METHOD FOR EVALUATING THE THROUGHPUT PERFORMANCE OF SHUTTLE BASED STORAGE AND RETRIEVAL SYSTEMS

Transcription

1 . Lerher i dr. Meoda za rocjenu roočne erformance auomaiziranih skladišnih susava s vozilima ISSN (Prin), ISSN (Online) DOI: /V MEHOD FOR EVALUAING HE HROUGHPU PERFORMANCE OF SHULE BASED SORAGE AND RERIEVAL SYSEMS one Lerher, Banu Y. Ekren, Zaki Sari, Bojan Rosi Original scienific aer In his aer a mehod for hroughu erformance calculaion of shule based sorage and rerieval sysems (SBS/RS) is resened. SBS/RS reresen a new echnology in auomaed sorage and rerieval sysems. Since i is imoran o design SBS/RS righ he firs ime due o he relaive inflexibiliy of he hysical layou, we rovide a roosed mehod for he hroughu erformance calculaion of hese sysems. he erformance of he sysem is considered as a hroughu caaciy of he SBS/RS as a whole. Keywords: auomaed warehouses; erformance analysis; shule based sysems; hroughu caaciy Meoda za rocjenu roočne erformance auomaiziranih skladišnih susava s vozilima Izvorni znansveni članka U ovom radu rezenira se meoda roračuna roočne erformanse skladišnih susava sa shule-ovima/vozilima (eng. SBS/RS). SBS/RS zasuaju novu ehnologiju auomaiziranih skladišnih susava. S obzirom na važnos isravnog oblikovanja (rojekiranja) SBS/RS susava "od rve" zbog relaivne nefleksibilnosi fizičke izvedbe, rezenira se redložena meoda roračuna roočne erformanse akvih susava. Performansa susava razmara se kao roočni kaacie SBS/RS kao cjeline. Ključne riječi: auomaizirana skladiša; analiza erformansi; roočni kaacie; susavi s vozilima (shule-ovima) 1 Inroducion Warehouses are criical for suly chains. o be able o increase sace uilizaion in a warehouse, managers refer a high-rise sorage area wih a relaively small foorin. Having numerous numbers of iers in sorage area creaes necessiy for fas and efficien sorage and rerieval sysem o sore/rerieve loads o/from sorage locaions o increase he hroughu caaciy. Wih advances in echnology, new auomaed maerial handling echnologies roviding greaer resonsiveness and addiional flexibiliy in fulfilling orders have been develoed [1]. A major segmen in he maerial handling indusry is he Auomaed Sorage and Rerieval Sysem (AS/RS). here are rimarily wo yes of AS/RS radiional, Crane-Based Auomaed Sorage and Rerieval Sysem (CBAS/RS) and he Auonomous Vehicle-Based Sorage and Rerieval Sysems (AVS/RS). Figure 1 Shule based sorage and rerieval sysem [3] CBAS/RS are widely used in warehouses hroughou he world. CBAS/RS usually consis of conveyors, sorage racks and auomaed Sorage/Rerieval (S/R) machine (crane) []. he S/R machine is fully auomaed and can ravel in narrow aisles beween he sorage racks o sore and rerieve loads. he S/R machine can maniulae eiher alles (uni load AS/RS) or oes/carons (mini-load AS/RS). he major difference beween he uni-load and he mini-load sysem is in he S/R machine design. he laer has he consequence on he kinemaic roeries of he crane and he hoised carriage, which can reach higher velociies and hroughu in he case of he mini-load sysems. Advances in Auonomous Vehicle (AV) hardware echnologies have heled manufacurers of maerial handling sysems o ursue he use of AV insead of fixed- cranes in Uni-Load (UL) warehouses. AVS/RS, a relaively new echnology for auomaed UL warehouses, has been imlemened a scores of faciliies, rimarily in Euroe [3]. Due o he abiliy of accessing any sorage osiions in he sorage racks and flexibiliy in changing he number of AV, his sysem has advanages comared o radiional CBAS/RS. ehnički vjesnik 3, 3(016),

2 Mehod for evaluaing he hroughu erformance of shule based sorage and rerieval sysems. Lerher e al. Shule Based Sorage and Rerieval Sysem (SBS/RS) is a new echnology in AVS/RS and usually works wih aisle and ier caive shules. his new echnology is mosly used for mini-load warehouses [4, 5]. he verical movemen of oes is faciliaed by elevaors lifing able mouned along he erihery of he sorage racks. Shule carriers follow horizonal movemen. I is imoran o design SBS/RS righ he firs ime due o he relaive inflexibiliy of he hysical layou and he equimen. o be able o evaluae he erformance of hese designs, fas working mehod is required. In his aer, he roosed mehod for he hroughu erformance calculaions of SBS/RS is resened. Lieraure review AVS/RS is firs sudied by Malmborg [3]. Malmborg [6] rooses an analyical model for esimaing he roorion of Dual Command (DC) cycles in AVS/RS. he roosed model rovides a useful ool in redicing he DC cycles, alhough i has some limiaions. Kuo e al. [7] roosed anoher analyical model for AVS/RS redicing he resource uilizaion erformance measure. he roosed model is erformed on welve differen scenarios o es is efficiency. I is observed ha he roosed analyical model rovides good esimaes of vehicle uilizaion and sysem cos for he sudied AVS/RS. Laer, Kuo e al. [8] roosed a model based on a queuing nework aroach o esimae he erformance measures from AVS/RS. he model is caable of efficienly generaing esimaes of resource uilizaions in AVS/RS based on alernaive class-based sorage schemes. Fukunari and Malmborg [9] develoed an efficien cycle ime model for AVS/RS based on queuing modelling and comare heir erformance wih radiional CBAS/RS. he model is based on an ieraive comuaional scheme considering random sorage assignmen olicy. his model also imroves uon earlier models by scaling efficienly for large roblems. he erformance of he rocedure is shown on realisically sized roblems. Laer, Fukunari and Malmborg [10] roosed anoher queuing nework aroach esimaing he resource uilizaions in AVS/RS. his model also rovides reasonably accurae esimaes for he resource uilizaion of he sudied sysem. Zhang e al. [11] sudied a queuing modelling aroach o esimae he waiing imes of ransacions in AVS/RS. he roosed model is variance based ha dynamically selecs among hree alernaive queuing aroximaions based on he Squared Coefficien of Variaion (SCV) of ransacion iner-arrival imes. he roosed model s resuls show greaer accuracy in esimaion of ransacion waiing imes and hereby enabling more effecive design conceualizaion. hey also resen he roosed models via online ools o le he warehouse designers and analyss develo alernae AS/RS and AVS/RS warehouse configuraions. Recenly, Ekren e al. [1], Ekren [13] and Ekren and Heragu [14] have sudied simulaion based erformance evaluaion of AVS/RS. hey sudy near oimum sorage rack configuraion design under re-defined scenarios of number of vehicles and lifs in he sysem. hey use simulaion based regression analysis [15] and imlemen a design of exerimens for an AVS/RS o idenify facors affecing is erformance [15]. Roy e al. [16] sudied a Semi-Oen Queuing Nework (SOQN) model o evaluae he design rade-offs in a single ier of an AVS/RS. heir model caures he effec of locaion of he vehicles wihin a ier using mulile vehicle classes and class swiching robabiliies. hey solved he develoed SOQN model by a decomosiion aroach. he resuls sugges ha having mulile zones is beer due o reducion in ravel ime along he cross-aisle. Ekren e al. [17, 18] also sudy SOQN o model an AVS/RS. hey use heir re-roosed exended algorihm [19] o calculae he erformance measures, aricularly uilizaion of resources and waiing imes in resource queues, from he sysem. By his sudy, hey showed ha he sysem could be modelled by SOQN and solved efficienly by heir exended algorihm. he mos relaed aer o he sudied sysem is comleed by Carlo and Vis [4]. hey sudy a ye of SBS/RS where here are wo non-assing lifing sysems mouned along he sorage rack. hey comlee heir sudy for a comany roviding soluions on hese sysems. hey focus on scheduling roblem where wo (iece-wise linear) funcions are inroduced o evaluae candidae soluions. Laer, Marche e al. [0] simulaed an SBS/RS o observe he main rade-offs. hey considered several warehouse design scenarios in erms of sorage rack design. hey rovide several erformance measures from he sysem also including cos. Lerher e al. [1] sudy muli-objecive oimizaion for auomaed warehouses. For he soluion rocedure, hey uilized geneic algorihm. Recenly, Lerher [] and Lerher e al. [5] have sudied energy efficien warehouse design in auomaed warehousing, e.g. in SBS/RS. he roosed models enable reducion of energy consumion and consequenly he CO emissions roduced in SBS/RS warehouses. Several design scenarios are considered in erms of sorage rack design and maerial handling equimen velociies o es how he energy consumion is affeced by hese designs. By hese sudies, i is believed ha he energy and environmen asec indubiably brough changes ino lanning of warehouses and caused a grea challenge for hose who are engaged in he auomaed warehousing lanning rocess. Lerher a al. [3] roosed analyical ravel ime model for he comuaion of ravel (cycle) ime for SBS/RS. he roosed model considers he oeraing characerisics of he elevaors lifing able and he shule carrier, such as acceleraion and deceleraion and he maximum velociy. he roosed model enables he calculaion of he mean ravel (cycle) ime for he single and dual command cycles, from which he erformance of SBS/RS can be evaluaed. Smewe al. [4] resened a simulaion sudy o define rade-off beween he conflicing objecives of maximising cusomer service level and minimising Work- In-Process. Bekker [5] roosed a comuaionally economic aroach o oimise hroughou rae and 716 echnical Gazee 3, 3(016),

3 . Lerher i dr. Meoda za rocjenu roočne erformance auomaiziranih skladišnih susava s vozilima allocaed buffer sace, which are he wo conflicing objecives of he buffer allocaion roblem. Regarding he warehouse informaizaion, Erkan and Can [6] roosed Analyic Hierarchy Process (AHP) and Fuzzy Analyic Hierarchy Process (FAHP) for selecing beween barcode and Radio Frequency Idenificaion (RFID) sysems for he comany warehouse daa collecion sysem. Differen from he exising sudies, we roose he hroughu erformance calculaions mehod of SBS/RS by imlemening several warehouse designs. We show our resuls for he seleced velociy rofile of he elevaors lifing able and for he shule carrier and several scenarios for sorage rack configuraions. 3 Mehod for he hroughu erformance calculaions SBS/RS are comosed of elevaors wih lifing ables ha are aached on a mas, shule carriers, buffer osiions and he sorage racks (Fig. 1). he elevaors lifing able rovides verical movemen for oes o reach he rescribed ier in he SBS/RS. he elevaors lifing able can reach u o v y = 1,5 m/s and more. Elevaors are usually bolenecks in he sysem so ha hey deermine he erformance of he whole sysem [, 3]. A shule carrier is a ier-caive auonomous vehicle wih four wheels ha ransors oes from buffer osiion o sorage locaions in he sorage racks. I is equied wih elescoic aachmen for maniulaing oes. he maximal weigh of a oe should no exceed 50 kg/shule carrier and is dimensions should be in he range of: min. ( ) mm, max. ( ) mm. A shule carrier can ravel u o v x = 4 m/s [, 3]. In SBS/RSs, here is usually a single shule carrier in each ier of sorage rack (ier-caive sysem). his assumion can be released if we use a secial shule elevaor a he back of he sorage rack, for moving shule carriers u and down o he rescribed ier in he sorage rack (ier-o-ier sysem) [, 3].here are wo buffer osiions, each serving one side in sorage rack a each ier. hese osiions are used for buffering oes carried by lifs for sorage rocess and by shules for rerieval rocess. he sorage rack is comosed of sorage columns C. By mulilying sorage columns C in he horizonal and iers in he verical direcion, he oal number of sorage locaions Q is achieved. When building he simulaion model of SBS/RS, he following assumions and noaions were considered [3]. he SBS/RS is divided ino wo sides in an aisle. So, oes can be sored a eiher side in a ier. he inu/ouu (I/O) locaion of he SBS/RS is locaed a he firs ier, nex o he lif locaion (Fig. 1). he sorage rack is divided by columns and iers. A each ier, here are wo buffer osiions (lef and righ) and a single shule carrier (aisle-caive sysem). he elevaor maniulaes wo lifing ables indeendenly one of which is locaed a he lef side and he oher one is locaed a he righ side of he elevaor. Each lifing able can serve one oe a a ime (Fig. 1). he elevaor and shule carrier comlee single and dual command cycles. Drive characerisics (v y, a y ) of he elevaors lifing able as well as he heigh H SR of he sorage rack are known in advance. Drive characerisics of he shule carrier (v x, a x ) as well as he lengh L SR of he sorage racks are known in advance. he heigh H SR and lengh L SR of he sorage racks are large enough for he elevaors lifing able and he shule carrier o reach heir maximum velociy v max in he verical and in he horizonal direcion. Randomized assignmen olicy is considered which means ha any sorage osiion is equally likely o be seleced for sorage or rerieval locaion o be rocessed. We summarize he acronyms and noaions in he aer as lised below: Abbreviaions: AS/RS Auomaed sorage and rerieval sysems. AVS/RS Auonomous vehicle sorage and rerieval sysems. AV Auonomous vehicle. CO Carbon dioxide. SCV Coefficien of variaion. CBAS/RS Crane based auomaed sorage and rerieval sysems. DC Dual command. I/O Inu and ouu. SOQN Semi-oen queuing nework. SBS/RS Shule based sorage and rerieval sysems. SC Single command. S/R Sorage and rerieval. UL Uni load. Symbols: a a x Acceleraion/deceleraion. Acceleraion/deceleraion of he shule carrier in he horizonal direcion. a y Acceleraion/deceleraion of he elevaors lifing able in he verical direcion. d() η τ h oe h COM H SR l oe l COM L SR C A v max (SC) lif (DC) lif Disance in deendence of ime. Efficiency. Execed boleneck. Heigh of he oe (lasic conainer). Heigh of he sorage cell (ier). Heigh of he sorage rack. Lengh of he oe (lasic conainer). Lengh (deh) of he sorage cell. Lengh of he sorage rack. Number of iers. Number of columns. Number of aisles. Maximum velociy. Single command cycle ime of he elevaors lifing able. Dual command cycle ime of he elevaors lifing able. ( ) lif DC Mean dual command cycle ime of he elevaors lifing able. ehnički vjesnik 3, 3(016),

4 Mehod for evaluaing he hroughu erformance of shule based sorage and rerieval sysems. Lerher e al. (SC) shule Single command cycle ime of he shule carrier. (DC) shule Dual command cycle ime of he shule carrier. ( DC) shule Mean dual command cycle ime of he shule carrier. P/S shule Picku and se-down ime of he shule carrier. P/S lif Picku and se-down ime of he elevaors lifing able. λ hroughu caaciy. λ(dc) lif hroughu caaciy of he elevaors lifing able. λ(dc) shule hroughu caaciy of he shule carrier. λ(dc) hroughu caaciy of SBS/RS in one aisle. λ(dc) SBS/RS hroughu caaciy of SBS/RS as a v() v x v y Q w oe w COM 3.1 Simulaion model of SBS/RS whole. ime. Velociy in deendence of ime. Velociy of he shule carrier in he horizonal direcion. Velociy of he elevaors lifing able in he verical direcion. Warehouse volume. Widh of he oe (lasic conainer). Widh of he sorage cell. o faciliae he erformance evaluaion of he SBS/RS, he discree even simulaion was emloyed [3].he simulaion model begins wih he rocess which marks all sorage locaions in he SBS/RS according o he rescribed sorage area. Afer creaing he lis of free sorage locaions, ener in he simulaion model he firs oe, which is siuaed in he inu/ouu (I/O) locaion of he SBS/RS. Furher on, he oe receives a sign, which belongs o he buffer osiion in he i h ier and he sorage locaion in he i h ier. he elevaors lifing able icks u he oe from he I/O locaion and moves o he buffer osiion in he i h ier. Afer conducing ransor o he buffer locaion in he i h ier, he elevaors lifing able se down he oe, which is waiing o be moved by a shule carrier. Nex he shule carrier icks u he oe from he buffer osiion in he i h ier and ravels o he j h sorage locaion, where he oe is se down by a shule carrier. For he sorage oeraion, he randomized sorage olicy has been used. Nex, he oe ha has been sored he i h sorage locaion is u on he waiing lis by a comuer (comuer daa base), where i wais for he rerieval oeraion. For he rerieval rocess he random reques selecion rule has been used. Afer he sorage oeraion in he i h ier, he shule carrier ravels o he j h rerieval locaion. he rerieval locaion is osiioned in he same ier (alicaion of he ier-caive sysem). Nex, he shule carrier icks u he oe and moves o he buffer osiion in he i h ier, where he oe is icked u by he elevaors lifing able. he average cycle ime for he ransacion is herefore associaed wih moving of he elevaors lifing able and ravelling of he shule carrier. Movemen of he elevaors lifing able and ravelling of he shule carrier in he simulaion model is based on he velociy-ime deendence. wo yes of velociy rofiles can be disinguished deending on wheher he obained eak velociy v( ) is less han v max (ye I) or equal o v max (ye II) (Fig. ). I can be verified ha ime <v max / a for ye I and >v max / a for ye II [3]. Figure Velociy ime deendence for ye I and II [3] Velociy-ime deendence for ye I he velociy in deendence of ime v() equals he following exression: a, (0, ) v () =, a ( ), (, ) he disance in deendence of ime d() equals he following exression: 0 a d( ) = v() d =, () 4 Because of he acceleraion and deceleraion are equal in magniude, he ime necessary o reach he eak velociy equals = /. For he verificaion of he exression see Aendix A. Velociy-ime deendence for ye II he velociy in deendence of ime v() equals he following exression: a, (0, ) v ( ) = vmax, (, ), a ( ), (, ) (1) (3) 718 echnical Gazee 3, 3(016),

5 . Lerher i dr. Meoda za rocjenu roočne erformance auomaiziranih skladišnih susava s vozilima he disance in deendence of ime d() equals he following exression: vmax max (4) a 0 d( ) = v() d = v, For he verificaion of he exression 4 see Aendix A. As a erformance measure for he SBS/RS, he mean cycle ime and consequenly he hroughu caaciy have been used. he hroughu caaciy reresens he number of ransacions (sores and rerievals) ha he sysem can erform in a given ime eriod. he hroughu caaciy is inversely deenden on he average cycle ime. 3. hroughu erformance of he elevaor he elevaor carries wo lifing ables a boh sides (lef and righ). Boh lifing ables work indeendenly of each oher and hus double hroughu caaciy can be achieved. he elevaors lifing able can work on a Single Command (SC) cycle, which means ha only one oe can be handled in a cycle. More advanced is Dual Command (DC) cycle, by which wo oes are handled in a cycle (Fig. 3). For he calculaion of he SC and DC cycles of he elevaors lifing able, he simulaion model of he SBS/RS has been emloyed. Figure 3 Dual command cycle of he elevaors lifing able [3] 3..1 Single command cycle In he case of SC cycle, he elevaors lifing able moves a oe from he I/O locaion o randomly seleced ier j, unloads he oe and moves back o he I/O locaion. he same sequence can also be erformed in he reverse order. Single command cycle ime (SC) lif can be calculaed by simulaion using exression (5): ( ) P/S lif I/O, j SC = +, (5) lif 3.. Dual command cycle In he case of DC cycle, he elevaors lifing able moves a oe from he I/O locaion o randomly seleced ier j, unloads he oe and moves furher o randomly seleced ier i, where he oe is rerieved. Afer loading he oe a ier i, he elevaors lifing able moves back o he I/O locaion (Fig. 3). Dual command cycle ime (DC) lif can be calculaed by simulaion using exression (6): ( ) P/S lif I/O, j ji, i,i/o DC = , (6) lif 3..3 hroughu erformance calculaion 3600 l ( DC ) = k n, (7) lif ( DC) lif where k =, due o he DC and n = due o he elevaor wih wo lifing ables. 3.3 hroughu erformance of he shule carrier A shule carrier can receive one oe a a ime and can oerae on a SC cycle or DC cycle. For he calculaion of he SC and DC cycles of he shule carrier, he simulaion model of he SBS/RS has been emloyed Single command cycle he oeraion of SC cycle encomasses eiher sorage or a rerieval assignmen. Afer comleing a given sorage or rerieval assignmen a oin P i, he shule carrier reurns direcly o he I/O ier j. In he case of SC cycle, he shule carrier oeraes only one oe in he cycle. Single command cycle ime (SC) shule can be calculaed by simulaion using exression (8): ( ) ier j SC = +, (8) shule P/S shule I/O, P i By considering (6) he hroughu erformance of he elevaors lifing ables in case of DC cycles er hour is calculaed by (7): ehnički vjesnik 3, 3(016),

6 Mehod for evaluaing he hroughu erformance of shule based sorage and rerieval sysems. Lerher e al. Figure 4 Dual command cycle of he shule carrier [3] 3.3. Dual command cycle he oeraion of DC cycle considers sorage and rerieval assignmen in a cycle (Fig. 4). Recall ha in DC cycle, he shule carrier ravels o wo sorage locaions beween successive reurns o he I/O ierj. Afer comleing a given sorage reques a oin P i, he shule carrier moves direcly o anoher sorage locaion for he nex rerieval reques a oin P j wihou reurning o he I/O ierj. Dual command cycle ime (DC) shule can be calculaed by simulaion using exression (9): ( ) P/S shule I/O ier j, Pi Pi, Pj Pj, I/Oier j DC = , (9) shule hroughu erformance calculaion By considering (9) he hroughu erformance of all shule carriers in case of DC cycles er hour is calculaed by (10): 3600 l ( DC ) = k m, (10) shule ( DC) shule where k is, due o he DC cycle and m = due o he alicaion of he ier-caive SBS/RS. 4 SBS/RS under sudy In his secion, main inu daa for he analysis are rovided and discussed. Sock keeing uni reresens a oe (lasic conainer) filled wih iems wih he dimensions: lengh l oe = 0,6 m, widh w oe = 0,4 m and heigh h oe = 0,4 m. Wih regard o he oe, he sorage comarmen (cell) has he following dimensions: lengh (deh) of he sorage celll COM = 0,6 m, widh of he sorage cell w COM = 0,5 m and heigh of he cell (ier)h COM = 0,35 m. Dimensions of he SBS/RS sorage rack (L SR and H SR ) deend on he number of columns C in he horizonal direcion and number of iers in he verical direcion, resecively. As i will be seen in ab. 1, nine (9) differen SBS/RS configuraions were analysed based on hree values of iers ( = 10, 15 and 0) and hree values of aisles A (A = 3, 6 and 9) [0]. oal number of sorage locaions - Q - is assumed o be aroximaely sorage locaions [0]. able 1 SBS/RS configuraions [0] RCi / A C L SR / H SR Q 1 10 / ,5 / 3, / / 3, / / 3, / / 5, / / 5, / / 5, / / 7, / / 7, / / 7, Since he hroughu caaciy λ grealy deends on he velociy characerisics of he elevaors lifing able and he shule carrier, seleced velociy scenario has been used in our analysis (ab. ). able Velociy scenario of he shule carrier and he elevaors lifing able Shule carrier ravelling in he horizonal direcion Lifing able movemen in he verical direcion v x (m/s) a x (m/s ) v y (m/s) a y (m/s ) 1,5 1,5 1,5 1,5 Noe: Velociy scenario is seleced according o he references of maerial handling equimen roducers and racical exeriences of he auhors. Oher daa ha were used in he analyses are resened in ab. 3. able 3 Oher daa used in analysis Pick u / Deosi ime Uni of measure Daa P/S shule sec. 3,0 P/S lif sec. 1,5 Noe: SBS/RS configuraions are seleced according o he references of maerial handling equimen roducers and racical exeriences of he auhors. 5 hroughu erformance of he SBS/RS ab. 4 summarizes mean DC cycle ime of he and he shule carrier elevaors lifing able ( DC) lif ( ) shule DC. ab. 5 summarizes hroughu erformance of he elevaors lifing ables λ(dc) lif and he shule carriers λ(dc) shule. ab. 6 summarizes he hroughu erformance of he SBS/RS as a whole. he hroughu erformance λ(dc) SBS/RS is calculaed according o he exressions (11), (1), (13) and (14). Because he SBS/RS are comosed of he elevaors lifing ables and he ier-caive shule carriers ha are 70 echnical Gazee 3, 3(016),

7 . Lerher i dr. Meoda za rocjenu roočne erformance auomaiziranih skladišnih susava s vozilima working indeendenly from each oher, he ossible boleneck is required o be found for calculaing he SBS/RS hroughu erformance. RCi column shows nine rack configuraions for he SBS/RS defined in ab. 1. Recall ha means DC cycle imes of he elevaors lifing able ( DC) lif and he shule carrier ( DC) shule are calculaed according o he large number of successive simulaions. able 4 ravel ime analysis DC (s) RCi ( DC) shule (s) ( ) lif 1 89,5 5,4 3 39,9 4 64,9 5 39,9 6 3,0 7 5,4 8 33,9 9 7,5 able 5 hroughu caaciy analysis λ(dc) shule RCi (oes/h) ,70 13,30 15,00 λ(dc) lif (oes/h) he hroughu erformance of he elevaors lifing ables λ (DC) lif and he shule carriers λ(dc) shule, are calculaed by using (7) and (10), resecively. he efficiency η of he elevaors lifing able and he shule carrier is calculaed by (11): ( l( ) l shule ( ) lif ) l( ) l( ) min DC, DC h =, (11) max DC, DC ( ) shule he execed boleneck is found by he leer τ and is calculaed by (1): lif ( ( ) ( ) ) = max l DC, l DC, (1) shule he hroughu caaciy of SBS/RS in one aisle is calculaed by (13): lif ( ) ( ) ( ) ( ) l DC = min l DC, l DC, (13) shule he whole SBS/RS sysem erformance λ(dc) SBS/RS is calculaed by (14): ( ) A λ( ) λ DC = DC, (14) SBS/RS According o he resuls resened in ab. 6, he hroughu erformance of he SBS/RS is influenced by he number of iers, number of aisles A, number of columns C, he velociy of he elevaors lifing able (v y, a y ) and he velociy of he shule carriers (v x, a x ). lif able 6 hroughu erformance of he SBS/RS RCi λ(dc) shule λ(dc) lif λ(dc) λ(dc) η (oes/h) (oes/h) lif η shule τ A SBS/RS (oes/h) (oes/h) ,65 1,00 shule ,00 0,90 lif ,00 0,68 lif ,00 0,65 lif ,00 0,40 lif ,00 0,3 lif ,00 0,35 lif ,00 0,3 lif ,00 0,18 lif NOE: λ(dc) SBS/RS = λ(dc) A he sysem erformance mainly deends on he erformance of he elevaors lifing ables feeding he sorage racks. Since a shule carrier can handle more work han an elevaor, he assumion of ier-caive shules can be released. In more advanced sysems, a shule carrier can by using a secial elevaor a he back of he sorage rack, oerae in more iers han in a single one. Since he hroughu erformance of a SBS/RS is deermined by he elevaor, he elevaor should receive he mos of he aenion when designing SBS/RS. 6 Conclusion In his aer, a mehod for calculaing he sysem erformance of a SBS/RS is resened. he roosed mehod consiss of calculaions for he hroughu caaciy of he elevaors lifing ables and he shule carriers of he SBS/RS. SBS/RS are usually used by he comanies dealing wih large number of small sized orders requiring o be rocessed in a relaively shor ime eriod. In racice, here is an aroximaion ha his sysem could reach u o 1000 oes er hour. he roosed mehod resens an efficien aroach for evaluaing he sysem (hroughu) erformance of he SBS/RS. he sysem erformance is manly influenced by he following decision variables: (i) number of iers, (ii) ehnički vjesnik 3, 3(016),

8 Mehod for evaluaing he hroughu erformance of shule based sorage and rerieval sysems. Lerher e al. number of aisles A, (iii) number of columns C, (iv) velociy of he elevaors lifing able (v y, a y ) and (v) velociy of he shule carriers (v x, a x ). Since he elevaor (elevaors lifing ables) works mos of he ime wih he efficiency η = 1,0 he sysem erformance will grealy deend on he number of columns C and number of aisles A. In case of small number of columns C and large number of aisles A (RC 3, RC 6 and RC 9 ), he sysem erformance is exressively higher comared o oher rack configuraions (see ab. 6). Anoher imoran issue is he velociy rofile of he elevaor (elevaors lifing ables), which was in our case moderae (v y = 1,5 m/s and a y = 1,5 m/s ). In case of efficien drives of he elevaors lifing ables, he ravel (cycle) ime will be lower, which will have a consequence o he sysem (hroughu) erformance of he SBS/RS. Of course, he velociy rofile for he verical movemen is always limied wih hysical boundaries of he load ha is being hoised. he roosed mehod roves o be useful when designing SBS/RS in racice. he roosed mehod could hel he warehouse designer o analyse he efficiency of layou along wih he kinemaic roeries of he SBS/RS in he early sage of rojec. he oenial limiaion is ha he simulaion model of he SBS/RS needs o be develoed by warehouse designers, since here is no general simulaion model in he marke. For he fuure work a mehod for he sysem (hroughu) erformance energy consumion and energy regeneraion of he SBS/RS should be considered simulaneously. I has been roven ha for an efficien SBS/RS design, boh hroughu erformance, energy consumion and energy regeneraion asec should be considered as a single objecive funcion. 7 References [1] Burinskiene A. 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9 . Lerher i dr. Meoda za rocjenu roočne erformance auomaiziranih skladišnih susava s vozilima [3] Modern auomaion in warehousing by using he shule based echnology. // Lerher,. Auomaion Sysems of he 1s Cenury: New echnologies, Alicaions and Imacs on he Environmen & Indusrial Processes. 013 New York: Nova Publishers, [4] Lerher,.; Ekren, B. Y.; Dukic, G.; Rosi, B. ravel ime model for shule-based sorage and rerieval sysems. // Inernaional Journal of Advanced Manufacuring echnology. 40, (015), DOI: /s [5] Smew, W.; Young, P.; Geraghy, J. Suly Chain Analysis Using Simulaion, Gaussian Process Modelling and Oimisaion. // Inernaional Journal of Simulaion Modelling. 1, 3(013), DOI:10.507/IJSIMM1(3)4.39 [6] Bekker, J. Muli-objecive Buffer Sace Allocaion wih he Cross-enroy Mehod. // Inernaional Journal of Simulaion Modelling. 1, 1(013), DOI: /IJSIMM1(1)5.8 [7] Ekran,. E.; Can, G. F. Selecing he bes warehouse daa collecing sysem by using AHP and FAHP mehods. // ehnicki vjesnik-echnical Gazee. 1, 1(014), Auhors addresses Associae rofessor dr. one Lerher Universiy of Maribor, Faculy of Logisics, Mariborska cesa 7, 3000 Celje, Slovenia one.lerher@um.si Associae rofessor dr. Bojan Rosi Universiy of Maribor, Faculy of Logisics, Mariborska cesa 7, 3000 Celje, Slovenia bojan.rosi@um.si Assisan rofessor dr. Banu Yekin Ekren Izmir Universiy of Economics, Dearmen of Indusrial Engineering, Izmir 35330, urkey banu.ekren@izmirekonomi.edu.r Professor dr. Zaki Sari Universiy of lemcen, Manufacuring Engineering Laboraory of lemcen, lemcen, Algeria zaki_sari@yahoo.com Aendix A. Verificaion of exressions and 4 Verificaion of he exression where he eak velociy v is less han v max. Condiion 1: d1() = v() d = a d = a, (15) Condiion : 1 (16) d () = v() d = a( ) d = a( ), Considering he condiion = /, he disance in deendence on ime d() equals he nex exression: a d ( ) = d1() + d() =, (17) 4 Verificaion of he exression 4 where he eak velociy v is equal o v max. Condiion 1: 0 a d1() = v() d = a d =, 0 0 (18) Condiion : - max max (19) d () = v() d = v d = v ( ), Condiion 3: - a d3 () = v() d = a( ) d =, (0) Considering he condiion = v max /a, he disance in deendence on ime d() equals he nex exression: max v d( ) = d1() + d () + d3() = vmax, (1) a ehnički vjesnik 3, 3(016),