Re-marshalling in automated container yards with terminal appointment systems

Abstract

As a result of scarce land availability, growing competition and throughput, container terminals are increasing the stacking height of yard blocks to fulfil the demand for storage area. Due to inadequate retrieval information at initial stacking, shuffle moves can occur during retrieval operations as containers may be stacked in a sequence which does not correspond to the actual retrieval sequence. Automated stacking cranes can perform re-marshalling during periods of no crane workload to shift unproductive moves during retrieval operations to phases of idle time. Terminal appointment systems (TAS) enhance landside sequence information when external trucks (XT) announce their arrival beforehand. Under these circumstances, it is beneficial for terminal planers to understand the effects of using re-marshalling in combination with TAS. The purpose of this work is to introduce an online rule-based solution method for the re-marshalling problem with and without TAS. A simulation model of a fully operating yard block is used as environment to compare the proposed method with a benchmark heuristic from the literature. All tests are conducted for single and multiple Rail-Mounted-Gantry-Crane systems with different yard block sizes. It is also shown that solving the re-marshalling problem with the proposed algorithm generates results that reduce shuffle moves by 30% on average and by up to 50% in the best case, while always performing better in the worst case in comparison with not performing re-marshalling. Afterwards, influences on the method of selected TAS parameters are evaluated numerically. Results show that imprecise XT arrival information, not deviating above a certain threshold, significantly contribute to reducing congestion by mitigating XT waiting time and levelling arrival peaks. These benefits can be achieved without imposing restrictions on the arrival schedule preferred by XT companies.

Appendices

Appendix 1: Strategy comparison of the means of performance indicators in multi-RMG-systems

See Tables 15, 16 and 17.

Table 15 Strategy comparison of the means of performance indicators for 10 simulation runs in TRMG-systems

Table 16 Strategy comparison of the means of performance indicators for 10 simulation runs in DRMG-systems

Table 17 Strategy comparison of the means of performance indicators for 10 simulation runs in TriRMG-systems

Appendix 2: Comparison of FCQ/TAS for different participation shares regarding main performance indicators

See Figs. 9 and 10.

Fig. 9

FCQ behaviour for participation shares in 36/8/5. a Re-marshalling moves, b shuffle moves, c total vehicle waiting time, d XT waiting time for retrieval jobs

Fig. 10

FCQ behaviour for participation shares in 36/8/6. a Re-marshalling moves, b shuffle moves, c total vehicle waiting time, d XT waiting time for retrieval jobs

Appendix 3: Comparison of FCQ/TAS for different slot lengths regarding main performance indicators

See Fig. 11.

Fig. 11

FCQ behaviour concerning container handling and waiting time for slot lengths in 44/10/6. a Re-marshalling moves, b shuffle moves, c XT waiting time for retrieval jobs

Appendix 4: Comparison of FCQ/TAS for different announcement times regarding main performance indicators

See Figs. 12, 13 and 14.

Fig. 12

FCQ behaviour concerning container handling for announcement times in 36/8/5. a Re-marshalling moves, b shuffle moves

Fig. 13

FCQ behaviour concerning container handling for announcement times in 36/8/6. a Re-marshalling moves, b shuffle moves

Fig. 14

FCQ behaviour concerning landside retrieval jobs for announcement times. a 36/8/5, b 36/8/6

Appendix 5: Detailed working example of Re-marshalling and TAS

After formalising the RMP and TAS separately, Fig. 15 gives an illustrative example of available container data and the generic mechanism that underlies the combined problem structure and serves as main working rationale for the subsequent development of the solution method. In more detail, it should provide an understanding of the fuzziness of assigning a container to a suitable slot in case of container retrieval data being available as intervals only. The decision rationale behind every optional container movement is explained for the movement of three containers. The three containers in this illustrative example are used as representatives for the movement types that can occur in the yard block. Hence, it shows the decisions that must be performed by an algorithm for solving the RMP with non-deterministic data. For reasons of clarity, only three bays for exchanging containers are considered here.⁶ The three bays are situated close to the waterside (blue), block centre (grey) and landside (green), respectively to illustrate the necessity of including crane movements into the solution process for the RMP. In this instance, a bay b contains four stacks s that are numbered consecutively from 1 to S throughout all three considered bays with four tiers per stack available for storage. An approximated time interval of retrieval is stated for every container, if available. This is the case for containers departing by deep sea vessel (marked by ‘W’) indicated by its berthing time and for XT (marked by ‘L’) indicated by the booked time slot through TAS. If no time interval is specified, departure data of the container’s retrieval vehicle are not available, i.e. for feeder vessels (marked by ‘W’) and XTs that have not booked a time slot (until the observed time point). Note that the interval depends on the mode of transport and TAS parameter for the slot length.

Fig. 15

Visualisation of the RMP with TAS information

At the time of no retrieval or storage jobs at the handover areas, the RMGC initiates its re-marshalling schedule. The aim is to find a blocked container in the yard that optimises crane movement and overall clearance of mis-overlays before a shuffle move of any container is induced. In the following, the RMP is decomposed into two main decision problems and a resulting procedure is described how a re-marshalling schedule may be constructed in Fig. 15:

Decision 1: Identification of a source stack for the relocation of its top container

Bay b might be used for sourcing a container being close to the current crane position and holding several stacks with potentially mis-overlayed containers in them. Analysing the approximated retrieval times, it is evident that no exact calculation of mis-overlays can be conducted as the intervals are overlapping. In this scenario, any container in bay b may be blocked by the container above depending on the exact retrieval time. An estimation of mis-overlays is particularly aggravated by containers departing by randomly arriving vehicles at the handover as in stacks $s+1$. Hence, a crisp decision about a specific container is not always possible. A solution method must define criteria to evaluate the suitability based on these imprecise intervals. Conceivably, the bottom container in stack $s+2$ seems to be a reasonable candidate for re-marshalling. Depending on the exact retrieval time of the stack’s topmost container, the identified container is blocked by two containers and will leave the yard block as one of the first. Thus, the urgency to free up this container is high and the precision of intervals is more reliable in comparison to the other stacks.

Decision 2: Stacking the sourced top container on a suitable stack

In finding a suitable new stacking position, Decision 2 faces the same issues with reference to overlapping time intervals as Decision 1. As a consequence, multiple options arise at this point. Firstly, the range of crane movement must be considered. On the one hand, there is a motivation to stay close to the source stack in order to avoid long moving distances. Notably, staying in the same bay b would avoid crane portal movement and the RMP would relate directly to the PMP. On the other hand, bay b is situated at the block centre implying that the crane has to move a long distance to the handover area of the respective container at the time of retrieval. As a result, the RMP does not only address the transformation of shuffle moves into re-marshalling moves but also shifts crane movement at the time of retrieval to movement during idle times. Following options arise to perform the needed re-marshalling move:

Move 1: Stacking a container leaving by deep sea vessel

Suppose the topmost container of stack $s+2$ (subsequently referred to as $c^{*1}$) was chosen in Decision 1. $c^{*1}$ is leaving the terminal by deep sea vessel as indicated by the given time interval and the index ‘W’. The blue arrow labelled ‘Move 1’ shows three possible stacking positions for $c^{*1}$ (a, b, c):

• a) Stack 1 could be used as there is only a small overlapping time interval of the two bottom containers with $c^{*1}$ and the top container is indeterminate, thus, posing a potential not to induce any shuffle move in future (dashed line).

• b) Stack 3 appears suitable as its top container has the same interval as $c^{*1}$ indicating that they are departing by the same vessel and may be interchangeable during online stowage planning (see Sect.  4.1). The bottom container of stack 3 will most likely leave the yard block at a later time than $c^{*1}$ (solid line).

• c) Stack 4 has one container departing by feeder as there is no time interval available. Placing $c^{*1}$ on this stack could either eliminate or induce a new shuffle move (dotted line).

Depending on the retrieval times of the two containers without time interval in stacks 1 and 4, an assessment of the stacking position can be made. The average container dwell time can be used as auxiliary estimator of the retrieval time for containers randomly leaving the block. However, the uncertainty in comparison to the fixed slots of berthing and TAS makes the mis-overlay calculation imprecise. Assuming similar arrival times of both containers without time interval in stacks 1 and 4, ‘Move 1a’ could be beneficial as the interval overlapping is small and this stack has potential to be a full stack without any mis-overlays. ‘Move 1c’ has also potential not to induce a mis-overlay. However, it seems to be less preferable since a full stack which is free of any mis-overlays leaves more slots open for future re-marshalling and stacking moves than a slightly occupied stack which is also free of any mis-overlays. If ‘Move 1a’ is chosen, there are more options to place containers on stack 4 that leave the block later than $c^{*1}$. In contrast, ‘Move 1b’ might be the best option in terms of balancing the uncertainty of inducing mis-overlays and leaving space for future handling moves. There is only slight overlapping of intervals so that most certainly this will not induce any mis-overlays.

Move 2: Stacking a container with no retrieval information and long distance to its handover area

While the bottom container of stack $s+2$ is still blocked it does not need to be always advantageous to do an empty crane move from bay 1 to bay b. Depending on the urgency to free up this container, another container near the current crane position of bay 1 could be selected to be moved towards the direction of bay b. Therefore, Decision 1 has to be performed again which leads to the conclusion that the only appropriate stack is the second one as it is the only one containing containers leaving by XT. If a mandatory TAS is applied, there is even certainty of a mis-overlay in this stack because the two containers without time intervals would have been booked if they left prior to the bottom container. As a consequence, the top container (subsequently referred to as $c^{*2}$) of stack 2 is chosen. With respect to the new stacking position of $c^{*2}$, there is only one possible stack in bay b that seems suitable eliminating the mis-overlay. The safest stack to place $c^{*2}$ is $s+1$. Although there still might be a mis-overlay induced, ‘Move 2’ is separating containers with known time intervals from containers with unknown time intervals, thus, facilitating the calculation of mis-overlays within stacks with known time intervals. Additionally by applying this move, $c^{*2}$ has passed half of the distance to its handover area outside of the time of retrieval. Distance-wise, it could be even more beneficial to move container $c^{*2}$ to bay B being closest to the handover area. However, as the urgency to free up the bottom container in stack $s+2$ is high, it seems advisable to put $c^{*2}$ near this stack. Thus, the crane is immediately close to its next re-marshalling job.

Move 3: Stacking a container leaving by XT with TAS information

The last type of container movement refers to the re-marshalling of containers leaving the block by XTs that booked a time slot through TAS. By dropping container $c^{*2}$ on stack $s+1$ the current crane position is at bay b again. The bottom container in stack $s+2$ is still (urgently) blocked by one container on top of it. Thus, Decision 1 should naturally lead to selecting the latter (subsequently referred to as $c^{*3}$) as suitable for re-marshalling. There are three potential slots for executing ‘Move 3’ towards the bay close to the relevant handover area (bay B) as stack $S-1$ is already fully occupied in this example:

• a) Stack $S-3$ stores only containers leaving by XT. Two of them have not been booked yet implying that these containers will leave later than $c^{*3}$ assuming a mandatory TAS. The middle container has the same interval as $c^{*3}$. Note that containers leaving by XT in the same interval are not interchangeable like in the case of deep sea vessels as they are picked up by different vehicles. As a consequence, this stacking move poses a risk for a shuffle move.

• b) The time interval of $c^{*3}$ is situated at the middle of the interval of the only container in stack $S-2$. The formation of a new mis-overlay cannot be stated definitely at this point.

• c) A ground slot is available in stack S. Ideally, these should be occupied by containers with very late retrieval time to facilitate a flexible stacking of many containers on top of them. $c^{*3}$ is a container leaving soon in comparison to the other containers in the block. However, stacking in this slot guarantees the elimination of future shuffle moves and opens the opportunity to yield the stack empty again soon.

In the case of ‘Move 3’, no clear identification of a target stack regarding the elimination of mis-overlays and leaving space for future handling moves can be made. Based on the generic analysis before, it can be stated that ‘Move 3a’ and ‘Move 3c’ seem to be preferable to ‘Mover 3b’ and that the actual decision depends on the design of the solution algorithm.

The representative instance discussed here illustrates the fuzziness in solving the RMP in terms of the three operationalised objectives for the overall goals introduced before:

• Reducing the potential for additional mis-overlays.

• Reducing empty crane movement.

• Leaving space for future shuffle-free container stacking.