Exact and heuristic methods for placing ships in locks

doi:10.1016/j.ejor.2013.06.045

European Journal of Operational Research

Volume 235, Issue 2, 1 June 2014, Pages 387-398

https://doi.org/10.1016/j.ejor.2013.06.045 Get rights and content

Highlights

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Complete and concise mathematical model for the ship placement problem.
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Exact decomposition method.
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Fast, near-optimal heuristics.
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High quality results on real-life instances.

Abstract

The ship placement problem constitutes a daily challenge for planners in tide river harbours. In essence, it entails positioning a set of ships into as few lock chambers as possible while satisfying a number of general and specific placement constraints. These constraints make the ship placement problem different from traditional 2D bin packing. A mathematical formulation for the problem is presented. In addition, a decomposition model is developed which allows for computing optimal solutions in a reasonable time. A multi-order best fit heuristic for the ship placement problem is introduced, and its performance is compared with that of the left-right-left-back heuristic. Experiments on simulated and real-life instances show that the multi-order best fit heuristic beats the other heuristics by a landslide, while maintaining comparable calculation times. Finally, the new heuristic’s optimality gap is small, while it clearly outperforms the exact approach with respect to calculation time.

Introduction

When entering or leaving a port, ships often pass one or more locks. So do barges travelling on a network of waterways. The locks provide a constant water level for ships while loading or unloading at the docks, or they control the flow and the level of inland waterways.

The growing number of container shipments causes high demands on sea ports (Wiese, Suhl, & Kliewer, 2010). Improving the ship handling can reduce their time in port and make a seaport economically more attractive, engendering a strong competition between (geographically close) seaports (Bish, 2003, Chen et al., 2006, Cullinane and Khanna, 2000, Günther and Kim, 2006). While many aspects of handling ships and containers in seaports have been extensively researched (Stahlbock & Voß, 2008), one key component of the port’s infrastructure has received little attention: the locks. A suboptimal usage of the locks’ capacity can however strongly increase the handling times of ships. When the lock is unable to transfer a given ship in time, this ship could miss its time window at the terminal, leading to a strong increase in total time in port and a reduced efficiency of the terminal. Improved operation of these locks can therefore play an important role in increasing a port’s efficiency and economical attractiveness.

The expected increase of intermodal transport is a major incentive for improving lock efficiency on inland waterways (European Commission, 2009, European Commission, 2011). Intermodal transport is the combination of multiple transport modes in a single transport chain without a change of container for the goods. Inland navigation is a most promising transport mode in the intermodal chain, with its availability of access capacity in the network and environmentally friendly character as most important benefits. This is especially true in the Belgian and Western-European context, where inland waterways play a crucial role in the hinterland access of major sea ports (Notteboom & Rodrigue, 2005). Increasing the efficiency of (intermodal) barge transport through better lock operations is therefore a key issue in supporting future freight flows and increasing the market share of inland navigation.

Section snippets

Literature review

Only a small number of academic papers focus on lock planning. Wilson (1978) investigates the applicability of different queuing models for lock capacity analysis. The research shows that good queuing models exist for single chamber locks, but not for locks with parallel chambers. Some of the other research has focussed on the Upper Mississippi River (UMR). On that river, barges are joined together into tows for transport, which then need to be transferred by single chamber locks that are often

Problem definition

Ships constitute the first major component of the ship placement problem. They are characterised by a width w_i, and a length ℓ_i. By assuming rectangular-shaped ships, we simplify the evaluation of the placement constraints. This simplification is common practice, as the exact shape of the ships is often not available to lock operators. It is necessary to maintain a certain safety distance between ships when they are placed together in one chamber. These distances are defined for each pair of

Algorithms for the ship placement problem

Three algorithms have been developed for solving the ship placement problem. We first describe a top level method that is used by all three algorithms. We then present a solution method based on the MILP model discussed in Section 3.2, where the FCFS constraint has been exploited to decompose the problem, and speed up the solution process (Section 4.2). Next, we shortly describe the modified left–right–left–back heuristic (Section 4.3), followed by the introduction of a multi-order best fit

Experimental setup

We compare the performance of the three algorithms on a set of (simulated) real-life instances. First, the exact decomposition approach is compared to a straightforward implementation of the mathematical model from Section 3.2 for a set of small test instances. Next, the effects of applying different orderings in the multi-order best fit heuristic are compared. Finally, the results of the multi-order best fit heuristic are compared with those obtained by the exact approach and the

Conclusion

Locks are a key component in a port’s infrastructure and an essential part on many waterways. Efficient lockage operation becomes increasingly important due to the growing number of goods transported by ships. We presented the ship placement problem, which is an important part of the lock scheduling problem. It has been identified as a variant of the 2D bin packing problem with additional constraints, and has proven to be different from 2D bin packing. A mathematical model for the ship

Acknowledgements

Research funded by a Ph.D. grant of the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen).

We would like to thank the Scheepvaartmanagement of the Port of Antwerp for sharing their experience and real-life data on the ship placement problem. The real-life data provided by IT-Bizz and nv De Scheepvaart was also greatly appreciated.

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Citation Excerpt :
A complexity analysis together with a polynomial time algorithm that applies to special cases for the single lock scheduling problem with multiple parallel chambers is presented in Passchyn, Briskorn, and Spieksma (2019). The problem of physically placing vessels inside the chamber of the lock has been addressed in Verstichel, De Causmaecker, Spieksma, and Berghe (2014a) and Verstichel, De Causmaecker, Spieksma, and Berghe (2014b). The joint optimization of multiple sequential locks on the river is considered by Passchyn, Briskorn, and Spieksma (2016a) and Prandtstetter, Ritzinger, Schmidt, and Ruthmair (2015).
We address the problem of minimizing the aggregated fuel consumption by the vessels in an inland waterway, e.g., a river, with a single lock. The fuel consumption of a vessel depends on its velocity and the slower it moves, the less fuel it consumes. Given entry times of the vessels into the waterway and the deadlines before which they need to leave the waterway, we start from the optimal velocities of the vessels that minimize their private fuel consumption, where we assume selfish behavior of the skippers. Presence of the lock and possible congestion on the waterway make the problem computationally challenging. First, we prove that in general, a Nash equilibrium might not exist, i.e., if there is no supervision on the vessels’ velocities, there might not exist a strategy profile from which no vessel can unilaterally deviate to decrease its private fuel consumption. Next, we introduce simple supervision methods to guarantee the existence of a Nash equilibrium. Unfortunately, though a Nash equilibrium can be computed, the aggregated fuel consumption of such a stable solution can be high compared to the social optimum, where the total fuel consumption is minimized. Therefore, we propose a mechanism involving payments between vessels, guaranteeing a Nash equilibrium while minimizing the fuel consumption. This mechanism is studied for both the offline setting, where all information is known beforehand, and online setting, where we only know the entry time and deadline of a vessel when it enters the waterway.

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Exact and heuristic methods for placing ships in locks

Highlights

Abstract

Introduction

Section snippets

Literature review

Problem definition

Algorithms for the ship placement problem

Experimental setup

Conclusion

Acknowledgements

European Journal of Operational Research

Journal of Transport Geography

Journal of Parallel and Distributed Computing

European Journal of Operational Research

Discrete Applied Mathematics

European Journal of Operational Research

Discrete Optimization

Procedia-Social and Behavioral Sciences

European Journal of Operational Research

Transportation Research

A tabu search algorithm for the integrated scheduling problem of container handling systems in a maritime terminal

European Journal of Operational Research