nhهftil0??LIST\trfltrfdPPPŹ'}?S'}?}žLISTobj flgsbbox2-obbx 2-2-usdn~LISTplgobloda$H hlp~ d. Embedding 194x  {}\>hъftil0??LIST\trfltrfdPPPŹ'}?L2p@'}?;Rtp@olelLISTobj spnd0flgs bboxKi2obbx Ki2Ki2usdnLIST(lgobloda$D`dhlpx| d.>TChъftil0??LIST\trfltrfdPPPŹ'}?g'}?v`oc@txsm0'}?g'}?v`oc@TUK|Calculate tj using txtjLISTobj flgsbbox"Oobbx "O"OusdnLISTplgobloda$H hlp~ d."Embedding 196x" ޏ$o\>hъftil0??LIST\trfltrfdPPPŹ'}?2A'}?'d3 AolelLIST8obj spnd0flgs bboxX"\ obbx X"\ X"\ usdnLIST(lgobloda$D`dhlpx| d.>U%p&Chъftil0??LIST\trfltrfdPPPŹ'}? G @ZA'}?5,i-Atxsm0'}? G @ZA'}?5,i-AUUKNtxtjLIST8obj spnd/flgs bbox2_^ 1 obbx 2_^ 1 2_^ 1 usdnLIST(lgobloda$D`dhlpx| d.>U7p8Chъftil0??LIST\trfltrfdPPPŹ'}?&'}?a$'.'Atxsm/'}?&'}?a$'.'AUUKYtxtjLISTobj flgsbbox3Sb obbx 3Sb 3Sb usdnLISTplgobloda$H hlp~ d.pKEmbedding 198xKLW2^ZTn>hъftil0??LIST\trfltrfdPPPŹ'}?Nd '}?8+,,AolelLIST\obj flgs bbox?[T+ obbx ?[T+ ćc” usdnLISTlgobloda$@X\`dl (d.x(N;wpFLIST\trfltrfdPPPŹ}2?}2 JOj ? ?),ALISTJobj flgs bbox cobbx c 7cusdnLISTlgoblodavv$<PTX\rv d.xPyDʈLIST\trfltrfdPPPŹ$')L?$`@LISTLobj flgs bboxvұobbx vұ6R usdnLISTlgoblodaxx$<PTX\tx d.xPQ' =pFLIST\trfltrfdPPPŹː}Z?'`s?c6ALISTLobj flgs bboxxPn0obbx xPn0Jt"T usdnLISTlgoblodaxx$<PTX\tx d.xR' =pFLIST\trfltrfdPPPŹ|D?DaAs?HLISTLobj flgs bbox4opobbx 4op4uL usdnLISTlgoblodaxx$<PTX\tx d.xS' =pFLIST\trfltrfdPPPŹ|D?8Z#s?Yȿ LISTLobj flgs bboxcbobbx cb&]shusdnLISTlgoblodaxx$<PTX\tx d.x@U' =pFLIST\trfltrfdPPPŹ٠z?9 s4CL?BALISTLobj flgs bboxұ4obbx ұ46.usdnLISTlgoblodaxx$<PTX\tx d.xV' =pFLIST\trfltrfdPPPŹː}Z?'`4CL?G,|ALISTLobj flgs bbox; ұobbx ; ұ6@ usdnLISTlgoblodaxx$<PTX\tx d.xW' =pFLIST\trfltrfdPPPŹː}Z?'`s? v"ALISTLobj flgs bboxو I) obbx و I)  m# usdnLISTlgoblodaxx$<PTX\tx d.x0Y' =pFLIST\trfltrfdPPPŹː}Z?oXs?<%'ALISTlgobloda@@$04<@d . ZLIST\trfltrfdPPPflgs??sumi8  7)`DRAWPATTERNSBn@Bn@STREAMSLISTWEmbedding 170FBn@Bn@Ole X FMicrosoft Equation 3.0 DS Equation Equation.39q  .  &@0 & MathType`Symbolw@ ^CwCw w0-2 (yCompObjYfObjInfo[OlePres000\Equation Native lwSymbolw@ ~CwCw w0-2 )ySymbolw@ _CwCw w0-2 (ySymbolw@ CwCw w0-2 )yTimes New RomanCwCw w0-2 jky2 ky2 &byTimes New RomanCwCw w0-2 dy2 .tyTimes New RomanCwCw w0-2 c 2 ; & "System !)Bw-NANI[ t bk() ;  d k() FMicrosoft Equation 3.0 DS EqEmbedding 172FBn@Bn@Ole nCompObjofObjInfoquation Equation.39qWT * .   & & MathTypePSymbolw@ CwCw w0-2 ~{ySymbolw@ BCwCw w0-2 ~H}yTimes New RomanOlePres000rEquation Native }HEmbedding 176FBn@Bn@Ole CwCw w0- 2 I...eSymbolw@ CCwCw w0-2 =.2 4P. & "System !)Bw-NANI,Y$ =...{}CompObjZOlePres000Equation Native <Embedding 178FBn@Bn@ FMicrosoft Equation 3.0 Equation.39q  .1   &` & MathType Times New Roman CE- 2 @4mSymbol- 2 @=Times New Roman CE- 2 @O&,MathTypeUU  m=O> 0CA & "System- 6 m=O FMicrosoft Equation 3.0 Equation.39qN  ; Ole CompObjZOlePres000:Equation Native |.1   &@  & MathTypeISymbol-2 'G{ISymbol-2 '}Times New Roman CE- 2 4tk 2 tk 2 - jkTimes New Roman CE- 2 @m 2 @jG 2 4,@ 2 4,@Times New Roman CE- 2  minkSymbol- 2 = 2  " 2   Times New Roman CE- 2  ;`k 2  `Symbol- 2  P';&lMathTypeUU` t m, =mint j, {} ; "jP & "System-`$ t m, =mint j, {} ; "jP FMicrosoft Equation 3.0 Equation.39q{d 2+ .1  @& & MathType`Embedding 180FBn@n@Ole CompObjZOlePres000Symbol-2 g{Symbol-2  }Symbol- 2 7P' 2 P' 2 = 2 \-Times New Roman CE- 2 m+&LMathTypeUU@ P=P-m{} & "System-Equation Native \Embedding 182Fn@n@Ole CompObjZ@0 P=P-m{}? 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