Comparison of Equipment Sizing Models for Horizontal Transportation ofShipping Containers using Automated Straddle Carriers

B. Anvari

Research Associate, CTS, Department of Civil & Environmental Eng., Imperial College London, SW7 2BU

A. Ziakopoulos

Student, CTS, Department of Civil & Environmental Eng., Imperial College London, SW7 2BU

J. Morley

Principal, Morley Designs Ltd, Office 2, The School House, 16 Church Street, Alwalton, Peterborough, PE7 3UU

D. Pachakis

Principal Engineer, Royal HaskoningDHV, 2 Abbey Gardens, Great College Street, Westminster, London SW1P 3NL

P. AngeloudisLecturer, CTS, Department of Civil & Environmental Eng., Imperial College London, SW7 2BU

Abstract

Ports have become freight distribution hubs. Due to fierce regional and international competition, port op-erators seek ways to maximise terminal throughput and productivity. This paper uses queuing theory, PetriNetworks (PNs) and discrete event simulation to compare the impact on the productivity of yard-side oper-ations in a container terminal of utilising different numbers of Automated Straddle Carriers (AStCs). PNsand discrete event modelling techniques divide complex continuous systems into subsystems and analysethe system as a series of sequential operations being performed on certain entities. Discrete event simulationis used for the utilisation of AStCs with gang and pooling deployment strategies. Venices new off-shoreterminal is used for modelling the complex processes of a container terminal in order to determine the op-timal number of AStCs. The equipment sizing results gained from the developed PN and discrete eventsimulation are closely matching with the optimal solution determined from various models of queuing the-ory. Given the different effort required for the three methods, it can be concluded that PN represents a fairtrade-off and is the methodology of choice for equipment sizing problems, compared to analytic queuingtheory and complex discrete event simulations.

Keywords: Ports Productivity, Automated Straddle Carriers, Petri Networks

Corresponding author. Tel.: +44(0)2075942706.Email addresses: b.anvari09@imperial.ac.uk (B. Anvari),

apostolos.ziakopoulos13@imperial.ac.uk (A. Ziakopoulos), james@morleydesigns.com (J. Morley),Dimitrios.Pachakis@rhdhv.com (D. Pachakis), p.angeloudis@imperial.ac.uk (P. Angeloudis)

1. Introduction

In our modern world of increasing consumer demand, the maritime sector is responsible fortransporting over 90% of freight [1]. With the introduction of the container in the 1950s, freightmovement became standardised, more efficient and less expensive [2]. Annually, there are about5000 container vessels ferrying over 580 million Twenty-feet Equivalent Units (TEUs) of con-tainers between ports in 200 countries worldwide [3]. These containerships use dedicated areasin ports called container terminals to handle their cargo. Due to fierce regional and internationalcompetition, terminal operators seek ways to maximise throughput and productivity [4]. Thethree groups of operations in a terminal which have the greatest influence on a ports productivityare: (un)loading containers to/from the vessel (quay-side operations), storing/retrieving contain-ers at/from the stacking yard-side (yard-side operations), and transporting containers between thequay-side and the yard-side (transfer operations) [5, 6]. The stored containers are usually eitherloaded to another vessels (transhipment containers) or carried out by rail or trucks.

The operational performance of a port has been studied and optimised using different strate-gies, such as using automated equipment [7, 8], changing the container stacking policies [6], andvarying the storing/retrieving mechanism [9]. These strategies, however, are rarely utilised by portoperators in their terminals due to factors such as the lack of skilled staff to deliver the service,the extensive lead time for procurement and implementation of new technology, incomplete andever-changing information about container movements and budgetary and physical constraints.

When designing a new container terminal, one can consider choosing Automated StraddleCarriers (AStCs) for storing/retrieving containers at/from the stacking yard. AStCs are capableof performing a variety of different functions independently, such as picking containers up fromthe ground, transporting the containers horizontally to the storage area and stacking them up to acertain height [10]. AStCs are not the most expensive machinery that operates in a port but theycan make significant differences to the productivity of any port terminal [10]. The productivityof AStCs is, however, dependent on their capacity, the assigned workload, the productivity of theShip-to-Shore (STS) cranes, and the size of the buffer zone under a STS crane [7]. The size of abuffer zone is critical since spillovers caused by lack of space will disrupt the nearby operations(i.e. movement of other horizontal and vertical equipment). On the other hand, buffer zones reducethe available space for container stacking.

Before choosing AStCs for the horizontal transport in a container terminal, therefore, feasi-bility and sizing analysis needs to be performed. Although queuing theory provides adequateresults for the initial planning stages, there is a strong tendency to use discrete event simulationfor tactical and strategic planning of container terminals [11, 12]. Another potential analyticalmethod is Petri Networks (PNs). PNs are similar to discrete event modelling techniques in thatthey divide complex continuous systems into subsystems and analyse the system as a series ofsequential operations being performed on certain entities. The objective of this paper is to providea comparative analysis of queuing theory, PNs and a discrete event model by applying them tothe same problem. The new off-shore terminal of Venice is used for modelling complex processesof a container terminal and determining the optimal number of AStCs required for efficient andeconomic operations at the quay- and yard-side of the terminal.

The paper is organized as follows: Section 2.1 presents an introduction to material handling

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equipments and explains the advantages of using AStCs. Research on performance analysis ofAStCs for a container terminal is reviewed in Sections 2.2. In Section 3, the container composi-tion, the shipment arrival and departure times and operating details of the AStC proposed to beused at the new Venice off-shore terminal are described. Different queuing theory formulations,PNs and discrete simulation are used for analysing the impact of different numbers of AStCs onthe productivity of yard-side operations in a container terminal in Sections 4.1, 4.2 and 4.3. Theperformance analysis using three models are compared in Section 5, while Section 6 summarisesthe general conclusions of this paper.

2. Background

2.1. Automated Straddle Carrier Operations

IEEE Robotics & Automation Magazine SEPTEMBER 200722

development and testing of the AutoStrad was carried out at aremote site in Sydney. Once the strike had finished, an area ofPort Botany Terminal in Sydney was allocated for testing.

The development and test phase initially focused onnavigation system performance as this was seen as the keyrisk component. Much work was undertaken in developingand tuning the mm-wave radar system, in improving theperformance of the GPS-IMU system, and in graduallyreducing the number of faults in the system. The planningand control system was also developed and tested at thistime. There were a number of teething problems associatedwith trying to precision-control a vehicle which is normal-ly manually operated. Continual testing again graduallyreduced the number of faults. Minimal condition monitor-ing and safety systems were implemented at this time. Theprototype was demonstrated to senior management at thebeginning of 2000.

The second, risk-reduction, phase of the project involvedboth the testing of a larger-scale multivehicle operation and agradual hand-over of the development work from the univer-sity to the company. For the second phase, a complete newterminal, Berth 7 Fishermans Island (FI7) in Brisbane, wasacquired by the terminal operators and dedicated solely totesting of a four-vehicle AutoStrad fleet. Using the experiencegained in the prototype stages, a new hardware design andmuch improved testing and analysis software were developed.The AutoStrad system design was unchanged from the proto-type, a testament to the design philosophy initially adopted.The straddle carrier design too remained unchanged. Respon-sibility for machine-level control was moved to the straddlecarrier manufacturer. After much testing and evaluation, FI7became operational in 2003, accepting its first ships and pay-ing customers.

The risk-reduction phase was absolutely critical in tran-sitioning this technology to production. The company andterminal operators worked on issues such as operationalprocedures, crane and land-side interfaces, refueling, andmaintenance, issues that are essential to successful opera-tion but are often well-beyond what is done in mostresearch projects.

On the basis of the risk reduction phase, approval for aproduction system was forthcoming. New straddle carrierswere designed, specifically as automated vehicles, with diesel-electric drives, no driver cabs, all CAN-bus, and all necessarymounts for automation components. An extended terminal(Berths 7, 8, and 9) was constructed to be serviced by 18 all-new AutoStrad straddle carriers. The new terminal beganoperation and receiving customers toward the end of 2004.Again, considerable teething problems had to be overcome,especially in the area of multi-vehicle planning and schedul-ing, in support services and in interfaces with hauler vehicles.Gradually fault rates and productivity were improved as morewas learned about how such systems should be operated inpractice. The terminal was officially opened by the Premier ofthe State of Queensland at the end of 2005. The terminaloperation can be viewed by Webcam at http://www.patrick.com.au/IRM/Content/technology/autostrad.html.

The AutoStrad terminal has been in continuous day andnight operation since early 2005 (Figures 9 and 10). Since thistime, individual straddle faults have been substantially reduced asmore is understood about operations in different conditions andunusual situations. Such faults are now rare and have little impacton overall terminal operations. The efficiency of the terminal, interms of box moves per vehicle is now approximately the sameas an equivalent manned fleet. Following the 1998 waterfrontstrike, manned operations have doubled in efficiency and so thedefinition of operational success for the AutoStrad has corre-spondingly increased. The main constraints on further improvedAutoStrad efficiency concern multi-platform planning andscheduling, and this is a current focus of our efforts. Interestingly,the AutoStrad has substantially reduced maintenance costs ascompared to manned vehicles. Tire wear and fuel costs in partic-ular have fallen by over a third per box move. This is a conse-quence of the fact that robot vehicles are better drivers thanmanual vehicles. The technical management of the AutoStradfleet is run remotely by a group in Sydney, over 1,000 km fromthe terminal. This is a true indication of the degree of autonomyand confidence that has been developed in the AutoStrad pro-ject. It is expected that the AutoStrad system will be applied toother terminals in Australia and world-wide in the coming years.

Figure 10. Four AutoStrad vehicles servicing the hook under aquay crane. The need for efficient scheduling is apparent.

Figure 9. Five AutoStrad vehicles operating in the yard area ofthe terminal. (a)

IEEE Robotics & Automation Magazine SEPTEMBER 200722

development and testing of the AutoStrad was carried out at aremote site in Sydney. Once the strike had finished, an area ofPort Botany Terminal in Sydney was allocated for testing.

The development and test phase initially focused onnavigation system performance as this was seen as the keyrisk component. Much work was undertaken in developingand tuning the mm-wave radar system, in improving theperformance of the GPS-IMU system, and in graduallyreducing the number of faults in the system. The planningand control system was also developed and tested at thistime. There were a number of teething problems associatedwith trying to precision-control a vehicle which is normal-ly manually operated. Continual testing again graduallyreduced the number of faults. Minimal condition monitor-ing and safety systems were implemented at this time. Theprototype was demonstrated to senior management at thebeginning of 2000.

The second, risk-reduction, phase of the project involvedboth the testing of a larger-scale multivehicle operation and agradual hand-over of the development work from the univer-sity to the company. For the second phase, a complete newterminal, Berth 7 Fishermans Island (FI7) in Brisbane, wasacquired by the terminal operators and dedicated solely totesting of a four-vehicle AutoStrad fleet. Using the experiencegained in the prototype stages, a new hardware design andmuch improved testing and analysis software were developed.The AutoStrad system design was unchanged from the proto-type, a testament to the design philosophy initially adopted.The straddle carrier design too remained unchanged. Respon-sibility for machine-level control was moved to the straddlecarrier manufacturer. After much testing and evaluation, FI7became operational in 2003, accepting its first ships and pay-ing customers.

The risk-reduction phase was absolutely critical in tran-sitioning this technology to production. The company andterminal operators worked on issues such as operationalprocedures, crane and land-side interfaces, refueling, andmaintenance, issues that are essential to successful opera-tion but are often well-beyond what is done in mostresearch projects.

On the basis of the risk reduction phase, approval for aproduction system was forthcoming. New straddle carrierswere designed, specifically as automated vehicles, with diesel-electric drives, no driver cabs, all CAN-bus, and all necessarymounts for automation components. An extended terminal(Berths 7, 8, and 9) was constructed to be serviced by 18 all-new AutoStrad straddle carriers. The new terminal beganoperation and receiving customers toward the end of 2004.Again, considerable teething problems had to be overcome,especially in the area of multi-vehicle planning and schedul-ing, in support services and in interfaces with hauler vehicles.Gradually fault rates and productivity were improved as morewas learned about how such systems should be operated inpractice. The terminal was officially opened by the Premier ofthe State of Queensland at the end of 2005. The terminaloperation can be viewed by Webcam at http://www.patrick.com.au/IRM/Content/technology/autostrad.html.

The AutoStrad terminal has been in continuous day andnight operation since early 2005 (Figures 9 and 10). Since thistime, individual straddle faults have been substantially reduced asmore is understood about operations in different conditions andunusual situations. Such faults are now rare and have little impacton overall terminal operations. The efficiency of the terminal, interms of box moves per vehicle is now approximately the sameas an equivalent manned fleet. Following the 1998 waterfrontstrike, manned operations have doubled in efficiency and so thedefinition of operational success for the AutoStrad has corre-spondingly increased. The main constraints on further improvedAutoStrad efficiency concern multi-platform planning andscheduling, and this is a current focus of our efforts. Interestingly,the AutoStrad has substantially reduced maintenance costs ascompared to manned vehicles. Tire wear and fuel costs in partic-ular have fallen by over a third per box move. This is a conse-quence of the fact that robot vehicles are better drivers thanmanual vehicles. The technical management of the AutoStradfleet is run remotely by a group in Sydney, over 1,000 km fromthe terminal. This is a true indication of the degree of autonomyand confidence that has been developed in the AutoStrad pro-ject. It is expected that the AutoStrad system will be applied toother terminals in Australia and world-wide in the coming years.

Figure 10. Four AutoStrad vehicles servicing the hook under aquay crane. The need for efficient scheduling is apparent.

Figure 9. Five AutoStrad vehicles operating in the yard area ofthe terminal.

(b)

Figure 1: Auto Straddle Carriers (AStCs) (a) operating at the yard-side [8] and (b) serving thehook under a Ship-To-Shore crane (STS crane) [8]

One of the strategic decisions at the design stage of a container terminal is the type of materialhandling equipment used for transporting containers. Frequently used material handling equip-ment at the yard-side are the gantry crane and Straddle Carriers (StCs). There are two types ofgantry cranes, Rubber Tyred Gantry (RTG) cranes and Rail Mounted Gantry (RMG) cranes. StCs,RTG cranes and RMG cranes have a storage capacity of approximately 500600 TEU per hectare,900 1100 TEU per hectare and over 1200 TEU per hectare respectively [4]. Thus, a terminalcan execute double volume when using a RMG crane compared to a StC [4]. Based on Wiese etal. [13, 14]s survey of 114 container terminals, however, 63.2% of container terminals use RTGcranes, 6.1% use RMG cranes (mainly in Europe) and 20.2% use StCs as their main material han-dling equipment. This makes StCs the second most used material handling equipment in storageyards.

Straddle Carriers are capable of self-lifting and stacking containers. Some container terminalsuse StCs both for transferring containers between the quay-side and yard-side, and for storingcontainers at the yard-side. StCs can be easily moved within the terminal based on operationalrequirements, and layouts are easy to change since no runways are needed. The latest type ofself-lifting StCs, see Figure 1, allow the handling of up to three or four containers at the same time

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(approximately 500750 TEU per hectare) and operate in a completely automated fashion. TheseAuto Straddle Carrier (AStC) systems are labour efficient and enable high crane productivity sincean effective buffer zone is created under the STSC. This makes it possible for the STS crane tooperate at maximum efficiency, thus optimising vessel productivity [15].

Following the material handling equipment decision, one of the problems at the tactical level isthe determination of the necessary number of transport vehicles, which is the focus of this paper.

2.2. Optimisation of AStCs for Horizontal Movement of Shipping ContainersAutomated Guided Vehicles (AGVs) and Automated Lifting Vehicles (ALVs) are used for hor-

izontal transportation of containers in the yard-side. AStCs belong to the class of ALV and canindependently lift and set down containers while AGVs require direct assistance by other yardcranes to complete their horizontal transportation task. A few studies have investigated sizingproblem of AStCs at container terminals, with a focus on maximising productivity. Zehendneret al. [16] studied allocation of Straddle Carriers (StCs) in the Grand Port Maritime de Marseilleterminal by adopting an optimisation model and developing a discrete event simulation with theaim of reducing delays at the tactical level. Vis et al. [17] developed a minimum flow algorithmof polynomial time to determine the required number of AGVs for horizontal transportation ofcontainers in the yard-side at known time periods. Vis et al. [7] studied the impact of using AGVsand ALVs for the horizontal transportation on unloading times of a ship by means of discreteevent simulation. In this study, AGVs and ALVs produced similar unloading times, however,higher number of AGVs (38% more than ALVs) were required to minimise the unloading times.They concluded that the purchasing cost of ALVs is cheaper than AGVs which can have a highimpact on the decision process. Vis et al. [18] proposed a integer linear programming model (an-alytical model) for equipment sizing problem within the release and due times and used discreteevent simulation to validate their results. Kozan [19] presents a network model for minimisingthe throughput time of containers from their arrival to their departure. This model is a decisionsupport tool for investment appraisal, rather than for improvements in operational methods. Therehave been a number of studies on task assignment and scheduling for StCs or AGVs at containerterminals at the operational level (e.g. [20, 21, 22, 23]), or scheduling of different types of han-dling equipment (e.g., [24, 25, 26, 27]). Scheduling is determination of a number of tasks (i.e.horizontal or vertical movement of containers), the assignment of tasks to resources allocated tothem and the sequencing and/or timing of the tasks based on the project horizon.

Currently, due to the time it takes to implement and test new algorithms, in practice, equipmentsizing for tactical purposes is performed by empirical ratios (e.g. see PIANC [28]) and verifiedby discrete event simulation at the final design stage. Empirical ratios reflect a standard geometry,which although it has been implemented and studied before, would be hazardous to apply in radi-cally different geometries. This paper presents an intermediate step, exploring how the adaptationof queuing theory models to the horizontal transport problem can yield results more tailored toeach specific geometry than a simple equipment ratio (e.g. 3 6 AStC to an STSC). Additionally,through the comparative study presented herein, the different types of insights afforded by differentmethods can be appreciated.

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3. Case Study of AStCs for Venice Port

A new container terminal is currently being designed for the port of Venice (Italy) by RoyalHaskoningDHV in coordination with Venice Port Authority. They are planning to increase thecapacity of the current terminal and reduce the vessel dwelling times so that the throughputs of theport of Venice is maximised. The new terminal aims not only at serving mainland Italy, but alsoa number of customers in central Europe such as Austria, Switzerland, south Germany, Hungary,Slovenia and Croatia. As shown in Figure 2a, the new port of Venice consists of 3-parts: anoff-shore terminal for (un)loading containers, a barge transfer system for feeding said containersto/from the mainland, and an on-shore mainland terminal (called MonteSyndial). This three partstructure allows the examination of the horizontal container transportation system at the port ofVenice, since the off-shore terminal will operate separately from the on-shore terminal. The layoutof the off-shore terminal of the new port of Venice is shown in Figure 2b.

Chapter 5 Case Study Background

[24]

part structure: the off-shore terminal will operate separately from the additional

movements of the on-shore terminal.

This threefold nature of the port of Venice is illustrated on Figure 5.2 below:

Figure 5.1: Geographical position of the port of Venice.

Source: Venipedia (2011)

Figure 5.2: On-shore and off-shore terminal locations.

Source: Venice Port Authority (2010) (a) (b)

Figure 2: The new port of Venice: (a) The on-shore and off-shore terminal locations [29] and (b)The off-shore container terminal layout [29]

This paper evaluates the application of AStCs for the horizontal transportation of containersat the off-shore container terminal. As shown in Figure 3, eight STS cranes (maroon colour) andten barge cranes (blue colour) are assigned for (un)loading containers to/from the vessels on thedeep sea side and on the barge side of this terminal in the planning stage. The productivity of theSTS cranes is based on the arrival and exit rates of containers to and from the off-shore terminal.The target STS crane productivity is 34 moveshr on the deep sea side and 30

moveshr on the barge side

1.The cycle times are thus 2.00 min and 1.76 min respectively. In order to estimate the numberof AStCs required to operate the off-shore terminal at the target throughput, some of the technicaland operational assumptions are summarised in Table 1. It is assumed that AStCs do not conductdirect crane-to-crane movements and that each STS crane has its own allocation of AStCs and

1PIANC [28] reports the range of low, medium and high productivity per STS crane in large container terminalsto be between 20 25 moveshr , 25 30 moveshr and 30 35 moveshr respectively.

5

Deep sea side

Barge side

Ship-To-Shore crane

Barge craneInside the

container stack

AStCs route

Stacking yard

Corridor

Barge Side

Vessel

S

T

Figure 3: The off-shore container terminal layout of Venices port at the planning stage [30] andthe route (green line) that each AStC travels in order to finish one cycle time. The start point isdesignated as S and the destination as T.

storage area. The average stacking height is set to up to 3 container heights with an extra meterfor the safety adjustments. The housekeeping operations are included in the cycle time of a AStCby adding 10% of the vertical movement time to the cycle time. The acceleration/decelerationtime of an AStC (i.e. when turning or stopping) is considered in the cycle time by adding 40 sto the horizontal movement time. Traffic and safety adjustments are also considered in the cycletime of AStC by adding 20 s to the horizontal movement time. Miscellaneous manoeuvres (i.e.positioning by STS crane) are covered in the cycle time of a AStC by adding 20 s to the horizontalcycle time. Delay is added as 25% of the sum of horizontal and vertical movement times, whichis added to the total cycle time of an AStC. It is assumed that each AStC stands by one of the STScranes in the waiting areas (coloured orange in Figure 3) for storing/retrieving containers at/fromthe stacking yard-side.

The cycle time of AStCs is calculated from the centre of each stack and the longest path isconsidered. The travel route of the AStCs is marked green with indicators along its entire lengthin Figure 3, and with the starting point and destination location symbolised with S and T,respectively. The dashed part of the AStCs route represents the part that is inside the containerstack. All types of StCs have higher speeds on corridors than inside container stacks. In order tominimise the in-block travel time, the corridor is used at least once in the route of the AStCs. Thetravel distance on the outside and inside block are 581.03 m and 38.60 m respectively. A containerwith 2.600 m height, 2.438 m width and 6.058 m length is considered in this paper. Consideringthe horizontal and vertical movements and including 25% delay allowance, the final AStC cycletime is about 600 s for the route in Figure 3. Thus, each AStC can finish approximately 10 moveshr

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Table 1: Operational assumptions for the AStC operation

Specification of the AStCs [31] Unit ValueMaximum travel speed outside the block [ms ] 6.9485% of the average travel speed outside the block [ms ] 5.90Average travel speed within the block [ms ] 1.39Time for 90 degrees turn [s] 2Housekeeping % 10Acceleration adjustments [s] 40Traffic and safety adjustments [s] 20Miscellaneous manoeuvring time [s] 20Stack average height [boxes] 3Maximum lifting speed for unloading [ms ] 0.33Maximum lifting speed for loading [ms ] 0.27Maximum lowering speed for unloading [ms ] 0.30Maximum lowering speed for loading [ms ] 0.25

in the stacking yard.

4. Modelling the AStCs Movements

Queuing theory is commonly used by port operators because of its solid theoretical basis, itsability to provide quick and indicative results in preliminary stages of a project. Queuing theory isalso widely used to verify the results of other methods such as simulations.

PNs are visual-graphical tools that can be formed to represent any system with discrete numberfunctions. A PN is formulated for the equipment sizing problem in shipping container terminalsand performance analysis is used to quantify buffer zone requirements (physical constrains) asso-ciated with choosing a number of AStCs.

FlexSim CT is an advanced discrete event simulation platform that is designed for detailedsimulation of container terminal operations. The software models both the physical attributes ofthe terminal (e.g. stack layout) and the container handling processes (i.e. the terminal operatingsystem). FlexSim CT Simulation software is used to model the off-shore container terminal andutilise the AStCs with two different deployment strategies.

4.1. Queuing TheoryThe standard notation established by Kendall [32] for defining every queue in its most basic

form is A/B/c/K/m, where A denotes the stochastic arrival time distribution, B represents thestochastic service time distribution, c is the number of operating servers in the system, K denotesthe capacity of the queue, and m represents the maximum number of customers. A and B arecommonly defined as a Poisson (or exponential) distribution (M), a deterministic value (D) or ageneral distribution (G). K and m are infinite when they are not defined. For instance, in theM/M/1 queuing system, both arrival and service distributions are a Poisson distribution and oneserver is operating in the system.

In this paper, seven types of queuing system, M/M/1, M/D/1, M/M/c, G/M/1: A specificinterarrival distribution (G/M/1[s.i.a.]),G/M/1: The Allen - Cunneen approximation (G/M/1[A

7

C]), G/M/c, and M/M/c/K are explored. In the model, the customers are the containers that are(un)loaded from a single STS crane at a rate of 34 moveshr and 30

moveshr on the deep sea and barge

cranes, respectively. The servers are the AStCs that are assigned to a single STS crane. Usingseven queuing theory formulations, the average number of container and waiting times of thesystem and the queue after assigning 4 6 AStCs per STS crane are calculated. The results aresorted by arrival rate in Figures 4a, 4b, 4c, 4d. Table 2 summarises the parameters used in thequeuing systems based on the case study. Results for the G/M/1[s.i.a.] and G/M/c queues aregrouped for the barge side, as their average approaches 30. It is evident from the results that theexamined quantities follow the same trends of improvement as the AStC number increases and decreases.

(a) (b)

(c) (d)

Figure 4: Queuing model results: (a) Average number of container in the system per STS crane,(b) Average number of container in the queue per STS crane, (c) Average waiting time in thesystem per STS crane, and (d) Average container waiting time in the queue per STS crane

If there is a container in the apron and the crane has to lay another one, the crane will needto wait (blocking). The approximate M/M/c/K queuing model was set to calculate the minimumnumber of AStCs needed to avoid blocking for more than 20% of the time. The productivity rateof 33 moveshr (weighted average productivity between deep sea and barge cranes) is considered here.The maximum size of the system K is set as the number of servers c plus one. This number c + 1

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Table 2: Parameters used in the queuing theories according to the case study

Parameter Parameter Meaning Deep Sea Side Barge Side [moveshr ] Arrival rate of STS crane 34 34 34 30 30 30c Number of operating AStCs in the system 4 5 6 4 5 6 [moveshr ] Service rate of AStC 10 10 10 10 10 10 Traffic intensity 0.85 0.68 0.57 0.75 0.60 0.50

corresponds to the situation where every AStC is carrying a container and there is one containerlaid on the transfer position at the apron. The results of this queuing model indicated that with threeAStCs assigned to a STS crane, the model is sufficiently busy (equipment utilisation is 67%) andstable (traffic intensity, defined as the ratio of arrival rate divided by number of servers multipliedby the service rate, is about 80%). In this case, the occurrence probability of blocking is 19% (withfour containers in circulation) as shown in Figure 5. Having four AStCs assigned to a STS cranewill reduce the blocking significantly to about 13% but reduces the equipment utilisation to about57%.

(a)(b)

Figure 5: Using the M/M/c/K queuing model, (a) blocking probabilities and the number of con-tainers in system when 3 6 ASTcS are assigned to a STS crane and (b) equipment utilisationprobabilities [30]

4.2. Using Petri NetsPNs consist of four elements (place, transition, arc and token) which are summarised in Table 3.

In PNs, an area, activity or state of the system can be modelled using a place and the number ofinstances of a place can be represented with tokens. Sequential processes are modelled with tokensprogressing through state machines. Arcs between resource places and transitions represent theacquisition (return) of some resources by a process. In the end, the process state machines can bemerged into a model of the whole system by combining the common resource places.

In mathematic terms, a PN consists of five parts [33]:

PN = (P,T, F,W,M0) (1)9

Table 3: Petri Net elements

Element Function Traditional Representation Graphical Representation

Place Area, activity or state of the system Circle

STSC Queue

Crane Loading Spot

Loaded

Reach Block

Entrance Block

Destination

Unloading

Reach Block

Exit

Transition Functions linking places Rectangular bar

STSC Queue

Crane Loading Spot

Loaded

Reach Block

Entrance Block

Destination

Unloading

Reach Block

Exit

Arc Connect places to transitions and vice versa, enforce conditions Vector (Arrow or curved arc)

STSC Queue

Crane Loading Spot

Loaded

Reach Block

Entrance Block

Destination

Unloading

Reach Block

Exit

Token Counting/controlling medium, the quantifying aspect of the net Dot

STSC Queue

Crane Loading Spot

Loaded

Reach Block

Entrance Block

Destination

Unloading

Reach Block

Exit

P is a finite set of places, P = p1, p2, ..., pi. T is a finite set of transitions, T = t1, t2, ..., t j. F isa finite set of arcs (flow relation) that F P T T P. W is a weight function and M0 is theinitial marking. The essence of the function of PNs is that a transition cannot fired until a series ofconditions have been fulfilled:

The destination place has capacity for incoming tokens. There are enough tokens available at the input places. No other transition fires simultaneously. Other conditions such as time or colour restrictions may apply, depending on the PN type.

One of the most important properties of PNs is that they are memoryless. This is a Markovianproperty which entails that any state in a PN is only dependent on the immediately previous oneand not the ones before that. PIPE (v4.3.0) [34] is used for modelling horizontal movements ina container terminal. The PN definitions and transition rates for modelling a full AStC cycle aresummarised in Table 4. The created PN model with five deep sea side AStCs and four barge sideAStCs at the initial stage and at a random one are shown in Figures 6a and 6b. Here, tokensrepresent the movements of AStCs.

Table 4: AStC transition rates in PIPE (v4:3:0)

P#: Origin place T#: Transition P#: Destination place Movement type Net time Delay time Final duration [s][s] [s] [s]

P1: STS Crane Queue T1,2: Safety Clearance P2: Crane Loading Spot Horizontal 29.24 7.31 36.54P2: Crane Loading Spot T2,3: Start Loading P3: Loaded Vertical 28.30 7.07 35.37P3: Loaded T3,4: Depart for Block P4: Reach Block Entrance Horizontal 88.07 22.02 110.09P4: Reach Block Entrance T4,5: Slow Down P5: Block Destination Horizontal 8.29 2.07 10.37P5: Block Destination T5,6: Start Unloading P6: Unloading Vertical 37.73 9.43 47.17P6: Unloading T6,7: Depart P7: Reach Block Exit Horizontal 8.29 2.07 10.37P7: Reach Block Exit T7,1: Speed up P1: STS Crane Queue Horizontal 88.07 22.02 110.09

Total 288.00 72.00 360.00

The results of each analysis for both terminal sides (sea side and barge side) after simulationsof 2000 firings and 30 replications are shown with their 95% confidence interval values in Table 5.PN analysis shows that, given the geometry and cycle times, the best option for the AStC queueappears to be four vehicles (1

Chapter 7 Petri Networks Theory and Application

[54]

As an example, the PN with 5 deep sea side ASCs and 4 barge side ASCs is shown in

the following Figures, at the initial stage and at a random one (barge side places with *):

In accordance with previous sections, this PN would be characterized as a Colored

Stochastic PN, due to its use of differently colored tokens and element of uncertainty

(every firing transition is determined from the eligible ones via a Java random function).

Moreover, it would be ordinary, live, persistent, regular, all stages would be reachable

and reversible, and 3-, 4-, 5- or 6-bounded depending on configuration.

The results of each analysis for both terminal sides after simulations of 2000 firings

and 30 replications are shown next, along with 95% confidence interval values.

Figure 7.2: The Terminal PN at the initial stage, M0

STSC Queue

Crane Loading Spot

Loaded

Reach Block Entrance

Block Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block Entrance

Block Destination

Unloading

Reach Block ExitSTSC Queue

Crane Loading Spot

Loaded

Reach Block Entrance

Block Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block Entrance

Block Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block Entrance

Block Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block Entrance

Block Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block Entrance

Block Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block

Entrance

Block Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block

Entrance

Block Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block

Entrance Block

Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block

Entrance Block

Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block

Entrance Block

Destination

Unloading

Reach Block ExitSTSC Queue

Crane Loading Spot

Loaded

Reach Block

Entrance Block

Destination

Unloading

Reach Block

Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block

Entrance Block

Destination

Unloading

Reach Block

Exit

Deep sea side

Barge side

P1T1,2P2T2,3P3

T3,4P4

P5P6

P7

T TT

T

4,5 5,6

6,7

7,1

(a)Chapter 7 Petri Networks Theory and Application

[55]

Figure 7.3: The Terminal PN at a random stage, Mi

Table 7.3: Terminal PN Simulation results for 3 ASCs

STSC Queue

Crane Loading Spot

Loaded

Reach Block Entrance

Block Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block Entrance

Block Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block Entrance

Block Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block Entrance

Block Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block Entrance

Block Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block Entrance

Block Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block

Entrance

Block Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block

Entrance

Block Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block

Entrance Block

Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block

Entrance Block

Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block

Entrance Block

Destination

Unloading

Reach Block Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block

Entrance Block

Destination

Unloading

Reach Block

Exit

STSC Queue

Crane Loading Spot

Loaded

Reach Block

Entrance Block

Destination

Unloading

Reach Block

Exit

Deep sea side

Barge side

(b)

Figure 6: The terminal PN at (a) the initial stage and (b) a random stage11

Table 5: Terminal PN simulation results for the average vehicle queue (AStCs)

AStC No. Average token on the deep sea side 95% confidence interval Average token on the darge side 95% confidence interval3 0.72 0,025 0.72 0,0254 1.73 0,035 1.70 0,0355 2.73 0,033 2.70 0,0336 3.73 0,026 3.71 0,026

Table 6: Buffer zone dimensions per Ship-To-Shore Crane (STS crane)

AStC Number Combined Vehicle Length Vehicle Width Buffer Zone Length Buffer Zone Width[m] [m] [m] [m]

1 12.03

5.00

16.24

6.75

2 24.06 32.483 36.09 48.724 48.12 64.965 60.15 81.206 72.18 97.44

4.3. Using Discrete Event SimulationIn discrete event simulation the aim is to determine the number of AStCs needed to operate

the off-shore terminal at the target throughput and to calculate the off-shore terminal storage areassize. The simulation model developed in FlexSim CT for the off-shore terminal of Venice canbe seen in Figure 7. The model is run with two deployment strategies, gangs and pooling, withvarying number of AStCs. For the gangs strategy, specific AStCs are assigned to specific deep seaside cranes, ensuring that the AStCs are available for berth operations regardless of vessel arrivaltimes or patterns. Nine AStCs are initially assigned to each STS crane. Housekeeping operations(customs and stack block optimisations) are carried out in AStC idle periods. For the pooling strat-egy, a central pool of AStCs is assigned to different tasks based on the order of priority. The sameoverall number of AStC is applied to the pool as the gangs strategy, with these being allocated todifferent berths or stack operations based upon demand. The workload for barges and vessels canbe estimated from their schedules, and depends on arrivals and volumes of barges and vessels. Theworkload for barges and vessels can be estimated from their schedules. In order to best analysethe terminal and its operational characteristics, two scenarios have been investigated. In order tobest analyse the terminal and its operational characteristics, two scenarios have been investigated.In scenario 1 - an average vessel schedule, regular vessels arrivals are from a uniform distributionwith up to 12 hours maximum variance before or after estimated time of arrival. In scenario 2 - acontingency vessel schedule, two vessels unload and load simultaneously, or one vessel unloadsand one vessel loads before the vessel schedule returns to a regular weekly pattern. The two de-ployment strategies, gangs and pooling, are run with the average and contingency scenarios. Theequipment utilisation results and the productivity rates are summarised in Table 7.

Nine AStCs were initially assigned to each STS crane in order to compare the deploymentstrategies. Simulations have been made with a number of AStCs pool sizes to compare their effect

12

Deep sea sideBarge side

Figure 7: The FlexSim simulation model for the off-shore terminal

on utilisation and waiting time (see Table 8). Maintenance routines and breakdowns are not in-cluded in the assessment of equipment numbers here. Instead, the numbers are assumed to be thenumber of regular equipment available for operations, and additional equipment will be allowedfor planned maintenance and breakdowns. A common policy is to acquire an additional 10% ofequipment for redundancy to cover maintenance and breakdowns. This equipment is run as muchas the regular equipment in turns so that all the machines have regular maintenance and about thesame working hours. In order to limit unnecessary congestion and be cost effective, the termi-nal should not keep more AStCs in operation than are required. However, sufficient equipmentshould be available to provide a regular supply to the berth and to not hold up the other parts ofthe operation. As shown in Table 8, increasing the AStCs pool size beyond 48 (six AStCs per STScrane) will only result in congestion and lengthy queuing at the berth. In Table 9, the simulatedSTS crane productivities for the berth with 48 AStCs in operation in the central equipment pool iscompared to the target STS crane productivities for both the deep sea side and barge side.The mainline berth occupancy over the course of these simulations is relatively low at approxi-mately 40%, reflecting the fact that the regular schedule would have one vessel at a time. Thebarge berth occupancy is very high at 95% however this is due to the operational rules of theterminal whereby the barge berth is also used as an extended storage buffer.

13

Table 7: AStCs utilisation and productivity rate for two deployment strategies (gangs and pooling)with two scenarios (1: An average and 2: A Contingency vessel schedule) [30]

Scenario Strategy AStC Utilisation Deep sea STS crane productivity Barge crane productivity[%] [moveshr ] [

moveshr ]

Scenario 1 Gang 38 27 20Pooling 43 31 24

Scenario 2 Gang 39 27 20Pooling 44 28 22

Table 8: AStCs utilisation and productivity rate for a pooling strategy with two scenarios (1:Anaverage and 2: A Contingency vessel schedule) [30]

Scenario AStC pool size AStC utilisation AStCs average cycle time Deep sea STS crane productivity Barge crane productivity[%] [min] [moveshr ] [

moveshr ]

Scenario 1 32 77 7 29 2340 68 9 31 2448 63 9 31 2456 57 9 31 2464 52 9 31 24

Scenario 2 32 78 6 27 2040 70 7 27 2048 65 9 29 2256 58 9 29 2264 52 9 29 22

Table 9: Simulated STS crane productivities and waiting times (1:An average and 2: A Contin-gency vessel schedule) [30]

Scenario Berth type Target STS crane productivity Average STS crane productivity Difference Average STS crane waiting time[moveshr ] [

moveshr ] [%] [%]

Scenario 1 Deep Sea 34 31 -9 3Barge 30 29 -4 3

Scenario 2 Deep Sea 34 29 -15 5Barge 30 26 -12 3

5. Comparison of AStC Sizing Models

Using different queuing theory formulations, average container numbers and waiting times for4 6 AStCs per STS crane showed a decreasing trend as the AStC number increases and de-creases (see Figure 4). Also, the blocking and utilisation analysis using M/M/c/K model for 3 6AStCs per STS crane suggested selecting three or four AStCs per STS crane in order to have asufficiently utilised and stable traffic.Queuing theory formulations are easy to implement, adapt to different deployment strategies andanalysis. They are approximate and moderately conservative though. The probability distributionused in different queuing theory formulations for arrival rates cannot reflect the reality. Capturingthe coordination between STS cranes and AStCs requires defining strong assumptions (i.e. servers

14

(AStCs) operate simultaneously) as well. Also, the selected queuing discipline greatly affectsanalysis results and it is not an easy task to find the discipline which reflects the reality closely(i.e. the layout and function of the port).

From the results obtained from PNs (see Table 6), four AStCs per STS crane is the optimumsolution for both sides (deep sea and barge sides). If three are assigned there will be some timeperiods without any AStCs standing by the crane (average tokens < 1.0). This might lead to flowdisruptions and waiting for the more expensive equipment (cranes and vessels). On the other hand,if five or more AStCs are assigned, it appears that they would form an unnecessarily large queuefor operations (average tokens > 2.0), leading to underused equipment (reduced efficiency) andneedless land occupation.The PN implementation is cost efficient and has great advantages, such as visualisation and easyoverview of the system examined, with direct display of its individual parts, and simplification ofcomplex environments. PNs inherently allow one transition at a time, which reduces their abil-ity to model simultaneous processes. Also, they are capable of modelling movements of a singleequipment type and not different equipment types (i.e. AStCs, barges and containers) simultane-ously. On the other hand, PNs can provide adequate detailed information on the equipment sizingproblem and buffer zone dimensions.

If discrete even simulation is applied, the results obtained from the two operating method-ologies (gang and pooling) show that the utilisation of AStCs in the gang allocation strategy isabout 5% less than that in the central pool strategy (see Tables 7, 8, 9). Berth productivity ratesare also lower in the gang strategy despite there being the same number of handling equipment.This indicates that the gang strategy, as set up in the model, is less efficient than a central poolstrategy. Productivity rates between the average and contingency runs are very similar, however,indicating that the gang strategy handles contingency events more consistently. The utilisation ofAStCs in the central pool strategy is also relatively low with this equipment allocation, however,berth productivity is good. The improved productivity is primarily due to the fact that AStCs canbe assigned to berth cranes in a more flexibly way with a higher straddle carrier to berth craneratio when additional straddle carriers are available. The same level of benefit is not observed onthe contingency scenario, where berth productivity falls to a similar level to that of the gang strat-egy. Due to the efficiency gains associated with the central pool strategy during normal operationscenarios, however, the central pool option was selected for further analysis. Overall, the previousresults confirm the well-known conclusion that pooling of equipment shares the workload moreevenly and achieves more uniform equipment utilisation. As such, it is expected to yield someequipment efficiencies. Given the results in Table 8, increasing the AStCs pool size beyond 48(six per STS crane) will result in congestion and lengthy queuing at the berth. With 48 AStCs inoperation, queues form on the berths during the unloading cycle with the large number of directdeliveries between the deep sea and barge side and the relatively short distances. However, thequeues do not negatively impact the berth or yard operation.Discrete simulation models allow realistic investigation of the processes in a terminal, and a fullevaluation of the performance of the layout, equipment and deployment strategy. However, devel-oping such a model is time consuming.

15

6. Conclusions

Multi-method approaches provide modelers insights into how common problems may be ad-dressed. This paper presented the equipment sizing problem for the horizontal transportations thattake place in terminal ports using AStCs, and presented solutions using queuing theory, PNs anddiscrete event simulation. The analyses were based on figures and layout from the new containerterminal of Venice. It was seen that PNs can replicate a port system in a way that is to a large ex-tent similar to discrete event models. It was demonstrated that queuing theory analysis has seriouspractical limitations while discrete event simulation is a more powerful, flexible and informativemethodology. Certainly, building a complex simulation model of operations in a container ter-minal requires the investment of considerable effort in logic development, debugging, model, andinput data collection. Given the different efforts required for the three methods, it can be concludedthat PN is a fair trade-off and the methodology of choice compared to analytic queuing theory anddiscrete event simulations for equipment sizing problems.

Acknowledgement

The authors are grateful to Venice Port Authority and Royal HaskoningDHV for providinginformation and supporting the research described in this paper.

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17

IntroductionBackgroundAutomated Straddle Carrier OperationsOptimisation of AStCs for Horizontal Movement of Shipping Containers

Case Study of AStCs for Venice PortModelling the AStCs MovementsQueuing TheoryUsing Petri NetsUsing Discrete Event Simulation

Comparison of AStC Sizing ModelsConclusions