ASSIGNMENT AND DEPLOYMENT OF QUAY CRANES AT A MARITIME CONTAINER TERMINAL

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1 ASSIGNMENT AND DEPLOYMENT OF QUAY CRANES AT A MARITIME CONTAINER TERMINAL Pasquale Legato (a), Danel Gullì (b) (a, b), Roberto Trunfo (a) DEIS, Unversà della Calabra, Va P. Bu C, 8706, Rende (CS), Italy (b) CESIC NEC Itala S.r.l., Va P.Bu B, 8706, Rende (CS), Italy legato@des.unal., danel.gullì@eu.ne.om, roberto.trunfo@eu.ne.om ABSTRACT The omplex logst proess of vessel berthng followed by ontaner dsharge/loadng, at marme ontaner termnals (MCTs), s foused n ths paper. Dsrete-event smulaton models are well apable of representng the entre proess n a stohast, dynam envronment. Hene, smulaton results to be an effetve plannng and ontrol tool for deson makng and evaluaton. The assgnment of quay ranes to berthed vessels and ther deployment along the berth represent rual desons that ould be well supported by nteger programmng (IP) models. Usually, these models are used as standalone tools. Startng from a dsrete-event smulator for the berth plannng, prevously developed for a real marme ontaner termnal, we propose two IP models that an be emboded whn the smulator to verfy whether or not the weekly plan of the berth shedule produed by the smulator self s feasble wh respet to the avalable quay ranes. If not, the manager would be asked to repeat the berth plannng step by rerunnng smulaton. The goodness of the proposed IP formulatons s establshed by a numeral omparson aganst a test ase taken from lerature. Keywords: shedulng problem, quay ranes, marme ontaner termnals, dsrete-event smulaton,. INTRODUCTION A marme ontaner termnal s a omplex set of physal and human resoures organzed around a set of logst proesses. In a pure transhpment termnal, logst proesses are defned around the pure store and forward funton of the termnal. Ths asks for the respet of hgh standards n the qualy of serve provded to shppng ompanes, otherwse, the termnal ould lose some of these ompanes to ompeton. Thus the nternal organzaton should be arefully optmzed. Ve versa, n a dfferent termnal devoted to an mport/export funton, possbly onneted to a dry port (Roso 007), the logst operatons and nfrastrutures for optmally supportng nland/outland transportaton by dfferent modal hoes should also be arefully onsdered (Parola and Shomahen 00) to mprove the reasons of ompetveness. Here we fous on a real termnal of pure transhpment: the ontaner termnal n Goa Tauro, Italy, whh s suated along the major marme routes from the far-east port soures n Asa to the ports of Northern Europe and other western destnatons. Our prelmnary onsderaton when addressng the modellng efforts referred to ths system, s that the major operatonal atves and resoures should be managed by onsderng that they belong to multple, nteratng logst proesses (e.g. vessel arrval and vessel dsharge/loadng proesses) where some lmed resoures should be adequately shared. Ths fat s ral for a ost-effetve management of the system and the hoe of the modellng approah for performane evaluaton and system optmzaton. Termnal ompetveness an be mproved by optmzng the nternal organzaton through the ntroduton of deson support systems n resoure alloaton and shedulng of logst resoures and operatons (Vs and de Koster 00, Steenken et al. 00), wh the objetve of dereasng the operatng osts and serve tmes. Several papers fous on IP models for spef proesses n port logsts (Park and Km 00, Ambrosno et al. 00, Legato and Monao 00, Cordeau et al. 00). Besdes, other papers based on smulaton, suh as (Yun and Cho 999, Legato and Mazza 00, Bell et al. 006, Canonao et al. 008) pont out the opportuny of evaluatng starvaton and ongeston phenomena ourrng at those major resoures on whh both the termnal produtvy and response tme strongly depend. Reently, a smulator (Canonao et al. 007) has been developed and tuned for the ontaner termnal loated at the port of Goa Tauro. The tool was manly requested to perform a senaro analyss meant to hghlght the possbly that the entrane hannel to the port ould beome the termnal bottlenek, as the hannel self beame progressvely more shared by dfferent flows of marme traff enterng the port of Goa Tauro. Currently, the same tool s beng refned to support the formulaton of the so alled weekly plan under the programmed flow of ontanershp arrvals,

2 provded that the statstal analyss of delays upon arrvals s ontnuously updated takng nto aount all the soures of unertanty of the arrval proess. In ths ontext, the estmaton of the vessel proessng tme (at berth) for dsharge/loadng operatons s reognzed as the seond key pont upon whh the effetveness of the whole plannng proess depends. The urrent release of the smulator asks the user to provde the so alled rane ntensy,.e. the average number of ranes that work, smultaneously, on the same vessel, as s fxed by formal agreement wh the shppng ompany to whh the same vessel belongs. Hene, a desonal problem arses for the ranes manager beause he should dynamally deploy the rght number of ral mounted quay ranes along the berth and assgn these ranes to the vessels that sueed at the varous berthng ponts, day by day, aordng to the weekly plan. The major onstrants onsst n respetng the vessels duetme of departure and shftng the ranes (on ral) along the quay-sde. The objetve to pursue s that of employng the mnmum number of quay ranes, whle maxmzng rane produtvy. In the language of Operatons Researh the above desonal problem may be referred as the quay rane deployment problem (QCDP) (Legato et al. 008). It s a omplex assgnment-shedulng problem that we takle by two separated IP-based formulatons. The frst s foused on the assgnment phase and produes the optmal number of ranes that must be assgned to eah berthed vessel on the bass of a one-hour tme-slot, under the guarantee that due-tmes of departure are respeted. In the seond IP formulaton, the umulatve number of ranes returned by the frst model s deployed over all the vessels prevously berthed, eah n ther own poson, n order to establsh whh ranes should serve any gven vessel on berth and mnmze the number of rane shfts between adjaent vessels. The paper s organzed as follows. In the next seton some neessary detals on the logst proesses of nterest are gven. Afterwards, the fous s on the QCDP and on the mathematal models appled whn the two-phase approah. Fnally, some omputatonal results are presented.. LOGISTICS AND DECISION PROBLEMS The ontaner termnal at the port of Goa Tauro s a logst platform of pure transshpment haraterzed by a relatvely large roadstead where nomng ontanershps have to stop and wa for a plot boat, before they are allowed to seze the entrane hannel for some mnutes (0 to ) and reah ther assgned berth poson. Berthng posons are all sequened on the unque avalable quay, whh amounts to,00 meters and bears dfferent levels of water depth. A sgnfant number of ral-mounted gantry ranes (RMGCs) are avalable along the quay, to allow for a sgnfant degree of parallelsm under a hgh dsharge/loadng rate of serve offered to berthed vessels. A fleet of several dozens of straddle arrers (SCs) are avalable to transfer ontaners between the berth and the yard and pk-up/delver ontaners from/to seleted storage posons reahed whn a very regular layout based on bloks. Eah yard blok s dvded nto approxmately 6 lnes of slots organzed on ters, therefore the average blok apay s about 00 TEUs. Contanershp entrane at the termnal s planned on the bass of s expeted tme of arrval (ETA), but depends on the followng requrements: ) formal ondons (e.g., ontratual agreements between the vessel s shppng lne and the port of all for the use of port fales), that ask for a prory poly when managng the port entrane queue; ) operatonal settngs (.e., plot/tug avalably, berth spae assgnment). If requrements are met, the vessel s maneuvered nto s berth slot by one or two plot tugs; otherwse must wa n the roadstead. Ths s the arrval of the so-alled vessel proess. Vessels are of two types: mother vessels and feeders. The frst one s a large ontaner shp (whose apay ranges between,000 and,000 TEUs) that overs transoean routes (hub-to-hub onnetons). Feeders are smaller shps that over short and mddle routes. They are wdely used to onnet the spokes to the transshpment hub (and ve versa). One a vessel s berthed, operatons for ontaner dsharge/loadng an be nated only f mehanal (and human) resoures are alloated; f not, the shp was n s berth poson untl resoure assgnment takes plae. Dsharge/loadng operatons are performed by RMGCs plaed along the berth: one or multple ranes move ontaners between the shp and the quay area. The maxmum number of quay ranes that may be assgned to eah vessel s restrted by ) the total number of ranes n the quay and ) the maxmum number of ranes allowed for eah vessel, due to physal (.e. the length of the vessel) and logal onstrants (.e. nterferene between ranes). Consderng the span of the ranes (approxmately 0 m) and the horzontal spae neessary to stak and transfer the nomng/outgong ontaners of a vessel, the maxmum number of ranes allowed for the longest vessel s usually (ths number s proportonally dereased for shorter vessels). When multple ranes are assgned to the same shp, rane nterferene has to be avoded and a omplex shedulng problem s requred to manage the relatonshps (preedene and mutual exluson) exstng among the holds of the same vessel. Consderng that the serve rate of an RMGC s 8 TEUs/hour, the performane of the dsharge/loadng proess hghly depends on the avalably of ths type of rane and the related turnover speed. Therefore, the best deployment of these resoures affets the overall ompleton tme of eah vessel... The Quay Crane Deployment Problem An IP formulaton of the quay rane deployment problem together the berth alloaton problem (BAP) has been suessfully dsussed by Park and Km (op ). In real lfe, the QCDP arses as follows.

3 The plannng offe of the termnal operatng ompany onstruts a weekly berth shedule, whh ontans the berthng poson and tme wndow for eah nomng vessel (ths beng the soluton to the so-alled berth shedulng problem). A tme wndow shows the expeted tme of berthng and un-berthng for a sngle vessel; tme wndows are onstruted usng the ETA (Expeted Tme of Arrval) and PTD (Promsed Tme of Departure) of eah vessel (a penalty ost must be sustaned f the departure of a vessel ours later than s prevously ommted PTD). Fgure shows an example of a berth shedule, where the berth tme and spae are partoned nto x grd squares ( onehour tme-slots). assgned when operatons starts. The maxmum number of ranes that an be smultaneously assgned to a vessel s lmed by vessel length. Ve versa, the mnmum number of ranes to be assgned (usually for mother vessels) depends on the ontrat terms between the termnal operatng ompany and the vessel s shppng ompany. By default, when operatons start on a vessel, mostly all of the tme-slots related to that vessel reeve one rane.. Quay ranes are RMGCs, so non-rossng onstrants must be guaranteed. Furthermore, ranes are never unavalable. tme-slot The soluton approah we propose here to the QCDP follows a prevous promsng researh study by Legato, Gullì and Trunfo (008). It s deomposed nto two phases, as shown n Fgure. Vessel F Berth shedule Vessel E Vessel D PHASE I: Crane Assgnment Vessel C Number of ranes assgned to eah vessel at eah tme-slot Vessel A Vessel B Fgure : An Example of Berth Shedule Presented by Park and Km The berth shedule s used to assgn the RMG quay ranes to the nomng vessels on a daly bass. The double goal s to ) mnmze the number of quay ranes to be employed and ) maxmze ther utlzaton, under the onstrant of ompletng the dsharge/loadng operatons, for eah vessel, whn the related expeted tme of un-berthng, The QCDP s solved under the followng assumptons.. Eah vessel has a tme wndow; the lower bound of the tme wndow s the vessel s expeted tme of berthng, whle the upper bound s the vessel s expeted tme of unberthng.. Eah vessel has a total number of TEUs to be handled whn s tme wndow: ths number s related to the ontaner dsharge/loadng moves requred by the vessel.. Eah vessel has a maxmum and mnmum number of ranes that an and must be PHASE II: Crane Deployment Deployment of RMGCs Fgure : The Shema of the Two-Phase Approah to the QCDP In the frst phase (rane assgnment phase), we solve an IP mathematal model usng CPLEX (ILOG 999) to dentfy the optmal number of ranes that must be assgned to eah vessel at eah tme-slot. Thus, the model s able to dentfy exatly when the dsharge/loadng operatons start and end whn the vessel s tme-wndow. In lerature, ths problem s known as the quay rane assgnment problem (QCAP) and s usually studed together wh the BAP as n (Mesel and Berwrth 006). In the seond phase, another IP model s used to deploy the ranes along the quay, wh the am of mathng the prevously dentfed vessel-rane assgnment n order to ) respet the non-rossng onstrants, and ) mnmze the number of rane shfts from one vessel to another. Wh respet to the two phases, the frst IP model s the well-known QCAP, whle the seond s alled the quay rane deployment problem; neverthless, one ould gve a mathematal model whh ombnes both of the prevous IP models and stll refers to a QCDP. 6

4 .. IP Model for the Crane Assgnment Phase The followng notatons wll be used for the formulaton of the QCAP: mn T : the set of tme-slots, wh T = N Ω : the set of vessels C : the set of quay ranes, wh C = M s : the serve rate for rane, expressed n TEUs per tme-slot m : the number of moves for vessel etb : the berthng tme for vessel,.e. the tme-slot startng from whh vessel s ready for the frst lft, where: etb N etu + etu : the un-berthng tme of vessel ; thus s the last tme-slot durng whh vessel s avalable for operatons, where: etb etu N mn : the mnmum number of ranes that must be assgned to vessel when operaton starts max : the maxmum number of ranes that an be assgned to vessel. We ntrodue the followng desonal varables: V : the maxmum number of ranes used to performs vessel operatons :, f rane works on vessel at tmeslot t, 0 otherwse φ :, f vessel s proessed at tme-slot t, 0 otherwse :, f operatons for vessel start at tme-slot t, 0 otherwse. η :, f operatons for vessel have not been ompleted at tme-slot t, 0 otherwse ρ : s the dfferene between the number of ranes assgned at tme-slot t and those assgned at the prevous tmeslot (t-). The QCAP an be formulated as follows: N V + s.to ( t+) η ( t+) η = φ etu Ω t= etb etu φ + ρ () Ω t= etb + Ω, t = etb etu η Ω, t = etb etu + + Ω, t = etb etu etu s = m Ω C t = etb () () () () etb C t = n C t = etu + Ω C C C = 0 Ω (6) = 0 Ω (7) max φ mn φ C ( t ) = ρ C Ω V C, t T (8) Ω, t = etb etu (9) Ω, t = etb etu (0) Ω, t = etb + etu () t T () V 0, Ν () ρ Ν Ω, t T () { 0,} Ω, C () φ,, η 0, Ω, t T (6) { } The objetve funton of the prevous mathematal model ams to the mnmzaton of ) the number of quay ranes employed n the plannng horzon, ) the overall number of tme-slots requred to perform vessel dsharge/loadng operatons, and ) the rane bak and forth movements (mplly aounted for by the ρ fator, to be lnearzed as usual). Clearly, funton () appears as the sum of nhomogeneous terms and must be suably adjusted for numeral experments. Constrants ()-() ensure that for every vessel, one dsharge/loadng operatons start, the operatons must be performed whout nterrupton untl they are ompleted (the vessel operatons annot be preempted). Constrants () spefy that for eah vessel, the dsharge/loadng operatons must be exeuted and ompleted whn the vessel tme-wndow. Constrants (6) and (7) ensure that no ranes an be assgned to a vessel before s etb and after s etu. Constrants (8) guarantee that every rane an be assgned to only one vessel at eah tme-slot. Constrants (9) and (0) ensure that the number of ranes assgned to a vessel durng s operatons tme s between a mnmum (.e., due to ontratual agreement) and a maxmum (.e., due to the vessel length). Constrants () evaluate the value of varables ρ. Constrants () guarantee that, for eah tme-slot t, the number of assgned ranes result not greater than the number of avalable ranes. Constrants ()-(6) are the bas onstrants on the deson varables. The IP model defned above s a refnement of the QCAP developed by Legato, Gullì and Trunfo (op )... IP Model for the Crane Deployment Phase As stated before, the soluton of the QCAP provdes the number of ranes that must be assgned n order to 7

5 omplete the operatons n tme. Ths data s used n the followng to deploy, for eah tme-slot, the RMG quay ranes. The deployment follows the rera of nonrossng ranes and rane shftng reduton between vessels durng dfferent tme-slots. In the followng we ntrodue the notatons that wll be used for the formulaton of the quay rane deployment problem (QCDP): T : the set of tme-slots, wh T = N Ω : the set of vessels C : the set of quay ranes, wh C = M a t : the number of ranes assgned to the vessels berthed at tme-slot t a : the number of ranes assgned to vessel at tme-slot t b : the number of ranes assgned to the vessels berthed at tme-slot t before (from the left-sde of the berth) vessel a : the number of ranes assgned to the vessels berthed at tme-slot t after (from the left-sde of the berth) vessel w : the tme-wndow of vessel ; ths tmewndow s omputed from the frst tme-slot n whh dsharge/loadng operatons start to the tme-slot n whh operatons end. Moreover, the followng desonal varables are ntrodued: φ :, f rane s assgned to vessel at tme-slot t, 0 otherwse :, f rane s after (or s self) the leftmost rane assgned to vessel at tme- slot t η :, f rane s before (or s self) the rght-most rane assgned to vessel at tme-slot t f : s the left-most rane assgned to vessel at tme-slot t l : s the rght-most rane assgned to vessel at tme-slot t sf : s the sum over tme of all the leftmost rane ndexes of vessel sl : s the sum over tme of all the rghtmost rane ndexes of vessel. The QCDP an be formulated as follows: mn sf ( ) sl M a t f + l t T Ω w w (7) s.to φ = a Ω, t T (8) C η + + η Ω, = M Ω, = M (9) (0) + η = φ + C C C C t T M b η M a + η l l f t T f = M + = 0 sf = sl = 0 ( M + ) w Ω, C () Ω, t T () Ω, t T () Ω, t T () Ω, t T () Ω (6) Ω (7) Ω, φ,, η { 0, } (8) C f l, sf, sl 0, Ν Ω, t T (9), j j In ths IP mathematal model, we am to dentfy the RMG quay ranes that must proess the berthed vessels at eah tme-slot, wh the goal of mnmzng the number of ranes shftng from one vessel to another (.e., f possble, the model tres to assgn to eah vessel always the same quay ranes,). Constrants (8) spefy that exatly the desred number of quay ranes s assgned to every vessel at eah tme-slot. Constrants (9)-() ensure that RMG quay ranes are assgned wh respet to non-rossng onstrants. Constrants () fore the assgnment of quay ranes to vessel at tme-slot t, one the preedng vessels along the berth have reeved the expeted amount of quay ranes. Lkewse, onstrants () ensure that rane assgnment to vessel at tme-slot t s done oherently wh the assgnment of the onsdered ranes to the vessels that follows along the berth. Constrants () dentfy the frst rane from the left-sde of the quay (.e., the left-most rane) that must perform dsharge/loadng operatons on vessel at tme-slot t; otherwse, onstrants () assgn the last rane from the left-sde of the quay (.e., the rght-most rane) that must perform dsharge/loadng operatons on the same vessel and at the same tme-slot. Lkewse, onstrants (6) and (7) extend onstrants () and (), respetvely, over all the tme-slots that onstute the vessel tme-wndow. Constrants (8)-(9) are the bas onstrants on the deson varables.. NUMERICAL EXPERIMENTS Numeral results obtaned by the exat soluton of the two IP formulatons proposed n prevous seton are ompared aganst the results reported by Park and Km (00). In Fgure we repeat the optmal assgnment reported n the paper by Park and Km based on the berth shedule prevously shown n Fgure. For eah vessel, rnged numbers dept the quay ranes assgned 8

6 to eah vessel. As s possble to see, the QCDP solved by Park and Km makes use of 9 ranes to omplete all the operatons n tme. In ths ase study, the mnmum number of ranes that must be assgned to the vessels durng operatons s one, whle the maxmum number of ranes that an be assgned to a spef vessel s equal to the number of ouped s (eah orrespondng to 0 meters). tme-slot Vessel F Vessel 6C Vessel A Vessel 6 E Vessel 8 9 D Vessel 7 8 B Fgure : The Optmal Deployment Found by the Park and Km Methodology The frst step of our approah produes the assgnment depted n Fgure. In ths berth shedule, the optmal value of a, for eah ouple of vessel and tme-slot t, s reported whn eah orrespondng retangle. As s easy to reognze, our mathematal model flls-n a berth shedule whle mnmzng the overall number of ranes that must be used to proess all of the vessels. In fat, the frst phase of our approah produed an assgnment of 7 quay ranes aganst the 9 quay ranes found by Park and Km. Moreover, n our soluton, one operatons start, no operaton dsontnuy an our for any vessel: ths s a prmary ontratual agreement requested to the termnal operatng ompany by shppng ompanes, along wh the mnmum number of ranes to be assgned and the respet of the bounds on operaton ompleton tme. As a result of the seond phase of our methodology, we propose the quay rane deployment shown n fgure. The mprovement obtaned wh the approah proposed n ths paper s not only due to the mnmzaton of the atvated ranes. In fat, n three ases ) we obtaned a reduton of the vessel overall ompleton tme and ) we mproved the average rane utlzaton (0.69 vs. 0.87). Vessel F Vessel E Vessel D Vessel C Vessel A Fgure : The Frst Phase Output of our Methodology tme-slot tme-slot Fgure : The Fnal Output by our Methodology. CONCLUSION We have reported on the possbly of mprovng the benef of usng a smulator when managng the logst proess of vessel berthng and dsharge/loadng at a marme ontaner termnal. Combnng dsrete-event smulaton wh nteger programmng models results n a very powerful tool, where the soluton of assgnment and shedulng problems plays a rual role. We have proposed a pratal soluton to the problem of guaranteeng the respet of the planned tme wndows (berthng unberthng) but also pursung the objetve of mnmzng quay rane dle tme. The novelty s that we avod handlng a unque, unmanageable formulaton and, furthermore, that for pratal applatons n real lfe, we may use a berth shedule produed by a 9

7 smulator,.e. n a more realst modellng envronment where operaton delays and unpredtable events may our. Thus we may ntegrate the IP models wh ther respetve soluton algorhms n a new release of the avalable dsrete-event smulator to support run-tme rane assgnment usng a berth shedule. A metaheursts based approah wll be learly pursued to develop soluton algorhms for real nstanes; ths wll also enable smulaton based optmzaton features whn the above dsrete-event smulator. REFERENCES Ambrosno, D., Somahen, A., Tanfan, E., 00. Stowng a ontanershp: the master bay plan problem. Transport Researh part A, 8, Bell, M., Boulmakoul, A., Rda, M., 006. Objet orented model for ontaner termnal dstrbuted smulaton. European Journal of Operatons Researh, 7, 7 7. Canonao, P., Legato, P., Mazza, R.M., 007. An Integrated Smulaton Model for Channel Contenton and Berth Management at a Marme Contaner Termnal. In Proeedngs of the st European Conferene on Modellng and Smulaton, -6. Prague, Czeh Republ. Canonao, P., Legato, P., Mazza, R.M., Musmanno, R., 008. A queung network model for management of berth rane operatons. Computers & Operatons Researh, (8), 6. Cordeau, J.F., Laporte, G., Legato, P., Moa, L., 00. Models and tabu searh heursts for the berth alloaton problem. Transportaton Sene, 9(), 6 8. ILOG CPLEX 6.. Mountan Vew, CA. Legato, P., Mazza, R.M., 00. Berth plannng and resoures optmsaton at a ontaner termnal va dsrete event smulaton. European Journal of Operatonal Researh,, 7 7. Legato, P., Monao, M.F., 00. Human resoures management at a marne ontaner termnal. European Journal of Operatonal Researh, 6(), Legato, P., Gullì, D., Trunfo, R., 008. The quay rane deployment problem at a marme ontaner termnal. Proeedngs of the th European Conferene on Modellng and Smulaton, -9, June -6. Nosa (Cyprus). Mesel, F., Berwrth, C., 006. Integraton of berth alloaton and rane assgnment to mprove the resoure utlzaton at a seaport ontaner termnal. Operatons Researh Proeedngs 00, 0-0. Park, Y.-M., Km, K.H., 00. A shedulng method for berth and quay ranes. OR Spetrum,,. Parola, F., Somahen, A., 00. Intermodal ontaner flows n a port system network: analyss of possble growths va smulaton models. Internatonal Journal of Produton Eonoms, 97, Roso, V., 007. Emergene and sgnfane of dry ports. Proeedngs of the World Conferene on Transport Researh (CD-ROM). June -8, Berkeley (Calforna, USA). Steenken, D., Voss, S., Stahlbok, R., 00. Contaner termnal operaton and operatons researh - a Classfaton and Lerature Revew. OR Spetrum, 6, 9. Yun, W.Y., Cho, Y.S., 999. A smulaton model for ontaner-termnal operaton analyss usng an objet-orented approah. Internatonal Journal of Produton Eonoms, 9, -0. Vs, I.F.A., De Koster., R., 00. Transshpment of ontaners at a ontaner termnal: An overvew. European Journal of Operatonal Researh, 7(), 6. AUTHORS BIOGRAPHIES PASQUALE LEGATO s an Assstant Professor of Operatons Researh at the Faulty of Engneerng (Unversy of Calabra), where he teahes ourses on smulaton for system performane evaluaton. He has publshed on queung network models for job shop and logst systems, as well as on nteger programmng models. He has been nvolved n several natonal and nternatonal appled researh projets and s servng as revewer for some nternatonal journals. Hs urrent researh atves are on the development and analyss of queung network models for logst systems, dsrete-event smulaton and the ntegraton of smulaton output analyss tehnques wh ombnatoral optmzaton algorhms for real lfe applatons n transportaton and logsts. Hs home-page s DANIEL GULLÌ reeved a Laurea degree (um laude) n Automat Control Engneerng from the Unversy of Calabra, Rende, Italy, n 00. He s devoted to researh n numeral smulaton at the Center for Hgh-Performane Computng and Computatonal Engneerng (CESIC) n NEC Italy. Hs urrent researh nterests nlude dsrete-event smulaton models for logst systems and parallel smulaton. ROBERTO TRUNFIO reeved a Laurea degree (um laude) n Management Engneerng from the Unversy of Calabra, Rende, Italy, n 00, and s urrently pursung a Ph.D. degree n Operatons Researh from the same unversy. Moreover, he s a logsts engneer at the Center for Hgh-Performane Computng and Computatonal Engneerng (CESIC) n NEC Italy. Hs urrent researh nterests nlude dsrete-event smulaton models and smulaton-based optmzaton of logst systems and parallel smulaton. Hs home-page s 0