Simulation analysis of models for estimation of empty travel time of vehicles in non-automated material handling systems

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1 Gora Dukic Ailiatio-Proessor Uiversity o Zagreb Faculty o Mechaical Egieerig ad Tihomir Opetuk Postgraduate researcher Uiversity o Zagreb Faculty o Mechaical Egieerig ad Hrvoje Cajer Assistat Proessor Uiversity o Zagreb Faculty o Mechaical Egieerig ad Matko Jakovljevic Ex graduate studet Uiversity o Zagreb Faculty o Mechaical Egieerig ad Simulatio aalysis o models or estimatio o empty travel time o vehicles i o-automated material hadlig systems I desigig or redesigig a acility like mauacturig plat or warehouse, a itegral part is a proper selectio o material hadlig system. Despite large alteratives, icludig automated material hadlig systems with coveyors or automated guided vehicles, most acilities today use or material hadlig ma-drivig vehicles (o-automated discrete material hadlig system). Proper desig o such systems requires determiatio o required umber o vehicles. Determiatio o empty vehicle travel time is based o either time cosumig simulatio or osimulatio approach usig estimatio. The mai goal o this paper is to review ad aalyse some proposed methods or empty travel time estimatio o o-automated discrete material hadlig systems. Results obtaied by estimatio methods are compared with the simulatio results. Keywords: Discrete o-automated material hadlig system, empty travel time estimatio methods, simulatio aalysis 1. INTRODUCTION I desigig a ew acility like mauacturig plat or warehouse, a itegral part is a proper selectio o material hadlig system. Despite large alteratives, icludig automated material hadlig systems with coveyors or automated guided vehicles, most acilities use ma-drivig vehicles (o-automated discrete material hadlig system), usually orklits. Proper desig o such systems requires determiatio o required umber o vehicles. Eve redesig o existig acilities, like improvemet o layout desig which is ote with the goal o reductio o total trasportatio, requires aalysis o proposed ew solutio icludig determiatio o required umber o vehicles. I most existig acilities today, especially smaller oes, we ca id oly oe or ew ma-drivig, o-automated vehicles used or loadig, trasport ad uloadig loads betwee departmets ad/or machies (workplaces). For determiatio o required umber o vehicles or or calculatio o vehicle s utilisatio i a proposed redesig, a proper method o calculatio o total trasport time is required. Based o umber o trips betwee locatios (rom-to matrix), distaces betwee locatios based o layout (distace matrix) ad trasport/hadlig parameters (speed o travel, loadig times, uloadig times), it is quite easy to calculate total time required or loadig, uloadig ad trasport o loads. However, determiatio o empty vehicle travel Correspodece to: Dr Gora Dukic, ull proessor Faculty o Mechaical Egieerig ad, Uiversity o Zagreb Ivaa Lucica 1, Zagreb, Croatia gora.dukic@sb.hr FME Belgrade, All rights reserved time is based o either time cosumig simulatio or o-simulatio approach usig estimatio. Searchig or methods to estimate empty vehicle travel time leads to plety papers dedicated to automated guided vehicle systems (AGVS), but surprisigly o papers especially dedicated to oautomated trasporters. I AGVS there exists a cotrol system with various dispatchig rules that are mostly ot applicable or trasport systems i smaller job shops, workshops or smaller warehouses. Proposed algorithms also usually assume larger leets where proper schedulig ad routig o automated vehicles is required due to the cogestios ad deadlocks. I smaller acilities oly ew vehicles are employed, sometimes eve oly oe, with mostly low utilisatio. The mai motivatio o the research preseted i this paper was to review proposed methods or empty travel time estimatio developed or AGVS ad to aalyse their usage or o-automated discrete material hadlig systems, especially those employig oly oe or two vehicles. For selected example o productio process, varyig throughput (productio volume) ad layout, results obtaied by estimatio methods are compared with simulatio results i order to get isights o estimatio errors, possible iluece o vehicle s utilisatio o estimatio error as well as possible iluece o layout desig (icreased ull travel time) o total empty travel time ad estimatio error. 2. EMPTY TRAVEL TIME ESTIMATION METHODS I this sectio several most cited methods or empty travel time estimatio, aalysed i this paper, are shortly preseted. The irst aalytical models, whose developmet bega i the early 1980 s, were desiged to provide alterative solutio or AGV system desig sice the Proceedigs o the XXII Iteratioal Coerece MHCL 17

2 process o desigig a simulatio model required much eort ad time. Most o the models were logically meaigul ad comprehesible, mathematically simple calculatio, used to determie the required umber o vehicles to carry out trasport processes based o prekow data (trasport itesity ad distace matrices, ad trasport ad productio parameters), i a shorter period o time. Still today aalytical estimatio methods are preerable tha simulatio i early stage o desig, durig selectio o material hadlig systems. Already i the desig o the irst models ocused o the AGV system desig it was oted the importace o determiig the time o empty travel, ad soo that part o the calculatio/estimatio became the key item to which the most attetio was give. Notatio used i models is as ollows: umber o workplaces umber o loaded trips (ull travels) required rom workceter i to workceter j d distace betwee workplaces, i meters D e total empty travel distace, i meters g expected umber o empty trips rom workceter i to workceter j d k umber o deliveries to workceter k s i umber o pick-ups at workceter i d e average empty vehicle travel distace per trip, i meters I [1] author preseted our models or estimatio o umber o required vehicles (NRV), however oe o them do t estimate empty travel but directly NRV (based o estimated blockig ad idle time). Two models were models preseted by Beisteier i [2] or this paper amed BEISTEINER 1 ad BEISTEINER 2 model. Fourth model was proposed by author, amed EGBELU model. BEISTEINER 1 model is very simple. It is assumed that the distace travelled by empty vehicles is equal to the distace travelled by ull vehicles. Thereore, or a give umber o trips betwee each pair i rom-to matrix ad distaces betwee workplaces, total empty travel is calculated as D e i1 j1 d BEISTEINER 2 model is based o calculatio o et traic lows ito workplaces, as i ji j1 j1 (1) (2) I there are more deliveries tha pickups at workplace, there will be empty rus orm that workplace to some others. Ad vice versa, i there are more pickups tha deliveries at workplace, there will be empty rus to that workplace. Total empty travel distace is approximated as average distace travelled by ull vehicles multiplied by umber o empty rus betwee workplaces, as d i1 j1 D e i (3) 0 i i1 j1 EGBELU model is based o the act that i a job shop eviromet the sequece at which load pickups requests are geerated is very radom ad assumptio o air dispatchig rule. It calculates expected umber o empty rus betwee two workplaces i ad j rom the expected umber o deliveries at workplace i ad expected umber o pick-ups at workplace j usig equatio g k1 ki i1 j1 k1 jk (4) Total empty travel distace is calculated simply multiplyig expected umber o empty trips betwee workplaces by distace betwee them, as De g d (5) I [3] authors preseted a model or calculatio o miimum required vehicles, based o miimizatio o empty travel. As i BEISTEINER 2 model, this MAXWELL-MUCKSTADT model calculates et traic lows ito workplaces, however determiatio o empty rus is doe by solvig trasportatio problem (miimizig total empty travel). While Egbelu s model is cosidered as expected case, this oe is cosidered as best case. For more details readers are reerred to reerece [3]. I [4], authors preseted a model or empty travel time estimatio based o assumptio that the vehicles that iish the trasportatio requiremets stay at their curret workplace. This assumptio assures that the umber o empty vehicles leavig a workplace is equal to the umber o loads dropped o at that workplace. Similarly, the umber o empty vehicles that will be eeded at a particular workplace is equal to the umber o loads that have to be moved rom that workplace. They also assumed that vehicles are assiged to workplaces (called rom ext workplace) accordig to a radom rule. The probability that vehicles are assiged to machie i whe they complete a delivery task at machie k, is a uctio o the proportio o those trasportatio requiremets to be trasported to ad uloaded at machie k, calculated as ik i1 d k i1 j1 (6) Proceedigs o the XXII Iteratioal Coerece MHCL 17

3 ad the proportio o those trasportatio requiremets to be picked up at machie i ad trasported to some other places, calculated as ik i1 s i i1 j1 (7) So the probability that a vehicle request at machie i is satisied by a vehicle at machie k is d k si. The average empty vehicle travel distace per trip ca be the calculated as de si d k dki i1 k1 (8) The model, amed here KOO-JANG model, calculates total empty travel as average travel distace per empty trip multiplied by umber o empty trips (which is equal to the umber o ull trips), as D e s i d k dki i1 k1 i1 j1 (9) Aalysis o the models preseted i metioed papers, as well as plety other papers dealig with AGV system desig (or more io about AGV systems desig ad cotrol issues see review papers [5] or [6]), revealed that the perormace o iteral trasport systems usig AGVs depeds o several actors such as umber o trips betwee locatios ad distaces (guidepath layout), but also vehicle schedulig ad routig system. Exact iormatio about load arrivals is usually oly kow a little momet i advace, thereore schedulig vehicles i these systems i advace is early impossible. The best solutio is to use o-lie dispatchig rules [7]. It was prove that dispatchig rules have ueglectable iluece o AGV system s perormaces, so dispatchig rules are a key actor i determiig the amout o empty vehicle travel [8].Vehicle dispatchig decisios are cocered with assigig vehicles ad delivery requests to each other i real time based o the state o the system [9]. Some examples are rules such as radom vehicle selectio, logest idle vehicle selectio, least utilized vehicle selectio, earest vehicle selectio (as workplace iitiated task assigmet rules), or radom workceter, shortest travel time, maximum outgoig queue size, miimum remaiig outgoig queue space, etc. (as vehicle iitiated task assigmet rules). However, i o-automated discrete material hadlig systems without computer cotrol most dispatchig rules are ot possible to employ (or at least they are impractical to empower). I some applicatios o AGV systems there are oly a ew vehicles ad jobs ivolved, with the simple schedulig algorithms. Jobs are usually hadled i a First-come-First-serve (FCFS) ashio, ad the earest idle vehicle is usually chose to serve a ew job. The missio o routig is to id a suitable route (e.g. shortest-distace path, shortest-time path or miimal eergy path) or every AGV rom its origi to destiatio based o the curret traic situatio. The route must be cogestio-, colict- ad deadlock-ree [10]. Here agai, i o-automated discrete material hadlig systems with oe or ew huma drivig vehicles routes are chose by driver ad it could be assumed that there are o colicts, cogestios, while routes are simple to id optimal. So i this paper above metioed aalytical models are applied to a classical productio system where the vehicle is ree to move i all directios betwee workplaces (alog paths), ad tasks are assiged to a ree vehicles (radom selectio) accordig to the FCFS strategy. 3. SIMULATION ANALYSIS For simulatio aalysis oe simple productio process was selected, cosistig o 4 products processed i a productio system with 8 discrete locatios i a layout iboud storage US (raw material warehouse), 6 workplaces RM 1 RM 6 (machies) ad outboud storage IS (iished goods storage). Simulatio model was built i Eterprise Dyamics 10 simulatio sotware. Figure 1 presets the 2D model layout represetig layout o the productio system, which was also used to calculate distace matrix eeded or aalytical models. Techological processes o products (sequeces o visitig workplaces) are give i Table 1, used also to deie rom-to matrix (umber o trips betwee locatios). Table 1. Routig o products (sequeces o operatios) Product Sequece o operatios P1 US RM 1 RM 3 RM 5 RM 2 RM 4 RM 6 - IS P2 US RM 5 RM 3 RM 1 RM 6 RM 4 RM 2 - IS P3 P4 US RM 3 RM 4 RM 5 RM 1 - IS US RM 2 RM 6 RM 4 RM 3 - IS Additioal data, like processig time per uit load, were selected or the purpose o simulatio i a way ot iluecig vehicle s travel. The average velocity o vehicles was set to 3 m/s (acceleratio ad deceleratio eglected), while loadig ad uloadig time per uit load was 5 secods. Simulatio rus were set to 50 hrs (assumig o shit breaks). The simulatio aalysis was doe with 4 dieret experimets [11]. I irst experimet productio volume (umber o products processed i a give time - throughput) was varied, i oe selected layout. The idea was to aalyse possible iluece o itesity o work (vehicle s utilisatio) o empty travel ad estimatio error (deviatio rom simulatio results). I secod experimet three additioal layout setups were made (chagig locatios o machies) or a selected throughput. The idea here was to aalyse possible Proceedigs o the XXII Iteratioal Coerece MHCL 17

4 iluece o layout desig (variatio o ull travel or same productio volume) o empty travel ad estimatio error. Third ad ourth experimet were same as irst two, however additioal vehicle was used. 3.1 Experimet 1 iluece o productio volume I experimet 1 productio volume was varied i 5 dieret scearios (M1-M5), leadig to the utilisatio o the vehicle rom 34% till 93%. Table 2 presets results obtaied with simulatio ad 5 aalytical estimatio models. As could be see, 3 models (that are assumig FCFS dispatchig rule) estimates empty travel quite well, while MAXWELL-MUCKSTADT ad BEISTEINER 2 models heavily uderestimates empty travel. EGBELU ad KOO-JUNG models were most accurate, however most simple BEINSTEINER 1 model is ot much worse. The greater iluece o traic itesity (vehicle s utilisatio) is oticed or low utilisatio, were models ted to have slightly higher deviatios (overestimatio), however o correlatio was oud. 3.2 Experimet 2 iluece o layout desig I experimet 2 three ew layouts were made, each deiig dieret distace matrix. Simulatio ad aalytical estimatio o empty travel, preseted i Table 3 (dieret layouts are marked L1-L4), were obtaied or two selected productio volumes, oe with lowest vehicle s utilisatio (M1) ad oe with highest vehicle s utilisatio (M5). Agai, as expected, same 3 models as i previous experimet proved useul. However some idigs were iterestig. Accordig to the simulatio results i u-optimized layouts, icreased ull travel (i table show as ull travel time, FTT i percetage o total time) is ot ollowed by the same amout o icreased empty travel. So aalytical models, where calculatio o empty travel is based o ull travel, ted to estimate higher amouts o empty travel. However errors are still withi several percet, expect BEINSTEINER 1 model where deviatios i overestimatig empty travel are up to 25%. 3.3 Experimets 3 ad 4 2 vehicles Experimets 3 ad 4 were extesios o previous two, with added vehicle ad correspodig icrease o productio volume. I experimet 3 productio volume was varied i 10 dieret scearios (added cases M6- M10). I experimet 4 same our layouts as beore were used or two selected productio volumes (agai represetig low ad high vehicle s utilisatio). Due to the eed o icreased product volume or aalysis o high utilisatio o two vehicles, simulatio model had to be slightly reworked by addig additioal machies per locatios. However this was t aect distace matrixes because workplaces were i this case workcetres (same locatio o pick-up ad delivery or all machies i a workceter). The results are preseted i Table 4 ad Table 5. The idigs are as ollows. Icrease o productio volume icreases ull travel ad empty travel. However aalytical models are estimatig higher amouts o empty travel compared to the simulatio results. The diereces i models were also oticed. While BEINSTEINER 1 model always overestimates empty travel (up to 13% i case o extremely low utilisatio), EGBELU ad KOO-JUNG models were more precise, slightly overestimatig empty travel i cases o low utilisatio while slightly uderestimatig empty travel i cases o high utilisatio o vehicles. Chages i layout coirmed idigs rom experimet 2. Icreased ull travel i u-optimized layouts is leadig to estimatio o higher amout o empty travel i aalytical models. BEINSTEINER 1 model agai teds to have sigiicat deviatios i some cases. 4. CONCLUSION Preseted aalysis o ive aalytical models or estimatio o empty travel o discrete vehicles showed that usig estimatio models without kowledge o assumptios (i this case dispatchig rules ad cotrol o the system) could lead to heavily uderestimated results i oe decides to use BEISTEINER 2 or MAXWELL-MUCKSTADT model. Other preseted models quite well estimate empty travel, while EGBELU ad KOO-JANG models beig more accurate tha BEISTEINER 1 model. The errors (deviatios rom the simulatio results) o three aalytical models are usually withi several percet (except BEISTEINER 1 model i some exceptioal situatios). Also, a certai iluece o productio volume ad layout desig o estimated empty travel time deviatios has bee established. Icreasig ull travel o vehicles aalytical models ted to estimate higher amouts o empty travel tha was obtaied by simulatio. However this should be take with a cautio, because oly oe layout with our variatios was aalysed. Sice total trasport time which leads to the required umber o vehicles is composed o ull travel time, empty travel time, loadig time ad uloadig time, small errors o empty travel time are causig eve smaller overestimatio or uderestimatio o total trasport time required. At least i early stages o iteral trasport system desig estimatio models could be used. But agai, models ca t take ito accout dieret dispatchig rules ad possible blockigs ad cogestios i case o larger leets. So i this cases, ad especially or ial veriicatio o chose trasport system, simulatio is preerred. REFERENCES [1] Egbelu, P.J.: The use o o-simulatio approaches i estimatig vehicle requiremets i a automated guided vehicle based trasport system. Material Flow, Vol. 4, pp , [2] Beisteier, F.: Strategies or the employmet o vehicles i a automated guided trasportatio system. Proc. 2d It. Co. o Automated Guided Vehicle Systems, Stuttgart, Germay, [3] Maxwell, W.L. ad Muckstadt, J.A.: Desig o Automatic Guided Vehicle Systems, IIE Trasactios, 14(2), pp , Proceedigs o the XXII Iteratioal Coerece MHCL 17

5 [4] Koo, P.-H. ad Jag, J.: Vehicle travel time models or AGV systems uder various dispatchig rules, The Iteratioal Joural o Flexible Mauacturig Systems, Vol. 14, pp , [5] Le-Ah, T. ad De Koster, M.B.M.: A review o desig ad cotrol o automated guided vehicle systems, Europea Joural o Operatioal Research, 171(1), pp. 1-23, [6] Vis, I.F.A.: Survey o research i the desig ad cotrol o automated guided vehicle systems, Europea Joural o Operatioal Research, Vol. 170, pp , [7] Le-Ah, T. ad De Koster, M.B.M.: O-lie dispatchig rules or vehicle-based iteral trasport systems, Iteratioal Joural o Productio Research, Vol. 43, pp , [8] Malmborg, C.J. ad She Y.-C.: Heuristic dispatchig models or multi-vehicle materials hadlig systems, Applied Mathematical Modellig, 18(3), pp , [9] Koo, P.-H., Jag, J. ad Suh, J.: Estimatio o part waitig time ad leet sizig i AGV systems, The Iteratioal Joural o Flexible Mauacturig Systems, Vol. 16, pp , 2005 [10] Qiu L., Hsu W.-J., Huag S.-Y. ad Wag H.: Schedulig ad routig algorithms or AGVs: A survey, Iteratioal Joural o Productio Research, 40(3), pp , [11] Jakovljevic, M.: Aalysis o aalytical models or evaluatio o empty travel time o trasporters (i Croatia), Diploma thesis, Uiversity o Zagreb, Faculty o Mechaical Egieerig ad Naval Architecture, Figure 1. Layout o the simulatio model Table 2. Empty travel time (t e) ad deviatios o aalytical models rom experimet 1 Sceario Nr o Sim. Beisteier 1 Beisteier 2 Egbelu/Koo-Jag Maxwell-Muckstadt products te, s te, s Dev., % te, s Dev., % te, s Dev., % te, s Dev., % M ,10% ,34% ,01% ,54% M ,43% ,50% ,59% ,42% M ,73% ,64% ,27% ,86% M ,29% ,41% ,13% ,40% M ,10% ,81% ,67% ,97% Table 3. Empty travel time (t e) ad deviatios o aalytical models rom experimet 2 Sceario Simulatio Beisteier 1 Beisteier 2 Egbelu/Koo-Jag Maxwell-Muckstadt FTT, % te, s te, s Dev., % te, s Dev., % te, s Dev., % te, s Dev., % M1 - L3 10, , , , ,99 M1 - L1 11, , , , ,54 M1 - L4 13, , , , ,03 M1 - L2 13, , , , ,79 M5 - L3 29, ,66% ,77% ,46% ,26% M5 - L1 30, ,10% ,81% ,67% ,97% M5 - L4 35, ,93% ,17% ,72% ,63% M5 - L2 36, ,12% ,31% ,09% ,09% Proceedigs o the XXII Iteratioal Coerece MHCL 17

6 Table 4. Empty travel time (t e) ad deviatios o aalytical models rom experimet 3 Sceario Nr o Sim. Beisteier 1 Beisteier 2 Egbelu/Koo-Jag Maxwell-Muckstadt products te, s te, s Dev., % te, s Dev., % te, s Dev., % te, s Dev., % M ,03% ,66% ,79% ,12% M ,57% ,79% ,23% ,94% M ,53% ,22% ,61% ,87% M ,13% ,44% ,28% ,45% M ,89% ,68% ,90% ,70% M ,45% ,47% ,61% ,38% M ,38% ,54% ,12% ,68% M ,97% ,65% ,02% ,10% M ,81% ,71% ,79% ,12% M ,30% ,28% ,32% ,94% Table 5. Empty travel time (t e) ad deviatios o aalytical models rom experimet 4 Sceario Simulatio Beisteier 1 Beisteier 2 Egbelu/Koo-Jag Maxwell-Muckstadt FTT, % te, s te, s Dev., % te, s Dev., % te, s Dev., % te, s Dev., % M1 - L3 10, ,40% ,28% ,44% ,87% M1 - L1 11, ,03% ,66% ,79% ,12% M1 - L4 13, ,85% ,96% ,40% ,76% M1 - L2 13, ,76% ,43% ,40% ,28% M10 - L3 58, ,12% ,31% ,34% ,24% M10 - L1 61, ,30% ,28% ,32% ,94% M10 - L4 71, ,54% ,24% ,65% ,55% M10 - L2 73, ,18% ,13% ,93% ,79% Proceedigs o the XXII Iteratioal Coerece MHCL 17