# A Lagrangian Relaxation based Heuristic for the Static Berth Allocation Problem using the Cutting Plane Method

### A. S. Simrin, N. N. Alkawaleet, A. H. Diabat

#### Abstract

One of the important seaside operations problems that received a lot of attention in the literature is the assignment of quay space and service time to vessels that have to be unloaded and loaded at a terminal. This problem is commonly referred to as the Berth Allocation Problem (BAP). Different approaches exist in the literature for the berth allocation problem (BAP). Some of those approaches consider static arrival of vessels, so called the static berth allocation problem (SBAP), while other approaches consider dynamic arrival of vessels, called the dynamic berth allocation problem (DBAP). Approaches also differ in the layout used for the quay. In this paper we study one of the SBAP models presented in literature. Since the SBAP is a non-deterministic polynomial-time (NP) problem, we applied a Lagrangian Relaxation heuristic technique with the application of cutting plane method on our problem. We coded the cutting plane method in Matlab, and ran it on different instances of the problem. In most of the cases that we studied, our solution technique converged to an optimal solution.

#### References

1. A. Imai, E. Nishimura., S. Papadimitriou, “The dynamic berth allocation problem for a container port,”, Transportation Research Part B 35 (4), pp. 401-417, 2001.
2. A. Imai, E. Nishimura, S. Papadimitriou, “Berthing ships at a multi-user container terminal with a limited quay capacity,” Transportation Research Part E 44 (1), pp. 136-151, 2008.
3. A. Imai, K. Nagaiwa, C. W. Tat, “Efficient planning of berth allocation for container terminals in Asia,” Journal of Advanced Transportation 31(1), pp. 75-94, 1997.
4. P. Hansen, C. Oguz, “A note on formulations of static and dynamic berth allocation problems,” Les Cahiers du GERAD 30, pp. 1-17, 2003.
5. D.-H. Lee, L. Song, H. Wang, “Bilevel programming model and solutions of berth allocation and quay crane scheduling.” in Proceedings of 85th Annual Meeting of Transportation Research Board (CD-ROM). Annual Meeting of Transportation Research Board. Washington DC, 2006.
6. C. Bierwirth, F. Meisel, “A survey of berth allocation and quay crane scheduling problems in container terminals,” European Journal of Operational Research 202 (2010) pp. 615-627, 2009.
7. M. Fisher, “An Applications Oriented Guide to Lagrangian Relaxation”, Interfaces vol 15 No 2 pp. 10- 21 (1985).

#### in Harvard Style

S. Simrin A., N. Alkawaleet N. and H. Diabat A. (2013). A Lagrangian Relaxation based Heuristic for the Static Berth Allocation Problem using the Cutting Plane Method . In Proceedings of the 15th International Conference on Enterprise Information Systems - Volume 1: SSOS, (ICEIS 2013) ISBN 978-989-8565-59-4, pages 565-569. DOI: 10.5220/0004628105650569

#### in Bibtex Style

@conference{ssos13,
author={A. S. Simrin and N. N. Alkawaleet and A. H. Diabat},
title={A Lagrangian Relaxation based Heuristic for the Static Berth Allocation Problem using the Cutting Plane Method},
booktitle={Proceedings of the 15th International Conference on Enterprise Information Systems - Volume 1: SSOS, (ICEIS 2013)},
year={2013},
pages={565-569},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004628105650569},
isbn={978-989-8565-59-4},
}

#### in EndNote Style

TY - CONF
JO - Proceedings of the 15th International Conference on Enterprise Information Systems - Volume 1: SSOS, (ICEIS 2013)
TI - A Lagrangian Relaxation based Heuristic for the Static Berth Allocation Problem using the Cutting Plane Method
SN - 978-989-8565-59-4
AU - S. Simrin A.
AU - N. Alkawaleet N.
AU - H. Diabat A.
PY - 2013
SP - 565
EP - 569
DO - 10.5220/0004628105650569