Analysis and Simulation Study on Multiple AGV Utilization Efficiency in AS/RS. Shicai Yang, Lindu Zhao *

Transcription

1 Aalyss ad Smulato Study o Multple AGV Utlzato Effcecy AS/RS Shca Yag, Ldu Zhao * Isttute of Systems Egeerg, Southeast Uversty Najg, Jagsu, 10096, Cha *Correspodg author. ldzhao@seu.edu.c, youth086@163.com POMS 0th Aual Coferece Orlado, Florda U.S.A. May 1 to May 4, 009

2 Abstract Wth the rapd developmet of advaced maufacturg techology, Automatc Storage ad Retreval Systems (AS/RS) ad Automated Guded Vehcles (AGV) are beg used more ad more wdely Cha. However, the utlzato effcecy of Multple AGV AS/RS s ot etrely satsfactory. I order to mprove the AGV schedulg maagemet AS/RS, the ueug theory ad soft computg methods are used to study the multple AGV schedulg problems; the meawhle, the schedulg strategy dffereces betwee sgle AGV ad multple AGV are explored. The the utlzato effcecy s aalyzed ad the smulato results of utlzato effcecy are gve. Keywords: AS/RS; AGV; soft computg methods; multple AGV schedulg; 1. Itroducto Advaced maufacturg techology has bee developed more ad more rapdly, whch s playg a crucal role moder socety. Wth the rapd developmet of advaced maufacturg techology, techologes of Automatc Storage ad Retreval Systems (AS/RS) ad Automated Guded Vehcles (AGV) have also got a rapd developmet, at the meawhle, AS/RS ad AGV are beg used more ad more wdely. AS/RS are major materal-hadlg systems, whch are wdely used automated productos ad dstrbuto ceters. The basc compoets of AS/RS are storage racks, storage/retreval maches (S/R maches) or automated stacker craes, put/output (I/O) locatos ad accumulatg coveyors [1].AS/RS have brought to

3 dustry the advatages of faster storages ad retreval of products, effcet utlzato of storage space, hgh relablty ad better cotrol vetory, mproved safety ad decrease damages of products. AS/RS whch are used maufacturg, warehousg ad dstrbuto ceters have to be desged to provde uck respose for storages ad retrevals of products order to keep the system operatg effcetly []. The moder warehouse must play the role ot oly storage for raw materals, parts, ad ed products, but also a dyamc vetory cotrol for a smooth logstc system, such as procuremet, producto, vetory, sales, ad dstrbuto, by establshg the formato system to update kds ad uattes of stored tems, whle AGV ca be the best horzotal trasportato method for materal hadlg may applcatos. Cosderg that, AS/RS has bee utlzed together wth AGV the above-metoed felds for more tha te years [3]. Performace aalyss of AS/RS s a complex problem. Some approaches exst for performg such a vestgato [4] [5]. Sce the veto of AGV, much research has bee devoted to the techology of AGV systems, ad rapd progress has bee wtessed. As oe of the eablg techologes, the path plag ad the routg algorthms of AGV have also attracted cosderable atteto [6] [7] [8]. At the same tme, some papers have focused o the warehouse desg based o the AS/RS ad AGV, ad some research has bee take dealg coflct or obstacle avodace of AGV. From the above summary, t ca be foud that much research has bee doe o

4 AS/RS or AGV. However, Cha, ASRS ad AGV has a certa degree of developmet, but ASRS the utlzato effcecy of AGV has ot bee gve suffcet atteto, especally the utlzato effcecy of Multple AGV AS/RS s ot etrely satsfactory. I ths study, the warehouse wth AGV ad AS/RS wll be preseted ad some basc hypotheses wll be gve. The through the data we got, a ueug model of sgle vehcle wll be bult to study the utlzato effcecy. Queug theory [9] [10] ad soft computg methods are adopted to research the utlzato effcecy of multple vehcles. Smulato results ad dscussos are gve fally.. The warehouse wth AS/RS ad AGV Before cosderg the models detal, t s essetal to specfy the geeral features of the warehouse system wth AS/RS ad AGV cosdered ths research. A layout for the warehouse s depcted Fgure 1. The warehouse comprses three major parts,.e., the AS/R maches ad the racks, the AGV system ad the coveyace system. The latter two parts wll be aalyzed.

5 Fgure 1 Layout of the warehouse wth AS/RS ad AGV I the whole warehouse cosdered ths study, there are two types of materal flow, that s, put materal flow ad output materal flow. The put materal flow works as follows. Each pallet or package eters at oe of the arrval statos to the coveyace system, the, t wll be coveyed to the AGV system drectly by coveyor belt ad t wll be loaded ad trasferred by a vehcle. Wth the movg of AGV, t wll be set to the I/O pot of the rack, the, t wll be stored the desgated place by AS/R maches. The output materal flow s smlar wth that. 3. Problems statemets 3.1 Descrptos ad hypotheses Based o the warehouse system whch has bee descrbed as above, what we cosdered s how to make AGV work more effcet. I order to study the workg laws of AGV, we attempt to buld the ueug models for AGV system. For the reuremet of models ad the computato coveece, the followg codtos are assumed. 1. The vehcles move at a costat speed, ad the accelerato wll ot be cosdered.. Oe vehcle oly recepts oe reuest at oe tme ad oe reuest meas oly oe pallet or package. 3. Oe vehcle s cosdered oe server. 4. The reuests of the system are mutually depedet, ad each reuest has the same arrval rate.

6 5. The maxmum umber of reuests allowed to arrve s fte. 6. Oe uarter of a hour s treated as the tme ut, whch meas the tme perod s oe uarter. 7. The ueug system adopts FIFO strategy. 8. Coflct problems are ot cosdered. Here are the parameters whch wll be used to buld the ueug models. : Arrval rate of the reuests (pallets or packages) wth a uarter : Servce dstrbuto rate, whch s the mea umber of reuests that are processed wth a uarter : Utlzato of all vehcles. That s, the reuest arrval rate dvded by the servce rate : Numbers of vehcles : Utlzato of each vehcle. T s : Average tme the system L s : Average umber the system T : Average watg tme,.e., tme the ueue L : Average umber of watg reuests P 0 : The probablty whle the system s dle 3. Queug Model ad aalyss for oe sgle vehcle There s oly oe sgle vehcle, so the umber of vehcles s oe, that s =1. I order to establsh the ueug model for oe sgle vehcle, we should study the probablty dstrbuto of the ter-arrval tmes ad the probablty dstrbuto of the

7 servce tmes frst. Frst we take a research o the probablty dstrbuto of the ter-arrval tmes. From the orgal data we got, t s easy to fd that the total umber of reuests s 970 uts ad the total tmes are 350 uarters. Besdes, t s foud that the arrval umber of reuests per uarter has eght kds of stuatos, that s, 0, 1,,3,4,5,6,7. Except these, t seems ute cofused ad complcated. I order to fd the dscerble law, we wll collate the raw data to the experece probablty dstrbuto show Table 1. Table 1 The experece dstrbuto of the arrval umbers Arrval umbers Freuecy f Probablty Total I order to exame whether the experece probablty dstrbuto follows a Posso dstrbuto, the ch-suare ( ) test s used ad the followg assumptos are made: H H 0 1 : F ( ) F : F( ) F 0 0 ( ) ( ) where F ( ) s the dstrbuto fucto of the followg Posso dstrbuto: 0

8 e p( ; ), 1,,3,! where s the parameter, 0. By the method of maxmum lkelhood, we obta the estmated value of 1 N f uts / tr where N meas the total tmes whch are 350 uarters, meas the actual arrval umber of the reuests, ad f s the freuecy of the experece dstrbuto. Thus, the probablty fucto of the dstrbuto s gve by: p e!.77 e!.77. The ch-suare test statstc s gve by: ( f Np ). Np 7 0 The calculatos are show Table. Table The calculato of f p N * p ( f Np ) Np Total From Table, we have acured the ch-suare test statstc result:

9 We ow have our ch-suare statstc (3.764). We set the alpha level of sgfcace (0.05), ad the degree of freedom s 6. Eterg the ch-suare dstrbuto table wth 6 degree of freedom ad readg alog the row we fd the value Therefore, we accept the hypothess, that the reuests arrval process ad the ter-arrval tmes follow a Posso dstrbuto wth the parameter. 77 uts / tr. Now we take a research o the probablty dstrbuto of the servce tmes. From the orgal data we got, t s easy to calculate the average servce tme of each reuest, that s: T tr. Thus, we acure the average servce dstrbuto rate: 3.5 uts / tr. Therefore, we assume that the probablty dstrbuto follows a egatve expoetal dstrbuto wth the servce rate 3. 5 fucto s gve by: 1 e F0 ( t) 0, t 0 3.5t, t 0 Thus, the desty fucto could be descrbes as: 3.5e f0( t) 0, t 0 3.5t, t 0 uts / tr. The the dstrbuto I the same way as above, the ch-suare ( ) test s used. Through the calculato of orgal data, combed wth the ch-suare test result, we accept the hypothess, that the probablty dstrbuto follows a egatve expoetal dstrbuto

10 wth the servce rate 3. 5 uts / tr. Based o the aalyss above, the ueug model we got could be otes as M/M/1, whch s show Fgure. Fgure M/M/1 ueug model Sce we have got the M/M/1 ueug model, we could aalyze the utlzato effcecy by the model. The parameters are calculated as follows:.77 uts / tr 3.5 uts / tr /.77 / % Ls Ts L T uts uarters uts ( ) uarters (1 ) From the results above, we could fd that, the utlzato effcecy of oe sgle vehcle s 85.3%, whch shows that the system s stable. However, the value of L, s T s, L ad T shows that the system s very busy. Now we take a umercal smulato aalyss o the utlzato effcecy, whch s show Fgure 3. We ca see that the utlzato effcecy ow s 85.3%, ad

11 wth the great crease of the average umber the system, the utlzato effcecy could oly get a lttle crease. At the same, the umber of the watg reuests the system creases uckly. It appears o the surface to be very effcet; however, actually the whole system has lttle effcecy. Fgure 3 Utlzato effcecy aalyss o M/M/1 model 3.3 Queug Model ad aalyss for multple vehcles I the utlzato effcecy study o oe sgle vehcle, we fd that, the system wth oly oe sgle vehcle s ot effcet. Wth the developmet of the eterprse, the throughout capacty of the warehouse wll be creased. Based o that, creasg the umber of AGV may be a good dea. Therefore, we eed to study the utlzato effcecy of multple AGV. The ueug theory wll be adopted aga, ad the ueug model has bee chaged to M/M/ model.

12 Accordg the ueug theory, the parameters of the M/M/ model are gve as follows )!(! P 0 1 ) (! P L / L T Wth the creasg of, the calculatos for the model parameters are beg more ad more dffcult. I order to study the utlzato effcecy of multple vehcles, we take a study o the smple stuatos frst, ad we set =, 3, 4, 5.Because t s hard to calculate, we take a smulato o the relatos betwee ad L, whch are show Fgure 4.

13 Fgure 4 The relatos betwee ad L (=, 3, 4, 5) We assume that, the utlzato effcecy of multple vehcles s approxmately, the mmum value of, whle chages a lttle, L chages greatly. From the fgure above, we could calculate the approxmate values of utlzato of each vehcle ( ) for each (=, 3, 4, 5).The results are calculated as follows. Optmal value of whle =: 1.4 / 70 % Optmal value of whle =3:.3 / % 3 Optmal value of whle =4: 3. / 4 80 % 4 Optmal value of whle =5: 4. / 5 84 % 5 From the results we obtaed, we fd that, wth the creasg of, the optmal value of s becomg larger. At the same tme, the larger also meas the more watg reuests. As vewed from ths, keepg a average utlzato effcecy of 75%~80% s a good dea. I ths stuato, the utlzato effcecy of AGV system

14 could be kept at a good level, ad the possblty of system obstructo could be greatly reduced, so that the operatg effcecy of the whole warehouse system could be greatly mproved. 4. Dscussos For the schedulg problems of oly oe sgle vehcle, t s easy to solve. As for the schedulg problems of multple vehcles whle the umber of vehcles s less tha sx, we could adopt the strategy as follows. Frst, we set a value of satsfactory utlzato effcecy, for example, we set t to be 80%, ad the we calculate the watg reuests L ad the watg tmes T, through ths step, we could calculate to search for the earest umber of vehcles we eeded. I ths way, the utlzato effcecy could be kept at a good level ad the vehcles ca also be used well. Whe the throughput of the warehouse s very large, ad there are more tha te automated guded vehcles the system, the strategy s stll effectve, but the calculato s very complex. Uder ths codto, soft computg methods wll play a vtal role. 5. Coclusos I ths paper, we aalyzes the operato laws of AGV based o the data of the warehouse, ad ueug models of oe sgle vehcle ad multple vehcles are establshed. By the smulatos ad aalyss o these two models, the utlzato effcecy of AGV AS/RS has bee studed. The schedulg strategy of multple AGV s explored. Wth the gradual deepeg of the study, the effect of dfferet strateges ad large umbers of AGV the system wll be aalyzed the future.

15 Referece [1] J. Baks, J. Carso. Dscrete-evet system smulatos [M]. New Jersey: Eglewood, [] I. Potrc, T. Lerher, J. Kramberger, M. Sraml. Smulato model of mult-shuttle automated storage ad retreval systems [J]. Joural of Materals Processg Techology, 004, : [3] S. Takakuwa. Desg ad cost-effectveess aalyss of large-scale AS/RS-AGV systems [C]. I Proceedgs of the 1993 Wter Smulato Coferece, Los Ageles, CA, 1993, [4] B.M. Pulat, P.S. Pulat. Performace aalyss of automatc storage ad retreval system a comparatve approach [C]. I Proceedgs of the 1988 Wter Smulato Coferece, Pscataway, NJ, 1988, [5] S. Takakuwa. Module modelg ad ecoomc optmzato for large-sole AS/RS [C]. I Proceedgs of the 1989 Wter Smulato Coferece, Pscataway, NJ, 1989, [6] M.C. De Guzma, N. Prabhu, J.M.A. Tachoco. Complexty of the AGV shortest path ad sgle-loop gude path layout problems [J]. Iteratoal Joural of Producto Research, 1997, 35(8), [7] S.Y. Huag, W.J. Hsu. Routg automated guded vehcles o mesh-lke topologes[c]. I Proceedgs of Iteratoal Coferece o Automato, Robotcs ad Computer Vso, 1994 [8] L. Qu, W.J. Hsu. A algorthm for cocurret routg of AGVs a mesh [C]. I Proceedgs of the 7th Australasa Coferece o Parallel ad Real-Tme Systems (PART 000),Uversty of New South Wales,Sydey,Australa,000,0-14 [9] J.T. Lu. Applcato of Queug Theory Fuel Pump Repar [J]. Systems Egeerg-Theory & Practce,000(6):83-90( Chese) [10] Y.K. Meg. Bass ad Applcatos of Queug Theory [M]. Shagha: TogJ Uversty Press, 1989( Chese)