Mathematical model for the Berth Allocation Problem in ports with cargo operation limitations along the pier

Rodrigues, Ivan Bridi Gimenes; Rosa, Rodrigo de Alvarenga; Gomes, Thiara Cezana; Ribeiro, Glaydston Matos

doi:10.1590/0104-530X2266-15

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Articles • Gest. Prod. 23 (04) • Oct-Dec 2016 • https://doi.org/10.1590/0104-530X2266-15 copy

Mathematical model for the Berth Allocation Problem in ports with cargo operation limitations along the pier

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Oil exploration in Brazil is performed by platforms at sea that require several loads carried by vessels. Thus, it is necessary to have ports to handle these vessels’ operation and, therefore, the ports assign specific segments along the pier to operate certain type of cargo, increasing the complexity of vessels berthing. Thus, this paper proposes a mathematical model for the Continuous Berth Allocation Problem that differs from the others because it considers that some cargos can be operated only in specific segments of the pier. We used real data from the Companhia Portuária de Vila Velha (CPVV) to evaluate the model. CPLEX 12.6 was used to run the model and instances up to 147 vessels with 440 meters of pier were optimally solved. The results are presented and compared to those achieved by the CPVV's manual method showing that it is possible to obtain significant gains.

Keywords:
Berth Allocation Problem; Port operation; Oil and gas logistics

Instance	Length of the Pier (m)	Planning Horizon (h)	Number of vessels
1	320	360	83
2	320	408	97
3	320	456	102
4	320	480	113
5	320	528	123
6	320	456	101
7	440	528	123
8	440	576	147

Instance	CPLEX (Mathematical Model)			Real Case - CPVV	Reduction CPLEX x Real Case
Instance	GAP (%)	Runtime (s)	Wait time to berth (h)	Wait time to berth (h)	Wait time to berth (h)	Wait time to berth (%)
1	0.00	26.41	5.89	7.53	–1.64	22%
2	0.00	30.03	12.32	21.32	–9.00	42%
3	0.00	997.14	14.23	19.17	–4.94	26%
4	0.00	2,718.92	15.49	27.46	–11.97	44%
5	0.00	4,345.17	16.08	45.13	–29.05	64%
6	0.00	993.45	13.56	17.32	–3.76	22%
7	0.00	6,345.78	10.34	-	-	-
8	0.00	7,439.56	15.45	-	-	-

Instance	CPLEX (Mathematical Model)			Real Case - CPVV	Reduction CPLEX × Real Case
Instance	GAP (%)	Runtime (s)	Wait time to berth (h)	Wait time to berth (h)	Wait time to berth (h)	Wait time to berth (%)
1	0.00	26.41	5.89	6.43	–0.54	8.4%
2	0.00	30.03	12.32	13.35	–1.03	7.7%
3	0.00	997.14	14.23	14.54	–0.31	2.1%
4	0.00	2,718.92	15.49	16.10	–0.61	3.8%
5	0.00	4,345.17	16.08	18.12	–2.04	11.3%
6	0.00	993.45	13.56	13.67	–0.11	0.8%
7	0.00	6,345.78	10.34	-	-	-
8	0.00	7,439.56	15.45	-	-	-

Universidade Federal de São Carlos Departamento de Engenharia de Produção , Caixa Postal 676 , 13.565-905 São Carlos SP Brazil, Tel.: +55 16 3351 8471 - São Carlos - SP - Brazil
E-mail: gp@dep.ufscar.br

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Instance	Length of the Pier (m)	Planning Horizon (h)	Number of vessels
1	320	360	83
2	320	408	97
3	320	456	102
4	320	480	113
5	320	528	123
6	320	456	101
7	440	528	123
8	440	576	147

Instance	Length of the Pier (m)	Planning Horizon (h)	Number of vessels
1	320	360	83
2	320	408	97
3	320	456	102
4	320	480	113
5	320	528	123
6	320	456	101
7	440	528	123
8	440	576	147

Instance	Length of the Pier (m)	Planning Horizon (h)	Number of vessels
1	320	360	83
2	320	408	97
3	320	456	102
4	320	480	113
5	320	528	123
6	320	456	101
7	440	528	123
8	440	576	147