ࡱ> egbcd5@bjbj22G XXoA    )))8*46+ $,~----!01t2<$۫R-ا =/@!0==ا. . --UqVGVGVG=r. l- -VG=VG"VGxGv4 , Zz-, pHF:)BD2y(0ZyHDPZz ~ h" h. . rz# j|780VG9:W2o56اا ).G( )Anita Gudelj, M. Sc. University of Split Faculty of Maritime Studies  Split CROATIA anita@pfst.hr Stjepan Vida i, D. Sc. Faculty of Organization and Informatics, Vara~din CROATIA Scheduling Model of an Automated Guided Vehicle System in Seaports Introduction In recent years, the explosive in the volumes of freight has resulted in heavier workloads at seaports. At the same time the number of container terminals worldwide increased considerably and they have become an important component of logistic networks. Their major function is to serve as multi-modal interfaces between sea and land transport. To satisfy customer demand, it is paramount that ships are unloaded and loaded promptly at the port. The above consideration necessitates the implementation advanced technologies and development of highly sophisticated container transportation systems, which accommodate the increasing number of container ships and efficient movement within the container terminal. A major challenge in port management is thus to reduce the turnaround time of the container ships. One direction for improving the overall productivity of a container terminal and to reduce the berthing times of vessels is to enhance the degree of automation of the handling and transportation equipment. Hence, manually operated cranes have been replaced by automated ones and Automated Guided Vehicles (AGVs) are used instead of manually driven carts. In this paper, we will focus on the challenges posed by the last method, specifically improving the performance of the horizontal transportation system using an AGV system. AGVs have been used in seaports for container handling that greatly improves the overall operational efficiency. The advantages of implementations such vehicles are as follows: they would save the port terminal space, they would be more cost effective and they would increase the efficiency. Container terminal logistics has been a prominent field of research and the term Automated Guided Vehicle Systems has become a keyword in publications. As one of the enabling technologies, scheduling of AGVs has attracted considerable attention. Many various kinds of model of container terminal and various techniques to solve its scheduling problem have been proposed. The former contains, e.g., network model or mathematical programming model, whereas the latter includes simulation, mathematical programming and heuristic algorithm. Literature is available to support these ideas. A comprehensive literature survey has recently been given by Steenken et al.  REF _Ref154975541 \r \h [10]. Important optimization problems include berth planning (see Guan and Cheung  REF _Ref154975827 \r \h [5], Imai et al. REF _Ref154975904 \r \h [7], Dai et al. REF _Ref154981716 \r \h [2]), quay crane planning (see Daganzo  REF _Ref155048309 \r \h  \* MERGEFORMAT [1]). Several papers have studied specific optimization problems arising in container terminals with automated equipment. Automated guided vehicles (AGVs) have been studied by Vis  REF _Ref156784699 \r \h [11]. A general model for scheduling equipment such as AGVs has been proposed by Hartmann  REF _Ref156164245 \r \h [6]. In this paper, we focus on highly automated terminals which employ AGVs. 1.1. Background of container terminal operation The process of unloading and loading a ship at an automated container terminal can be described as follows. When a vessel arrives at the container terminal for transshipment, there are two types of operations that need to be carried out. These are to discharge containers from and/or to load containers onto the vessel. We consider an automated container terminal equipped with special quay cranes (also called gantry or container cranes), Automated Guided Vehicles (AGVs) which are used for the transportation of containers and Automated Stacking Cranes (ASCs) for the handling of containers in the stack. In this paper, we only address the unloading process. Usually, quay cranes (QCs) first unload a ship and thereafter load containers on the ship. Unloading and loading operations are only mixed during a very short time period. In addition, it has already been determined at which position the vessel is berthed and which quay cranes will be working on the vessel. The unloading sequence of the containers is known in advance for each vessel. At the same time, the final destination in the storage area is determined for each container and the AGVs transport the containers to storage locations in the yard area where they are dismounted from the AGVs by yard cranes. These automated guided vehicles transport the containers along a predefined path, usually a loop layout, to the stack. Storage area consists of a number of blocks where containers can be stored for a certain period. The retrieved containers are internally transported to other transportation modes, such as barges, trucks or trains. Outgoing containers are loaded onto the ship after the majority of incoming containers have been discharged. The outgoing containers from the yard are mounted onto the AGVs using yard cranes. These containers are then carried by AGVs from the yard to the quay area where they are loaded onto the ship by a quay crane. Figure 1  REF _Ref156165932 \r \h [11] illustrates a layout of a port container terminal, which was used in numerical experiment of this study. The input data are obtained from the report of Celen et al. (1997)  REF _Ref156165932 \r \h [11] for the port of Rotterdam. The QCs and ASCs are connected by a multiple lane loop layout. This loop is a fixed sequence of pick-up and delivery points at QCs and ASCs. AGVs travel over these fixed guidepaths to handle all transportation requests. During the unloading process AGVs travel full from a QC to an ASC and empty from an ASC to a QC. To avoid the common problems of a loop layout, in which vehicles can not pass each other, container terminals can use the concept of multiple lanes. As can be seen, vehicles drive counterclockwise from the parking area A, where they receive a transportation request, from a certain QC. At arrow B, the vehicle is dispatched to an ASC.  Figure  SEQ Figure \* ARABIC 1: Example of processes and layout of an automated container terminal. The particular difficulty of AGV dispatching in a highly automated container terminal is that AGV pick-up and drop-off times for each container have to coincide with the schedules of the quay and stacking cranes to avoid idle times of this equipment and to guarantee short berthing of the vessels. The aim of AGV scheduling is to dispatch a set of AGVs to achieve the goals for a batch of pickup/drop-off (or P/D for short) jobs under certain constraints such as deadlines, priority, etc. In this paper, we shall present a Petri net model and a mathematical model of the AGV scheduling problem. The token movement behavior in a Petri Net model can make a balanced dispatching schedule of AGVs through the marking planning. That is, AGVs are represented by tokens and the planned marking in the places governs the dispatching of the AGVs in a way that the AGV supplies jobs for cranes and makes the cranes as busy as possible. Then the proposed GA as a solving methodology that constructs an AGV dispatch schedule is introduced. Petri net model of container terminal operation Petri Nets is a graphical model of computation introduced by C.A. Petri in his PhD "Communication with Automata'' (1962). Discrete-event dynamic systems are probably the most appropriate formalism to describe container terminals. In particular, PN can systematically represent all the terminal activities, the shared resources, the synchronized or parallelize process, etc  REF _Ref155062565 \r \h [8]. Now we will shortly introduce the basic definitions and theory of Petri Nets. A Petri Net is a particular case of directed graph with an initial state called the initial marking. There are two kinds of nodes: places and transitions. Arcs are either from a place to a transition or a transition to a place. Therefore Petri Nets are formed by a four-tuple N = (P, T, A, M0). In modeling, places represent conditions and transitions represent events. Places in set P and transitions in set T are linked by arcs in set A to represent how the system state changes, as tokens, representing resource-units or containers in process, flow through the net. More specifically, places are of two different types: the first one is able to model the execution of activities; the second one is used to model an available resource like ships, loading/unloading station... Each place is depicted by a circle. Note that each resource ri has a finite capacity C(ri) (number of units) to host containers. If a marking assigns a place p with a nonnegative integer k we say that "p is marked with k tokens". A transition (event) has a certain number of input an output places representing the preconditions and postconditions of the event. The presence of a token in a place is interpreted as holding the truth condition related to that place. In other words, k tokens are put in a place to indicate that k data items or resources are available. Transitions are graphically represented by bars and model events changing the state. Each state value is defined by the function, which assigns an integer non-negative number to any place in the net: M : P ({0,1,2,}, where M(pi) gives the current number of tokens in pi (P. An unmarked place doesnt contain tokens and a marked place contains as many tokens as M(pi). M0:P({0,1,2,} is the initial marking. Arcs may be distinguished between input arcs from places to transitions, and output arcs from transitions to places, and all are drawn as arrows. They show us how places and transitions are connected. Namely, a transition t has a certain number of input (and output) places which are the pre-conditions (post-conditions) associated with t. The pre-conditions enable transition t, while the post-conditions are defined after the occurrence of the event modeled by t. So, the Petri Net states (or markings) do change according to the following basic rules: enabling rule: a transition is enabled if each of its input places is marked, but an enabled transition may or may not fire (depending on whether or not the event actually takes place); firing rule: a firing of an enabled transition consumes a token from each input place and produces a token for each output place. Figure 2 illustrates a Petri Net model of the control logic for a loading/unloading container by cranes and transporting containers by AGVs. Model represents the transportation of a container from a pick-up location to a delivery location. A workstation (or an Input station) is located at a fixed node P10 and is visited there by crane to have a pickup operation k, k=1,2,...,n (n=10) through T1. An AGV has to transport the container to its staging place. When this happens, starting processing of transportation is enabled (transition T2 fires).  Figure  SEQ Figure \* ARABIC 2: A Petri net model of an AGV system During transportation, a token resides in P3. At the end of the transportation, transition T3 fires, and the container is unload from AGV by ACS crane (transition T13 fires). AGV becomes available, as marked by the token in P18. AGV has to travel empty towards the place where the part requesting transport is located (transition T4 fires) and then starts transporting next container (the token returns to place P7). If AGV is not assigned for new job (transition T5 fires), it has to wait in place P8 for a job. When this happens, the AGV is bound to travel empty again. The quay crane will eventually wait in place P1 for the AGV to be available, i.e. for a token to be in place P7. Advantages and disadvantages of Petri nets The advantage of Petri nets over many other graphical modeling tools is that it has a mathematical formalism that makes the dynamic behavior of the underlying system well-defined and amenable to theoretical analysis using results from e.g. linear algebra and graph theory. Petri nets have some drawbacks however. First of all, even if places and transitions are labeled with names of the corresponding states and events, a reader must learn Petri net basics before he can understand the model. Secondly, according to elementary notations, even simple systems can give rise to very complex Petri nets, defined by a lot of places, transitions and arcs. Petri nets tend to become graphically very muddled for all but small examples. Typically, the number of Petri net states is combinatorial exploding. Then, the Petri net models are not easy to be implemented. Description of the problem We consider the problem of assigning jobs to AGVs. Each job corresponds to the transportation of a container from a pick-up location to a delivery location. An AGV can be assigned one job at a time. After completing a job, an AGV can start another job. From the perspective of the scheduling domain, the following assumptions are introduced in this study: Every AGV serves more than one QC. That is, any one AGV is not dedicated to one QC. All the AGVs are the same in their functions. The queuing time of AGVs are not considered. The primary focus of this paper is the discussion of ideas to reduce the time in port of container vessels. In this regard, we concentrate on the contemplation of the Waterside Transshipment Process, in particular, on the container movements to and from the berth area, performed by AGVs. 3.1. Mathematical formulation For a more formal definition, let J be the set of the jobs to be assigned, and let V and K be the set of AGVs and the set of QC, respectively. Moreover, let ( be travel cost per unit time of an AGV and ( be penalty cost per unit time for the delay in the completion time. It is assumed that (<<( and m0 and mF equal to . Mathematically, the problem is formulated as follows:  (1) subject to , for (k(K', i =1, (, mk (2) , for (l(K'', j =1, (, ml (3) , for (k(K', l(K'', i =1, (, mk, j =1, (, ml (4) , for (k(K', i =1, (, mk-1 (5) , for (k(K', i =1, (, mk-1 (6) , for (k(K', l(K'', i =1, (, mk, j =1, (, ml (7) where yik The event time of the event eik that corresponds to the beginning of a pickup (or release) of a container from an AGV for a task related to the ith operation of QC k sik The earliest possible event time (, for (i(V) mk The number of task for QC k During iterative procedure of this algorithm, it is attempted to minimize the total travel time of AGVa, which is the first term of objective functions (1), and to minimize sum of tardiness travel time. Genetic Algorithms Genetic Algorithms (GAs) are adaptive search and optimization algorithms based on the mechanics of natural selection and natural genetics  REF _Ref150642034 \r \h [3]. GA is based on the principles of survival of the fittest, where weak individuals die before reproducing, while stronger ones survive and bear many offspring and breed children,. GA begins with a population of strings created randomly. The string is called a chromosome and each bit is called a gene. Each chromosome has a fitness value assigned to it based upon a fitness (objective) function. The fitness value determines the relative ability of the chromosome to survive over the generations. The population is then operated on by three main operators; reproduction, crossover and mutation to create a better population (see  REF _Ref156756315 \r \h [3]). The termination criteria are designed based on the available response time within which the solution should be obtained and/or the minimum satisfying performance level expected. If the termination criteria are not met, the new population is again produced by the above three genetic operators and evaluated. This procedure is continued and repeated until the termination criteria are met. 4.1 Application The number of AGVs required to minimize the unloading times of the ship is limited to Nagv vehicles due to the costs for operating as well as space on the terminal. Initially, we assume that the capacity of an AGV equals two twenty foot containers or one forty feet container. In our study, we assume a constant average time tg; g({1,2, ,G} for each of the G quay cranes allowing to define a sequence of jobs jg;i with fixed transshipment times where i( {1, ,ng } with ng being the number of jobs in the sequence. A job j denotes a container transport from one location to another one. The container movements (jobs) on the terminal are coded in a permutation vector (individual) with a job being a gene. The size of the population is a parameter of the algorithm and depends on various factors (e.g., the structure of the problem) and cannot be determined beforehand in general. The objective function (1) is used for the fitness of the individuals. An individual is a permutation vector containing the jobs with n being the number of jobs at all quay cranes. 871 62 3 4 5Agv1Agv2Agv3Agv4Figure  SEQ Figure \* ARABIC 3: Representation of an individual The solution vector is divided into Nagv segments of which each represents a certain number of jobs to fill a shift of T seconds for one AGV. Therefore, the solution vector implies the number of AGVs as well as the sequences for each of them, ck with k({1,2,Nagv}. In this study, we use nearest-vehicle-first QC-initiated dispatching rules (i.e. a free AGV at the smallest distance is dispatched to the QC needing an AGV). Figure 4 describes the calculation of the objective function value for a shift of length T.  Figure  SEQ Figure \* ARABIC 4: Pseudo-code for the objective function calculation The function getTime (si) calculates the time that an AGV needs to fulfill the job si. It is composed of the time to reach the starting position (pick up), the time for the transport of the container, and the waiting time that can occur if the AGV arrives before the expected time. For each container it is decided which size it has. If it is 40 feet container, the AGV needs to transport the container directly to the stack. In other case, 20 feet container, the AGV needs to wait for the next QC job, because during the unloading process AGVs travel full from a QC to the stack. Note, that the number of AGVs is increased whenever the sequence of jobs for the AGV exceeds T or the AGV waits for the next job and a quay crane Qsi is scheduled before its predecessor Qsi-1 (AGV transports the container along a predefined path) or the AGV needs to transport 40 feet container. In this paper, a one-point crossover operator is investigated. A repair function guarantees that new individuals are feasible, i.e., the uniqueness of a job (gene) in the solution is kept. The location l as the crossover point within one of the two individuals, s1 and s2, is selected randomly from a uniform distribution of the C-1 possibilities in a way that the sequences are not destroyed. The recombination is done as shown in Figure 5. s1871 62 3 4 5Agv1Agv2Agv3Agv4Agv4s22 34 7 8151 6Agv1Agv2Agv3Agv3Agv4s1871 62 51 6s22 34 7 813 4 5Figure  SEQ Figure \* ARABIC 5: Crossover operator Note, that the crossover is allowed to split segments in the second individual s2. The duplicate jobs in the offspring can be replaced either in the fragment f1= {s11, s21,, sl1} or in the fragment f2= {s1+11, sl+21, , sn1} by jobs that are missing in this individual. The repair mechanism selects one of the fragments with a probability of 50%. After that, with a probability of mutation pm = 1/n, the contents of two randomly selected locations k and l with k,l ( {1,,n} in s are exchanged such that sk ( sl and sl ( sk. The mutated individual replaces the original offspring. The creation of the next population is based on the selection of individuals from the current population and the replacement strategy. Ranking selection uses the absolute fitness values to compute a rank for each individual in the population. This rank determines the probability to be drawn as a source for the recombination operator to create new offspring for the next population. Last replacement generates the next population by refreshing the worst parents with a specified number of the best offspring if and only if these individuals (offspring) have a better fitness than the worst parents. The number of individuals determines the speed of improving the population and the ratio of convergence. Computational Results Initially, we assume that 50% of the containers have a length of 20 feet and the other 50% have a length of 40 feet. The speed of a full AGV equals 4 m/s and the speed of an empty AGV is 5.5 m/s. The weights of the objective function have been set to  = 0.9 and (= 0.1 which should be a reasonable choice in practice  REF _Ref156784699 \r \h [11]. GA parameters: Population size = 20 samples Crossover probability = 0.500 Mutation probability = 0.005 Termination criteria = 100 generations (or) a satisfactory predefined minimum value for the objective Function, whichever occurs first. The computation time for the genetic algorithms is ignored in this paper because we are mainly interested in the potential of these algorithms to improve given solutions. The first step in the generational loop is to create the initial population of jobs which implies the number of AGVs as well as the sequences for each of them(Table 1). The scheduls of job sequences The scheduls of AGVs sequences 2 3 1 4 5 6 7 8 Agv1 ( j2, j3; Agv2 ( j1; Agv3 ( j4, j5; Agv4 ( j6, j7; Agv5 ( j8 5 6 1 2 3 4 7 8 Agv1 ( j5, j6; Agv2 ( j1; Agv3 ( j2; Agv4 ( j3; Agv5 ( j4; Agv4(j7; Agv7 ( j8;      Min 2336. Mean 4749.12 Total 94982.4 Table  SEQ Table \* ARABIC 1: An initial population The GA iterates around the generational loop until Termination criteria is achieved and then terminates. The optimal solution of our problem is given in Table 2. The schedul of job sequences The schedul of AGVs sequences 5 7 1 2 4 3 6 8 Agv1 ( j5 j7; Agv2 ( j1 j2; Agv3 ( j4; Agv4 ( j3 j6; Agv5 ( j8 Min 1810.5. Mean 3453.88 Total 69077.6 Table  SEQ Table \* ARABIC 2: The optimal solution If the results of the first generation and the optimal solution would be compared, it can be concluded that: a) The minimum value of the fitness function has been reduced from 2336 to 1810.5 (about 22%). b) The average value of the fitness function has been reduced from 4749.12 to 3453.88 (37%). Conclusions In this paper, we have studied the problem of dispatching AGVs to containers. Our model consists of a Petri net model, an integer programming formulation and a genetic algorithm. The main contribution of this paper is the development of rule-based methods for the AGV dispatching problem in seaport container terminals and their evaluation. For future research, it will be useful to investigate how integrate simulation model (Petri net model) and optimization algorithm. This combined system can be the main component of a decision support system for terminal management, where the port managers can test and evaluate different strategies, comparing their own choices with the computer generated ones, then selecting the best suited for the current situation. REFERENCES Daganzo C. F., The crane scheduling problem. Transportation Research, 23B (3): 159-175, 1989. Dai J., Wuqin L., Rajeeva M., Chung-Piaw T., Berth Allocation Planning Optimization in Container Terminal, August 2003. Revised June 2004. Goldberg, D. E., Genetic Algorithms in Search, Optimization, and Machine Learning, Reading, Massachusetts: Addison-Wesley, 1989. Grefenstette J., Gopal R., Rosmaita B., Van Gucht D., Genetic Algorithms for the Traveling Salesman Problem. Proceedings of the First International Conference on Genetic Algorithms and their Applications, Lawrence Erlbaum Associates, New Jersey, 112-120, 1985. Guan Y., Cheung R. K., The berth allocation problem: Models and solution methods. OR Spectrum, 26:7592, 2004. Hartmann S., A general framework for scheduling equipment and manpower at container terminals, OR Spectrum, 26:5174, 2004. Imai A., Nishimura E., Papadimitriou S., The dynamic berth allocation problem for a container port. Transportation Research B, 35:401417, 2001. Murata T., Petri nets: properties, analysis, and applications, Proceedings of the IEEE, 77(4):541-580, April 1989. Qiu, L., Hsu W-J., Huang S. Y., Wang H., Scheduling and Routing Algorithms for AGVs: a Survey, International Journal of Production Research, 40(3), pp. 745-760, 2002. Steenken D., Vo S., Stahlbock R., Container terminal operations and operations research a classification and literature review, OR Spectrum, 26:349, 2004. Vis, I.F.A., Bakker M., Dispatching and layout rules at an automated container terminal,  HYPERLINK "ftp://zappa.ubvu.vu.nl/20050008.pdf" ftp://zappa.ubvu.vu.nl/20050008.pdf - last check of address: October, 2006. Zaffalon M, Rizzoli A.E., Gambardella LM, Mastrolilli M, Resource allocation and scheduling of operations in an intermodal terminal. In: ESS98, 10th European Simulation Symposium and Exhibition, Simulation in Industry, Nottingham, UK, pp. 520528, October, 1998. ftp://ftp.idsia.ch/pub/luca/papers/ess98.ps.gz last check of address: July 30, 2006. Anita Gudelj Stjepan Vida i Scheduling Model of an Automated Guided Vehicle System in Seaports SUMMARY Automated guided vehicles (AGVs) are now becoming popular mode of container transport in seaport terminals. These unmanned vehicles are used in terminal operations for transfer containers between ships and storage locations on the shore. In the past few decades, much research has been devoted to the technology of AGV systems and rapid progress has been witnessed. As one of the enabling technologies, scheduling of AGVs has attracted considerable attention. The aim of AGV scheduling is to dispatch a set of AGVs to improve the productivity of a system and reduce delay in a batch of pickup/drop-off jobs under certain constraints such as deadlines, priority, etc. The final goals are normally related to optimization of processing time or minimization the number of AGVs involved while maintaining the system throughput, or minimization the total travel time of all vehicles. To maintain competitive advantage and increase the efficiency of the container terminal it is necessary to determine the appropriate number of AGVs to deploy, and formulate good dispatching strategies for these AGVs. This paper first considers to introducing what AGV and then gives a Petri net model which represents the transportation of containers from pick-up locations to delivery locations. In addition to this proposed genetic algorithm as a solving methodology that constructs an AGV dispatch schedule is introduced. Keywords. AGV, AGV transportation system, scheduling, optimization Anita Gudelj Stjepan Vida i SA}ETAK Automatski upravljana vozila (AGV) danas postaju pristupa an na in prijevoza kontejnera u lu kim terminalima. Ova automatska vozila se rabe za prijevoz kontejnera izmeu brodova i skladiata na kopnu. 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mnogo se istra~ivala tehnologija AGV sustava i zabilje~en je nagli napredak. Kao jedna od moguih tehnologija, odreivanje rasporeda AGV privukla je zna ajnu pozornost znanstvenika. Cilj rasporeda automatski upravljanih vozila je rasporediti skup AGV kako bi se poboljala ukupna produktivnost sustava i smanjilo kanjenje u nizu poslova tipa pokupi-spusti, a pri tome se mogu uzeti u obzir zastoji, prioriteti Krajni ciljevi se odnose na optimalizaciju vremena obrade ili na minimalizaciju broja AGV koji su uklju eni i odr~avaju protok u sustavu ili na minimalizaciju ukupnog vremena putovanja svih vozila. Kako bi se odr~ala konkurentska prednost i pove ala efikasnost kontejnerskog terminala nu~no je odrediti odgovarajui broj AGV i odrediti dobre strategijeRlT67϶{qk^ZRRRjhL;TUhLxh"[hL;TCJmHsH hL;TCJhL;TCJmHsHh"[hL;TCJmHsHh"[hL;TCJhL;TjhL;T0JU hDlAh"J hYh"JhYh"J^JhYh"J5^Jh9yhP^JmHsHUh9yhN`^JmHsHh9yh"J^JmHsHh"Jh"J^JmHsHhP^JmHsH rasporeda za ta vozila. U ovom radu prvo se razmatra ato su AGV, a zatim je uporabom Petri mre~e prikazan model prijevoza kontejnera izmeu broda i skladiata na kopnu. Za odreivanje rasporeda AGV predlo~en je genetski algoritam kao metoda rjeaavanja. Klju ne rije i. AGV, AGV transportni sustav, raspored, optimalizacija  Celen, HP, Slegtenhorst, RJW, Nagel, A, Vos Burchart, R de, Berg, J, van den Evers, JJM, Lindeijer, DG, Dekker, R, Meersmans, PJM, Koster, MBM, de, Meer, R, van der, Carlebur, AFC, Nooijen, FJAM (1997) FAMAS NewCon. Concept TRAIL Report, Technical University of Delft and Erasmus University Rotterdam, The Netherlands      hDlAh"Jhh~FjhL;TUhL;T6&P 1h:p3. 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