Eindhoven University of Technology MASTER Modeling the use of a multi trailer in a container terminal Ansems, R.P.W.M.

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Eindhoven University of Technology

MASTER

Modeling the use of a multi trailer in a container terminal

Ansems, R.P.W.M.

Award date:

2011

Link to publication

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Master 's Thesis

Modeling the use of a multi trailer in a container termin al

R.P.W.M. Ansems (0509047)

SE420660

Supervisor : Prof. dr. ir. J .T . Udding

EINDHOVEN UNIVERSITY OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING SYSTEMS ENGINEERING GROUP

Eindhoven, July 18, 2011

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Summary

Transportation is an important business for the industrialized world. The use of standard sized containers increased the efficiency of transporting and handling of cargo. Truck, trains and vessels are equipped to handle these containers. The containers that are transported over sea are loaded onto and clischarged from vessels at specialized container terminals at sea ports all over the world. MSC Home Terminal at the port of Antwerp is such a container terminal. Containers are dischargecl from the vessels by quay cranes, and transported by straddle carriers to the yard where the containers are temporarily stored. At a later point in time the containers are retrieved from their position in the yard again so they can be loaded onto trucks, trains or an other vessel for further transport. The transport in the yard is usually clone by straddle carriers, but at MSC Home terminal for driving long distances a multi trailer can also be usecl. The multi trailer consists of a truck that pulls multiple trailers with a container onto it. The multi trailer travels along a fixed route and is meant to be used for traveling long distances within the yard.

To operate the terminal as efficient as possible schecluling algorithms are used to determine the optima! berthing position of the vessels along the quay and the positioning of the containers in the yard. An existing model of another container terminal at the port of Antwerp is aclaptecl to represent the situation at MSC Home Terminal. This model consists of a Berth Allocation Problem (BAP) to calculate the berthing position of the vessels along the quay and a Yard Allocation Problem (YAP) to calculate the position of the containers in the yard. These problems are solvecl in an alternating way, and the output of one model serves as input for the other model. The BAP is adapted to fit the layout of the terminal and some terminal specific berthing constraints are taken into account. Next to that the use of the multi trailer, that was not yet included into the model is implementecl by changing the cost function and aclding constraints.

The value of the multi trailer costs are estimated by tuning the model parameters in such a way that the behavior of the model represents the situation at MSC Home Terminal. When these multi trailer costs are known, a sensitivity analysis is performed to investigate how the model reacts on changes in the other parameters that describe the multi trailer in the model.

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Il Summary

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Samenvatting

Transport neemt een belangrijke rol in in de industrile wereld. Door het gebruik van ges- tandaardiseerde containers kunnen goederen efficient gehanteerd worden tijdens het transport. Vrachtwagens, treinen en schepen zijn allemaal uitgerust om deze standaard containers te kunnen vervoeren. De containers die verscheept worden, worden in gespecialiseerde container terminals in en uit de schepen geladen. Een voorbeeld van zo'n container terminal is MSC Home Terminal in de haven van Antwerpen. De containers worden door kade kranen uit een schip geladen en worden vervolgens door straddle carriers naar de yard gebracht waar ze tijdelijk worden opgeslagen. Later worden de containers weer door straddle carriers uit de yard gehaald zodat ze op vrachtwagens, treinen of andere schepen geladen kunnen worden.

Het meeste transport in de yard wordt door straddle carriers gedaan, maar in MSC Home Terminal worden ook multi trailers gebruikt voor het vervoeren van de containers over lange afstanden. De multi trailer bestaat uit een trekker die meerdere trailers met een container erop trekt. De multi trailer rijdt over een vaste route en wordt in MSC Home Terminal gebruikt voor het afleggen van grote afstanden binnen de yard.

Om alle operaties in de container terminal zo efficint mogelijk te laten verlopen wordt gebruik gemaakt van scheduling algoritmes. Hiermee wordt de optimale aanmeer-positie bepaald van de schepen aan de kade en de posities van de containers in de yard. Een bestaand model dat gemaakt is voor een andere terminal in de haven van Antwerpen is aangepast aan de situatie in MSC Home Terminal. Dit model bestaat uit een Berth Allocation Problem (BAP) dat de posities van de schepen aan de kade berekent en een Yard Allocation Problem (YAP) dat de posities van de containers in de yard berekent. Deze twee delen worden om en om berekend zodat de uitkomst van het ene deel dient als input voor het andere deel van het model en andersom. De BAP is aangepast voor de layout van MSC Home Terminal en de specifieke manier van werken in de terminal. Daarnaast is ook het gebruik van de multi trailer toegevoegd aan het model door de kostenfunctie aan te passen.

De hoogte van de kosten voor het gebruik van de multi trailer in het model worden geschat door het model zo in te regelen dat het de situatie in MSC Home Terminal goed weergeeft.

\Vanneer deze multi trailer kosten op deze manier bepaald zijn kan een gevoeligheidsanalyse uitgevoerd worden om te zien wat voor effect veranderingen in de andere modelparameters van de multi trailer hebben op het totale model.

iii

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iv Samenvatting

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Chapter 1 Introduction

In the last decades, transportation has become more and more important for the industrialized world. Not only people can travel to almost any place in the world, also cargo is transported all over the world. A lot of this cargo is transported by sea. Nowadays, about 90% of this cargo is handled by sea ports. One of the things that has greatly improved the efficiency of transport by sea is the use of containers of standard dimensions. Because the standard containers are used all over the world, no specialized pieces of equipment are needed for all sorts and sizes of cargo. The capacity of such a standarcl container is incli- catecl by "TEU" which is an abbreviation of the term "Twenty foot Equivalent Unit". One TEU equals the the size of a 20ft container with the climensions of 600 by 230 by 230 cm. Next to the twenty foot container, also 40ft containers are usecl with twice the length of a twenty foot container and with a capacity of two TUE. Vessels are specifically clesignecl to accommoclate such containers. Vessels like MSC Beatrice, one of the largest vessels in the world, can carry up to 14.000 TEU.

The vessels sailing from one port to the other are ownecl by shipping companies like Maersk and MSC, the two biggest container shipping companies in the world. The vessels are loadecl and clischargecl at specializecl container terminals at the sea ports. In genera!, the terminals are not ownecl by the shipping companies themselves. Terminal operators are paicl to take care of all the operations at the terminal. Terminal operators have to make sure that all containers are loaclecl on to and clischargecl from the vessels in time for the vessel to leave the port again.

1.1 Container terminal operations

Every container transportecl by sea has to be loaclecl onto the vessel, and be clischargecl again when it has arrivee! at the port of clestination. For this operation, specializecl container terminals are built. At a terminal, a vessel can berth at the quay which lies clirectly by the water. At this quay, large rail mountecl quay cranes can be positioneel next to the vessel. In Figure 1.1 a vessel can be seen which has alreacly berthecl at the quay. Three quay cranes are servicing the vessel. These quay cranes are high enough to reach over the

1

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2 Chapter 1. Introduction

vessel and hoist the containers in and out of the vessel. White a quay crane extends tens of meters over the water, at the land side it can not reach very far.When a quay crane is servicing a vessel, it will not move until the bay of the vessel it is working on is completely discharged and then loaded with containers again. Because of these characteristics of the quay crane it has only a very small buffer for containers on the land side it has to work with.

Figure 1.1: Quay cranes servicing a vessel

Additional devices are needed to take care of further transport of the containers at the land side of the quay. Different devices can be used to take care of this work, but in this research we assume that this is done by straddle carriers. Straddle carriers are human driven vehicles that can pick up one 40ft or two 20ft containers at a time. The straddle carriers transport the containers from the quay cranes to the yard where the containers are temporarily stored. In this yard, containers can be stacked on top of each other. Straddle carriers are specifically designed to drive over such a stack of containers while carrying a container itself. In Figure 1.1 some quay cranes can be seen, reaching over a vessel. Beneath the quay cranes a straddle carrier is located close to the vessel.

The yard of a container terminal is used as a buffer to temporarily store containers. The containers do not only arrive or leave by vessel, but also by other means of transportation. A railway track is located next to the terminal so containers can be transported by train. Truck parkings are located at the terminal so containers can be transported by road as well. It is also possible that a container has to go on another vessel to reach its destination.

Straddle carriers take care of all the container movements between the vessels and the yard, and again between the yard and the next means of transport.

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1.2. Scheduling terminal operations 3

1.2 Scheduling terminal operations

The vessels calling at a certain port can only berth for a predetermined period of time.

This means that there is limited time to perform all the container moves necessary. The port operator has to make sure that enough quay cranes are available for each vessel, and enough straddle carriers for each quay crane. The port operator is also responsible for the stacking of the containers in the yard. Each move of a container takes time and costs money. Containers have to be moved by straddle carriers which consume fuel and have to be clriven by an operator. One thing the port operator tries to do in order to complete the servicing of the vessels as fast as possible and to reduce the costs, is to minimize the total distance the straddle carriers have to travel. This distance of course depends on the position of the vessel and the positions of the containers in the yard. To minimize the total straddle carrier driving distance for all of the containers is not something that is easily done by hand. That is why schecluling techniques are usecl to fine! a solution for this problem.

When containers are transported from a vessel to the yard, they will most likely be stacked somewhere between the vessel it was discharged from, and the next means of transport of the container. When the container continues its journey by train, it will be placed close to the railway. When it has to be loaded onto a truck, its position in the yard will be close to one of the truck parkings, and when the container has to be loaded onto another vessel it will be stacked close to the scheduled position of that vessel. Scheduling techniques can help to calculate the positions of the containers in the yard in such a way that the overall straddle carrier distance is minimized. The travel clistance of the straddle carriers not only depends on the position of the containers in the yard, but also on the position of the vessels.

This means that the berth and yard planning problems have to be combined.

1.3 MSC Home Terminal

MSC is one of the biggest shipping companies in the world. It ships containers to 335 ports all over the world through 200 direct and combinecl weekly liner services. In Figure 1.2 all MSC liner services around the world can be seen. Vessels sail along fixed routes and call at the ports at regular times. One liner service connecting multiple ports is called a loop.

One loop can for instance connect the ports of Shanghai and Antwerp, and some ports in between. The voyage from Shanghai to Antwerp and back takes about 10 weeks, so 10 vessels are neecled to sail along in this loop in order to ensure a weekly service. This means that each week one of these 10 vessels will arrive at for instance the port of Antwerp. By adjusting the number of vessels in one loop, a weekly service on loops of different lengths can be accomplished by the shipping company.

The port of Antwerp is the second biggest port of Europe, and the seventh biggest port in the world. The port is located 80 kilometer inland of the Belgian coast, and vessels arrive at the port by the river Scheldt. The port itself consists of multiple terminals where the ships can be serviced. One of these terminals is located at Delwaide doek and is called MSC Home Terminal. The terminal, in which the freight handling company PSA HNN and MSC are partners, functions as the European hub for the MSC services. With more than 1400 vessel calls per year MSC is by far the largest shipping line in the port of Antwerp. In order to service all these ships, the terminal uses the complete south side of Delwaide doek and

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4

~~ ... ,1lilfil•.._•,.--~,- C6_ '"

. '

Chapter 1. Introduction

Figure 1.2: lVlSC liner services connect scaports all over the world

also a part of the north side of the doek. Together they have a quay length of 2.9km. On the quay a number of 21 rail mounted quaycranes can service multiple vessels at a time.

124 straddle carriers take care of the transport between the quay cranes and the yard where the containers are temporarily stored. In Figure 1.3 a computf'r enhanced overview of lVISC Home Terminal can be s0en. lVISC Home Terminal is abl0 to handle a total of 4.1 million TEU per y0ar.

Every week one vessel of each loop is scheel uled to arrive at MSC Home Terminal at a predetermined time. Vessels arriving at rvISC Home Terminal have to berth along the quay of the terminal. vVhile the vessel's time of arrival at the terminal is determined by the shipping company, the vessel's berthing position at the quay is cletermined by the port operator. The operator has to make sure that each vessel has enough space to berth. Vessels sailing in one loop have similar capacities, so they will also be of similar sizes. This makes it possible for the port operator to make one scheel ule of vessels berthing at the terminal every week. In this schedule space along the quay is assigned to each loop for a certain periocl of time. In this time the vessel has to be clischarged and loadecl again. In order finish the operation in time, quay cranes have to be assigned to the vessel for the discharge and loading operation, and a number of straddle carriers for the transport between the quay crane and the yard.

1.4 Details of MSC Home Terminal

As mentioned before, MSC Home Terminal functions as the European hub for MSC services. To fully make use of the capacity of the vessels, a lot of containers do not have a direct route to their port of destination. Instead they make a stop in Antwerp to be transshipped to another vessel and continue the journey to its port of clestination. These so-called transshipment containers make up approximately 60% of the total container hanclling at MSC Home Terminal, which is compared to other terminals a very high percentage. This means

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1.4. Details of MSC Home Terminal 5

Figure 1.3: Overview of MSC Home Terminal in Antwerp

that the berthing sched ule of the vessels can have a big impact on the sched ule to position the containers in the yard and vice versa.

Another special characteristic of MSC Home Terminal is the layout of the terminal. As mentioned before, the terminal makes use of the north and the south sicle of the Delwaicle doek. About 2500 meters of quay is situatecl at the south side of the doek and about 440 meters of quay is situated at the north side of the doek. Each part of the quay has also a yard situated bebind to store the containers. Most of the vessels are serviced at the south quay, but there is not enough space for all of the vessels to berth at one side. A few vessels have to berth at the other side of the water. As can be seen in Figure 1.3, if containers from these vessels have to be transshipped to vessels at the south quay, they have to travel all around the end of the doek to be stored in the yard over there. This means that the layout of this terminal causes some extra travel distance. While most of the transportation of the containers on the ground is done by straddle carriers, they are not designed to travel long distances. This is why another device, a multi trailer, is used for the transportation of containers from the one side of the doek to the other. Such a multi trailers consists of a modified truck which can pull a number of trailers. Containers are fetched from the yard and loaded onto the multi trailer by straddle carriers. A multi trailer transports the containers between the north and south side of the terminal, and another straddle carrier unloads the containers from the multi trailer and stores them in the yard.

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6 Chapter 1. Introcluction

1.5 Related work

The issues faced in operating a modern day container terminal have becorne more and more complex. In [Hen09], three different layers of decisions are distinguished, a strategie, tactical and operational level. Examples of strategie decisions are the size of a terminal, the type of operations performed and the number of quay cranes available at a terminal. These are the decisions made for a period of months. Decisions made for a middle-long period of time are called tactical. Tactical decisions include the scheduled arrival and departure times of vessels, the scheduled quay crane capacity assigned to each vessel, berth positions for each vessel at the quay and zones for various types of containers in the yard. Operational decisions can be seen as short term adjustments to the tactical plans. Vessels will not always arrive exactly in time, but can arrive early or late due to the effects of weather and cranes for example can break down. The container operator continuously has to rescheclule the current operations in order to deal with these disturbances and return to the tactical plan as soon as possible.

The studies of [Sta08], [Ste04], [Vis03] provide an overview of descriptions, classifications and solution methods for the main logistic processes in container ports. In these studies, the Berth Allocation Problem (BAP) has been iclentified as one of the key issues. In most studies container vessels are allocated in time and space to minimize a certain objective function. The objective is to create the best possible berthing plan. At most terminals however, the terminal operator cannot influence the berthing times of the vessels as they are determined by the shipping company. Vessels only have to be allocated in space, so a 1-dimensional packing problem remains.

!\lost studies like [Ima08], [Gua04] use a vessel turnaround time as objective. In [Ima08] is stated that the total travcl distance of straddle carriers strongly depends on the location of the containers in the yard. The assumption is made that all containers are stacked as close as possible to the vessel it was unloaded frorn. The total straddle carrier distance is approximated by the distance between the source vessel and destination vessel for transshipment containers. At MSC Home Terminal, transshipment containers are stacked close to the destination vessel, instead of the source vessel. Special containers like reefers, IMCO and empty containers are stacked at designated arcas. In [Hen09] the capacity of the stack is also taken into account. Capacity constraints make that containers cannot always be stacked at the most favorable position.

In [Henll] a method is suggested to solve the BAP while container positions are taken into account. The original MIQP is clivided into a Berth allocation part, formulated as a MILP and a Yard allocation (YAP) part, formulated as an LP. The two parts have the same objective function and are solved alternatingly. This method will serve as a starting point of this research. In the BAP studied in this research additional constraints will be taken into account to model the specific berthing constraints of the terminal under consideration.

For the YAP, the use of an additional means of transportation is added by changing the objective function and adding additional constraints.

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Chapter 2 Original model

As stated in section 1.5 the objective of the BAP is to minimize the total straddle carrier driving distance. In the case of a container that has to be transshipped from one vessel to another, this distance is the sum of the vessel-to-stack and stack-to-vessel distance. This means that the total straddle carrier driving distance depends on the berthing location of the vessels and the location of the containers in the yard. In [Hendriks09] the original BAP is formulated as two different optimization problems with the same objective function. One set of constraints is used to describe the berth allocation problem and another set of constraints is used to describe the yard allocation problem (YAP). For the sake of completeness, a summary of the original model of [Hendriks09] is presented in this chapter.

2 .1 Constraints

In Figure 2.1 a schematic representation of a container terminal can be seen. The relevant characteristics of the terminal are presented in the figure. The total size of the terminal is made up by the length of the quay Q and the width of the yard B. The yard is divided into N stacks of containers, in the figure N

=

15. Each stack has a capacity of Cn, n E {l, ... , N}

containers. The position of stack n is defined by the x and y coordinates, with the origin located at the lower left corner of the terminal. In Figure 2.1 two vessels v have berthed at the quay, each with length Lv. A total number of V vessels per cycle will berth at the quay and leave again.

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8 Chapter 2. Original model

Legend

lltt:l! Group of containers

§à Straddle carrier

□ Quay crane lml) Vcsscl

L, ⁴ L,

•

13

0 X

◄ ►

Q

Figure 2.1: schema.tic representa.tion of a container terminal

As mentioned in section 1.5 different types of conta.i11ers are imported into and exported out of the yard. In this case, a number of T

=

4 different types of containers is taken into account. Containers are imported from each vessel into the yard, and each container has a destination v

=

1, ... V for each vessel and destination O represents the "hinterland". Containers can also enter the yard from the hinterland, and be transported to one of the vessels. We assume that a.11 container destinations of the entire cycle are known, and fixed for a Jonger period of time. The timetable of arriving a11d departing vessels is also known, as it is determined by the shipping company. When we assume that a vessel is first completely discharged before it is loacled again with containers, we can divide the total berth time into a discharging and an loading part, proportional to the fraction of import and export containers of that vessel. The number of containers that have to be ( un) loaded is assumed to be distributed uniformly among the total (un)loading time.

At MSC Home Terminal, the berthing plan has a cyclic nature. Every week one vessel from every loop will arrive at the terminal. This means we can create one weekly berthing plan.

The time period of one week is divided into time slots of one hour. Because the arrival and departure times of all vessels are fixed, the vessels that berth simultaneously can be determined. Set S consists of those vessel pairs (·i, _j) where a.t some point in time vessel i and vessel

.i

are berthed simultaneously. In Figure 2.2 an example of a. berth plan can be seen. Note tha.t this is a cyclic schedule, so vessels like vessel 4 in the example can arrive at the end of a cycle and depart at the beginning of a cycle.

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2.1. Constraints

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E i=

--- - --- -- --- D '

[JD

7

Space

Q

Figure 2.2: Example of a berthing plan. In this example the set of Pairs S {(1,2), (1,3), (1,4), (2,3), (2,4), (3,4), (4, 7), (5,6), (6, 7)}

9

The containerflow from the vessels into the yard can now be represented by the parameters If.j(k) indicating the total amount of containers of type t flowing into the yard from source i, i E {O, ... , V} to destination j,j E {l, ... , V} at time k and O;(k) indicating the total amount of containers of type t flowing from the yard to vessel v, v E {l, ... , V} at time k.

All relevant parameters can be found in Table 2.1.

parameter definition

V N umber of vessels in the set

s

Set of pairs of vessels that berth simultaneously N N umber of stacks in the yard

Lv Length of vessel v [m]

J( Number of discrete time slots in the cycle Q Quay length [m]

B Terminal width [m]

Xn x-position of stack n Yn y-position of stack n

et

_n Capacity of stack n for containers of type t

I;j ( k) # containers of type t with source i and destination j flowing into the yard at time k

O;(k) # containers of type t flowing from the yard to destination v at time k Table 2.1: Model parameters

The transport of the containers is done by straddle carriers. We assume that there are

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10 Chapter 2. Original model

enough straddle carriers available to perform all the container moves necessary and enough quay cranes are available to discharge and load the containers from and onto the vessels.

The straddle carrier driving distance is measured in Manhattan distance, meaning the distance covered in x-direction plus the distance in y-direction.

2.2 MIQP

The objective of the BAP is to create a berth schedule for the vessels which minimizes the total straddle carrier clriving clistance. Constraints that have to be taken into account are non-overlapping of vessels, as two vessels can not be servicecl at the same place at the same time, and vessels cannot berth outside the quay.

Decision variables

Pv

·il (k)

IJTI

0~₁₁

(k)

( real) (natura!) (natura!)

Auxiliary variables

(boolean) ( real) (natura!)

Position of the center of vessel v

# containers of type t with origin ·i and clestination j flowing to stack n at time k

# containers of type t flowing from stack n to destination v at time k

{

1 if vessel i is positioned left of vessel j, 0 if vessel i is positioneel right of vessel j

Manhattan distance between the center of vessel v and stack n

# containers of type t with destination v in stack n at time k

The straddle carrier travel distance of a certain arnount of containers between their vessel and their stack is equal to the product of i) the amount of containers and ii) the distance between the corresponding vessel and the designated stack. Hence, we have to minimize the sum over all products of container amounts and their related distances. The container arnount are calculated in the YAP and are used as input for the BAP.

Objective function

(2.1)

Constraints on vessel positions

Pv > 'vv

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2.3. Alternatïng optimization 11

Pv < ^Q ^- ^L^v Vv

P; - Pj > ^L^{; + t}- Qe;J V(i,j) é S

2

Pi - Pj > ^L^{; +}^L^j- Q(l - C;j) V( i, j) E S

2

Zvn > Pv - Xn

+

Yn Vn,vé{l, ... ,V}

Zvn > -pv

+

Xn

+

Yn Vn,vE{l, ... ,V}

Zvn B - Yn Vn,v

=

0 (2.2)

The first two constraints make sure that the vessels are not positioned outside the quay.

Non-overlapping of vessels is ensured by the third and fourth constraint. The fifth and sixth constraint specify the ivianhattan distance between vessel v and stack n. The seventh constraint specifies the Manhattan distance between the hinterland v

=

0 and stack n.

Constraints on container positions

L

N ^iLn(k) ^Jl^?^,J^(k) ^V^t^,^{i, j, k}

n=l

L

N ^o~n(k) ^O~(k) ^{Vt,v, k}

n=l

V+l

S~n(k)

+ L

^i}vn(k)^- ^O~n(k) Vt, v, n, k

i=l

T V+l T V+I V+I

L L

⁸^~n(^k⁾ ^< ^Cn^-

L L L

^{i}vn ( k)} ^Vn,v ⁽²^.3)

l=l v=l l=l v=l i=I

The first two constraints ensure conservation of containers, i.e. all containers of type t with origin i and destination j that flow into the yard during timeslot [k, k+ 1) will be distributed over stacks 1, ... , N and all containers of type t with that flow from different stacks in the yard into vessel v during timeslot k should be equal to the sum of containers of type t that have to flow from the yard to vessel v during that timeslot. Because reefer, IMCO and empty containers (t

=

2,3,4) have designated stacks in the yard, parameters iLn(k) and

otn (

^k)are given for these types of containers. This means that in the stacking problem we only have to take 1 type of container into account.

2 .3 Alte rnating optimiz a tion

The original MIQP has an objective function which is non-convex and has many variables.

These properties make the problem hard to solve. As shown in the sets of equations (2.2) and (2.3), the variables for the berth and yard allocation can be separated and two different sets of constraints can be formulated, each of which describe now a convex problem. The total MIQP can now be solved by alternatingly solve the MILP of the berth allocation and

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12 Chapter 2. Original model

the LP of the yard allocation which are coupled in the objective function. The local optimum that is found by this alternating procedure is not guaranteed to be a global optimum.

The local optimum that is found strongly depends on the chosen initia! conditions.

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Chapter 3 Problem definition

To optimize the berth planning at a container terminal in combination with the yard planning is quite a challenge. That is why numerical solvers are used to solve this problem. One method for modeling such a scheduling problem is proposed in [Hendriks09]. Although the combined berth and yard planning problem is a non-convex MIQP, it can be turned into an alternating optimization problem consisting of an MILP and an LP. This method was tested on a terminal at the port of Antwerp.

The goal of this research is to apply the method proposed in [Hendriks09] to the current situation at MSC Home Terminal. Terminal specific constraints have to be taken into account for both the berth allocation and yard operations.

For the yard allocation the constraints are listed below.

• Large vessels can only berth at a certain part of the terminal

Not all quay cranes at the terminal are high or long enough to handle the largest vessels.

• Vessels in the set of mother vessels can not overlap in berthing position.

Even when arriving out of schedule, mother vessels must always be able to berth. To accomplish this even in the case of all mother vessels arriving at the same time, the mother vessels can not overlap in berth position.

• Vessels with the same Shipping Port Of Destination (SPOD) have to berth close to each other.

Last minute changes in loading schedules occur regularly, even when containers are already loaded onto a vessel. Experience has learned between which vessels containers can be exchanged by the shipping company at the very last moment.

In order to react to the last minute changes, these vessels need to berth close to each other.

For the yard operations, the use of a multi trailer is added to the model. Therefore the objective function is expanded and constraints are added.

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14 Chapter 3. Problem definition

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Chapter 4 Berth allocation at MSC Home Terminal

In this chapter we explain how the berthing problem for MSC Home Terminal is modeled.

Some extra constraints will be acldecl to the original berth model to model the specific layout of the terminal and some of the operational issues that have to be taken into account in this particular terminal. In each section one of the additional constraints will be discussed.

4.1 Additional constraints for terminal layout

A schematic overview of MSC Home terminal can be seen in Figure 4.1. In order to reduce the number of variables in the model, the layout of the yard has been simplified. At MSC Home Terminal the yard at the south side of the quay consists of 39 groups of containers, which are called stacks. These stacks are arranged 13 wide (in x-direction) and 3 deep (in y-direction). To be able to give clear instructions to the straddle carrier drivers, these stacks are grouped in 7 zones. Such instructions can for instance be to store a container maximally 2 zones from the vessel it was discharged from. In the model we will use these zones to indicate the location of a container in the yard, and we will refer to them as stacks. As we can see in Figure 4.1 there are 7 stacks at the south side of the terminal and 2 at the north side.

As mentioned in section 1.4 the layout of MSC Home Terminal has some characteristics that have effect on the implementation of the BAP. MSC Home Terminal makes use of both the north and south side of the terminal. At the end of the terminal no vessels can berth and no containers can be stored. In Figure 4.1 we see three different types of stacks in the yard. The stacks with no name inside are stacks that are usecl for regular 20ft or 40ft containers. The reefer and Imco stacks are each used for a special type of container. Reefer containers are temperature controlled, and therefore need electricity. Imco containers contain hazardous goods which have to be stored separately.

In figure 4.2 the schematic representation of MSC Home Terminal is changed to match the standard representation of a container terminal as described in section 2.1. The north and south side of the terminal are now placed next to each other. We use both sides of the quay together as one long quay, with a space where no vessel can berth in between.

15

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16

1 1

' 1

1 ,_

[1mco

Chapter 4. Berth allocation at MSC Home Terminal

container yard 2

i

9 8 1 •

i 1l

i er

quay cranes

vessel

>

vessel

>

²^km ^vessel

>

quay cranes quay cranes

1

1 2 3

1

5 6 7

1

[1mco ^Reefer ^Reefer

container yard 1

Figure 4.1: schematic representation of MSC Home terminal

ship

>

²^km ^ship

^>

quay cranes quay cranes

1 1

2 3

1

4 5 6

~~

Reefer Reefer

container yard 1

T,

i 7

1

Î2

1 1 1 1

:;;

~

sh,p

>

quay cranes

l

^L⁹

container yard 2

Figure 4.2: modified representation MSC Home terminal

In section 2.2 we created constraints on vessel position. Non-overlapping constraints are used to make sure that two vessels can not berth at the same place, at the same time. We can use these constraints to create a space where no vessels can berth. A non-existing vessel,

VJ, is placed between the two sides of the terminal. This vessel will be positioned there for the entire length of the cycle, so no other vessel can berth at that position.

constraint for v1

p1 = ( 4.1)

By setting the berthing time of VJ equal to the cycle length of the model, every real vessel

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4.2. Additional constraints for large vessels 17

will overlap in time with v1 . This is why every vessel in combination with v1 is added to set S. The length of this imaginary vessel will be equal to the distance between the north and south side of the terminal.

No container stacks are located at that end of the quay. The positions of the container stacks are fixed, so in the model simply no container stacks are placed at these positions.

4.2 Additional constraint s for la rge v essels

Next to the characteristic layout of MSC Home Terminal, also some operational constraints have to be taken into account. Vessels of different sizes berth at the terminal. As vessels increase in size, most of the times vessels also increase in height. In fact, containers on some of the largest vessels are stacked so high that not all of the quay cranes at MSC Home Terminal can reach over them. This means that the largest vessels can only berth at a specific area of the quay. In the situation at MSC Home Terminal, this area consists of the left part of the south side of the terminal. This fact is used to construct the constraint specified by equation 4.2. The vessels to which this constraint applies are specified by the terminal operator and added to the set of large vessels S1.

Constraint for large vessels

(4.2)

4. 3 Additional c onstraint s for mother v essels

As mentioned in section 1.4 MSC Home Terminal functions as the European hub for MSC services. Smaller vessels transport containers to MSC Home Terminal that have to be shipped again on another (bigger) vessel. One mother vessel takes care of the long distance transport, and the feeder vessels take care of the local transport so the mother vessel does not have to call at many small ports. These mother vessels have priority over the feeder vessels. Whenever a mother vessel calls at MSC Home Terminal, quay space has to be available, even when the vessel does not arrive at the right time. When a mother vessel doesn't arrive at the right time, the feeder vessels will be moved to an other position. To ensure that the mother vessels can always berth, two mother vessels can not have the same berth position in the schedule. To prevent overlapping of the mother vessels' berth positions, all combinations in pairs of mother vessels are added to set Sm, to which the overlapping constraints apply.

Constraints for mother vessels

p; - Pj

>

^L^;

+

Lj

- Q · eij Y(i,j) é Sm 2

Pi - Pj

>

^L^{; +}^Lj- Q · (1 - eij) Y( i, .i) é Sm

2 ( 4.3)

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18 Chapter 4. Berth allocation at MSC Home Terminal

4.4 Additional constraints for SPOD

One of the advantages for MSC in being a big shipping company is the amount of routes they service. This can be used by MSC to increase flexibility. How this also affects the terminal operator can be illustrated by a small example, indicated by figure 4.3.

Figure 4.3: example of trading routes

In this example, vessel A sails on the route from Antwerp to Asia, and makes a few stops along the route. One of these stops is Istanbul. Vessel B sails on a route only from Antwerp to Istanbul and back.

Both of the vessels will call at the port of Istanbul, so both of them can be used to ship a container to that port. When vessel B is already full, and vessel A is not, the shipping company can schedule a certain container to be shipped to Istanbul by vessel A. lt is possible that some last minute changes in the planning are made and vessel B, that originally was scheduled to be full, still has some space left. For various reasons, the shipping company may decide that the available space on vessel B will be filled with containers that were originally scheduled to be shipped by vessel A. The terminal operator however may already have received the container at the terminal and stored it in the yard in such a way that it is located close to vessel A. When the distance in berthing position of vessel A and vessel B is very large, straddle carriers will have to tra.vel a long distance to deliver the container to the right vessel. When this applies for more containers and there is only limited time to react to these (sometimes last minute) changes, it may not even be possible to get all the containers transported over such a long distance in time. For this reason, it would be beneficia! for the terminal operator to position the two vessels A and B in the example close

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4.5. MIQP 19

to each other in the berthing schedule.

The example above illustrates why it is convenient to berth certain vessels close to each other. These pairs or groups of vessels, as well as the maximum relative berthing distance that is allowed between these vessels, are chosen by the terminal operator, based on experience. All combinations of pairs of vessels to which the SPOD constraint applies are added to set S8 in the model.

SPOD constraint

(4.4)

4. 5 MIQP

In the previous sections of this chapter the MSC Home Terminal specific constraints are explained. We can now formulate the entire BAP for MSC Home Terminal. Note that only the constraints on vessel position have changed compared to the original model described in section 2.2, and some parameters are added. These constraints and parameters are marked with an asterisk.

parameter definition

V N umber of vessels in the set

*vi Imaginary vessel that models the end of the quay

s

Set of pairs of vessels that berth simultaneously (including v₁), extended with pairs of mother vessels

*S1 Set of large vessels

*Ss Set of pairs of vessels that need to berth close to each other D.;j Maximum distance between two SPOD vessels

N N umber of stacks in the yard Lv Length of vessel v [ m]

K N umber of discrete time slots in the cycle Q Quay length [m]

B Terminal width [m]

*Ti x-coordinate of the end quay 1

*T2 x-coordinate of the front quay 2 Xn x-position of stack n

Yn y-position of stack n

et

_n Capacity of stack n for type t

Ifj ( k) # containers with source i and destination j flowing into the yard at time unit k

Ot(k) # containers flowing from the yard to destination v at time k Table 4.1: Model parameters

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20 Chapter 4. Berth allocation at MSC Home Terminal

Position of the center of vessel v Pv(k)

i~jn ( k) # containers of type t with origin i and destination j flowing to stack n during time unit k

# containers of type t flowing from stack n to destination v cluring time unit k

Auxiliary variables

{

1 if vessel i is positioned left of ves ·el j, 0 if vessel i is positioneel right of vessel j

Manhattan distance between the center of vessel v and stack n

# containers of type t with clestination v in stack n cluring time unit k Objective function

Constraints on vessel positions

> ^Lv

Pv ^-

2

Pv < ^Q^- ^L^v

L

+L

Pi - Pj > ^,. ^J - Qe;j

2

P; - PJ > ^L;⁺^L¹- Q(l - e;j)

T1 +2 T2

*

^PI 2

*

^Pv ^< ^Q1

*

^{P; -} ^PJ ^< ^~^s

Zvn > Pv - Xn

+

Yn

Zvn > - pv + Xn + Yn

Zvn B - Yn

Constraints on container positions

L

N ^iLn(k) n=I

L

N ^o~n^(k) ^O;(k) n=l

V+I

Vv Vv V(i,j)t S V(i,j)tS

V(v) t S1 V(i,j)tSs Vn,vt{l, ... ,V}

Vn,vt {l, ... ,V}

Vn,v

=

0

Vt,i,j,k

Vt, v, k

s~n(k)

+ L

^iivn^(k)^- ^O~n(^k) ^Vt^{, v}^,ⁿ^{, k}

i=l

T V+l T V+l V+I

L L

^s~n(k) ^< ^Cn^-

L L L

^{i;vn (k)} ^Vn^,v

t=l v=I t=l v=l i=l

( 4.5)

(4.6)

(4.7)

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4.6. Validation 21

4.6 Validation

In this section the new constraints on vessel position are validated. In order to do so, a small scale example is implemented and tested for each constraint we added in section 4.5.

validation scenarios

• Original model

• Large vessels

• Mother vessels

• SPOD constraint

When we test a new constraint in the example, the constraints of the original model cannot be violated. The new constraints we added each apply to a specific set of vessels. The behavior of the other vessels is not directly affected by the new constraints. In the example, three vessels are positioned along a quay with a length Q = 10 and /( = 5. Three container

·tacks are located in the yard. Table 4.2 shows for each vessel how many containers will go to each stack.

vessel stack 1 stack 2 stack 3

A 15 0 0

B 10 5 0

C 0 0 20

Table 4.2: container movements in the validation examples

4.6.1 Original model

In section 2.1 the constraints for the berth model are stated. These constraints make sure that no vessel can berth outside the quay, and no vessels can overlap in position and time.

Next to that, the model bas to make sure that the vessels are positioneel in such a way that the total straddle carrier distance is minimized with respect to the given positions of the containers in the yard. These properties are validated in this example.

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22 Chapter 4. Berth allocation at MSC Home Terminal

, ,

^······ ...

- [ ~ ]

A

' ' ' '

1)-!--- - + - - - + - - - - + - - - - + - - - l - - t - - - - + -- - + - - - + - - - - +-

I) 11) l:

[J

Figure 4.4: All vessels are positioneel inside the quay and do not overlap

vessel position clistance to clistance to clistance to weightecl stack 1 stack 2 stack 3 clistance

A 2 1 3 7 15

B 5 4 0 4 40

C 9 8 4 0 0

Table 4.3: Straddle carrier clriving clistance

In this example the containers for wssels A and B are locatecl at the left of the quay.

For both of the vessels, the berthing position at the middle of stack 1 generates the least straddle carrier driving clistance. Because these two ves:;els overlap in berthing time, the non-overlapping constraint is testecl. Next to that, in figure 4.4 it can be seen that none of the vessels is allowed to berth outside the quay, while that position is favorable for vessel A with respect to the objective function. In table 4.3 the position of the vessels and t.he distance to the stacks is inclicated. When we sum the straddle carrier driving distance of vessels A, B and C we see that the total straddle carrier driving distance is 55 meters. When othcr possibilities are checked, we see that this schedule has the least amount of straddle carrier driving clistance when all constraints are taken into account.

4.6.2

Large vessels

In order to validate the large vessel constraint, we acid this constraint to the example. All parameters are kept the same, only this time we assume that vessel C is too large to berth at its favorable position, so it is addecl to set S1• We assume that vessel C can only berth at the left side of the dotted line in figure 4.5. When we look at the figure, we see that this constraint has not affectecl the other two vessels. Vessel C is moved to the left over a distance of 4 meters, so this constraint generates 80 meters of extra straddle carrier distance, compared to the original example. With the Large vessel constraint acting on vessel C, this is the schedule with the least amount of straddle carrier clriving distance.

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4.6. Validation

k

:, - -- --- --- - ----

^-^□^-

--- --- -- --- -:

C :

1 1 1

' 1

13 A

() +----+---+----+---+---+-- - - + - - - + - -- - + - - - + - - - + -

() 10 ,·

[J

Figure 4.5: Vessel C can only berth at the left side of the quay

vessel position distance to distance to distance to weighted stack 1 stack 2 stack 3 distance

A 2 1 3 7 15

B 5 4 0 4 40

C 5 4 0 4 80

Table 4.4: Straddle carrier driving distance

23

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24 Chapter 4. Berth allocation at MSC Home Terminal

4.6.3 Mother

vessels

Mother vessels are vessels that have a high priority to berth. They must always be able to berth, at any time in the schedule. This is why two mother vessels cannot overlap in berthing position. To valiclate the mother vessel constraint we acid vessel pair (B, C) to set Sm. Both vessels had the same berthing position in the previous example. Because vessel B cannot overlap with vessel C in berthing time anymore, it is movecl to the right sicle of ves. el C. The position of vessels A and C is not affectecl by this constraint, so this constraint generates an extra 30 meters of straddle carrier driving distance. An other solution coulcl for instance have a scheclule where vessels B and C are both move 2 steps to the left. Now vessels B and C would still not overlap in berthing position. That schedule however would gencrate a total straddle carrier clistance of 175 meters, 10 more then the schedule we see in Figure 4.5.

k

:, -- - - -- - - - -- -- - - --

^-□-

--- --- -- -- - ---- :

C :

' ' '

A

'

□

' '

()+-- - + -- - + - ---+-- - +- - - i - - + - - - - + --' -+---- + - - - + -

() 111 .T

[J [J

Figure 4.6: Mother vessel constraint applied to vesselpair B and C

vessel position distance to distance to clistance to weightecl stack 1 stack 2 stack 3 clistance

A 2 1 3 7 15

B 7 6 2 2 70

C 5 4 0 4 80

Table 4.5: Straddle carrier clriving distance

4.6.4 SPOD constraint

With the SPOD constraint the clistance between berthing position of two vessels is limitecl.

Again we acid this constraint to the example and apply it to vessels A and B. This means that we acid vessel pair (A, B) to the set S8 • We assume that these two vessels have to berth right next to each other. When we look at figure 4.4 we see that vessel A is now positioneel next to vessel B, and that it is overlapping in berthing time with vessel C. This is allowed

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4.6. Validation 25

because the vessel pair (A, C) is not in set Sm. An other solution could for instance have a schedule where all three vessels are moved two steps to the right. All constraints would still be respected, but that schedule would generate 20 meters of extra straddle carrier distance.

k

13 A

() +--- - + - - - + - --+---+----+-- ! - - - + - --+-- -+---+--

() 10 X

[J

Figure 4.7: SPOD constraint applied to vessel A and C

vessel position distance to distance to distance to weighted stack 1 stack 2 stack 3 distance

A 2 1 3 7 15

B 5 4 0 4 40

C 3 2 2 6 120

Table 4.6: Straddle carrier driving distance

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26 Chapter 4. Berth allocation at MSC Home Terminal

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Chapter 5 Yard Allocation at MSC Home Terminal

In Chapter 2 the original BAP is formulated as an MIQP. In Chapter 4 extra constraints have been added to the model in order to implement the characteristics of the berthing procedure at MSC Home Terminal. As described in section 1.4, at MSC Home Terminal multi trailers are used to transport containers over long distances in the yard. This means that the terminal operator has two different means of transportation at his disposal to transport a container in the yard, each of which has its specific characteristics. In order to add this functionality to the model, some parameters and constraints have to be added and the cost function has to be adapted.

5.1 Yard layout

In Figure 5.1 we see a schematic representation of MSC Home terminal in Antwerp with nine stacks in the yard. As we explained in section 4.1, this representation of the stacks in the yard is a simplified version of MSC Home Terminal. In Figure 5.1 we see no stacks for reefer or imco containers. These stacks are not modeled in the yard allocation problem because not much optimization can be done there. Not very much possibilities exist, and the reefer and imco containers are simply stored in the designated stack that is closest to the vessel it is discharged from. As a result, in our model the multi trailer will never have to transport some of these containers.

A multi trailer consists of a special truck that pulls multiple trailers. Each trailer can carry one 40 ft or two 20 ft containers. In this way the multi trailer can be compared to a small train on wheels. At MSC Home Terminal the multi trailer has two fixed interchange zones where containers can be loaded onto or discharged from the trailers. The multi trailer travels along a fixed route between these two interchange zones. In Figure 5.1 these two interchange zones, named MZB and MZD, and the multi trailer path can be seen.

At the interchange zones, straddle carriers discharge containers from the multi trailer and load new containers on the multi trailer again.

27

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28 Chapter 5. Yard Allocation at MSC Home Terminal

D D D D

440m ^□

□

330m

D

... ---.!!!!!!!!!~---_J!!!!!!!!e~_..2.:

D D D D D D D D D D D D

2

quay c,anas

1 ~ 40 :,,: m ~--~!!!!~:.J

D D D

□ □

□□□□□□□

_MZB

~

Figure 5.1: schematic representation of MSC Home terminal

5.2 Multi trailer variables and constraints

In the original MIQP each container that needs to be loaded onto a vessel will be transported by straddle carrier directly from the yard to the vessel, and the other way around. With the introd uction of a multi trailer to the model, an alternative way of transport can be used. When transport by multi trailer is chosen, a container will be transported by straddle carrier from its position in the yard to the interchange zone that is located at that side of the terminal. There it will be placed onto the multi trailer and be transported to the interchange zone at the other side of the terminal. Once it has arrived there, the container will be discharged by a straddle carrier, and be stacked in the yard again. After this transport the container still needs to be transported to the vessel by straddle carrier. This means that the transport by multi trailer does not actually transport a container from the yard to a vessel, but only from one stack in the yard to an other stack that is located closer its destination.

Pv /_tJn:. (k)

Position of the center of vessel v

# containers of type t with origin i and destination j flowing to stack n d uring timeslot k

# containers of type t flowing frorn stack n to destination v during timeslot k

# containers of type t with destination v flowing from stack m to stack n at time unit k

Table 5.1: Decision variables

Eindhoven University of Technology MASTER Modeling the use of a multi trailer in a container terminal Ansems, R.P.W.M.