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

28 Chapter 5. Yard Allocation at MSC Home Terminal

D D D D

440m ^□

□

330m

D

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

2

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

□ □

□□□□□□□

~

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 trans-ported 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 inte r-change 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 ves-sel, but only from one stack in the yard to an other stack that is located closer its destination.

Decision variables

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

5.2. Multi trailer variables and constraints 29

30 Chapter 5. Yard Allocation at MSC Home Terminal

we can see in equation Equation 5.6, the cost for transporting a container by multi trailer consists consists of three parts. The values of Zmu and Zun depend only on the distance between stack and interchange zone. As mentioned before, the value of Cu is constant.

Objective function

5.3 Multi trailer cost

In the original model described in chapter 2, the cost function only depends on straddle carrier distance between the vessels and the stack in the yard. In section 5.2 we introduce three additional variables to describe the cost of multi trailer transport. When the multi trailer is used, first the container has to be retrieved from the yard and be transported to the interchange zone. This is clone by straddle carrier, therefore the cost of this action is modeled as the manhattan distance that has to be covered. Variables ^Zmu and ^Zun in table 5.2 describe this distance for every stack in the yard. The multi trailer travels along a fixed path, so the distance covered by multi trailer itself is always the same. However, not all trailers always have to be full before the multi trailer will start moving. It may even be the case that the multi trailer will have to make an empty one-way trip to collect containers at the other side of the terminal. In the actual situation at MSC Home Terminal, cost c"

will therefore depend on the number of containers that are transported in one multi trailer move. This fact is not taken into account in this model. However, in practice the multi trailer is almost always fully loaded. Therefore, we assume that the cost of a multi trailer move can be expressed as a cost per transported container.

In figure 5.2 an example illustrates the total cost fora transshipment container when making use of the multi trailer. The total cost is the sum of five moves. Four moves are related to straddle carrier distance and the cost of the multi trailer move itself is fixed.

In the original model of [hen08] all costs were expressed in straddle carrier driving distance.

When we introduce the multi trailer to the model, this poses a problem. Using the multi trailer has some advantages that can not be expressed in terms of distance. For instance, multi trailers are designed to travel Jonger distances while straddle carriers are not. When straddle carriers travel long distances tires wear out faster and because of the instability of their construction, more maintenance is needed. Another advantage of the multi trailer is the transportation of multiple containers in one time. Straddle carriers transport the containers one by one, while multi trailers can transport eight TEU in one time. Therefore multi trailers consume less fuel per container and only one operator is needed to transport these containers. Since the use of the multi trailer will reduce the distance the straddle ca r-riers drive in the yard, there will be less congestion in the yard. Therefore, straddle carriers can work faster as there will be less situations where staddle carriers have to slow down or stop to let another staddle carriers pass. There are also some operational disadvantages to the use of multi trailers. Multi trailers can not pick up containers by them selves, they have to be loaded by straddle carriers or other devices. In practice, at MSC Home Terminal

5.4. Validation 31

1 ~ - - ~ 1

: 1 MZD 1 :::::==-=:..-=:..-=..--=,~