TY - JOUR
T1 - A fuzzy optimization model for the berth allocation problem and quay crane allocation problem(BAP + QCAP) with n quays
AU - Lujan, Edwar
AU - Vergara, Edmundo
AU - Rodriguez-Melquiades, Jose
AU - Jiménez-Carrión, Miguel
AU - Sabino-Escobar, Carlos
AU - Gutierrez, Flabio
N1 - Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2021/2
Y1 - 2021/2
N2 - This work introduces a fuzzy optimization model, which solves in an integrated way the berth allocation problem (BAP) and the quay crane allocation problem (QCAP). The problem is solved for multiple quays, considering vessels’ imprecise arrival times. The model optimizes the use of the quays. The BAP + QCAP, is a NP-hard (Non-deterministic polynomial-time hardness) combinatorial optimization problem, where the decision to assign available quays for each vessel adds more complexity. The imprecise vessel arrival times and the decision variables—berth and departure times—are represented by triangular fuzzy numbers. The model obtains a robust berthing plan that supports early and late arrivals and also assigns cranes to each berth vessel. The model was implemented in the CPLEX solver (IBM ILOG CPLEX Optimization Studio); obtaining in a short time an optimal solution for very small instances. For medium instances, an undefined behavior was found, where a solution (optimal or not) may be found. For large instances, no solutions were found during the assigned processing time (60 min). Although the model was applied for n = 2 quays, it can be adapted to “n” quays. For medium and large instances, the model must be solved with metaheuristics.
AB - This work introduces a fuzzy optimization model, which solves in an integrated way the berth allocation problem (BAP) and the quay crane allocation problem (QCAP). The problem is solved for multiple quays, considering vessels’ imprecise arrival times. The model optimizes the use of the quays. The BAP + QCAP, is a NP-hard (Non-deterministic polynomial-time hardness) combinatorial optimization problem, where the decision to assign available quays for each vessel adds more complexity. The imprecise vessel arrival times and the decision variables—berth and departure times—are represented by triangular fuzzy numbers. The model obtains a robust berthing plan that supports early and late arrivals and also assigns cranes to each berth vessel. The model was implemented in the CPLEX solver (IBM ILOG CPLEX Optimization Studio); obtaining in a short time an optimal solution for very small instances. For medium instances, an undefined behavior was found, where a solution (optimal or not) may be found. For large instances, no solutions were found during the assigned processing time (60 min). Although the model was applied for n = 2 quays, it can be adapted to “n” quays. For medium and large instances, the model must be solved with metaheuristics.
KW - BAP
KW - Berth allocation problem
KW - Combinatorial optimization
KW - Fully fuzzy linear programing
KW - Fuzzy optimization
KW - QCAP
KW - Quay cranes assignment problem
KW - Robust optimization
UR - http://www.scopus.com/inward/record.url?scp=85100815126&partnerID=8YFLogxK
U2 - 10.3390/jmse9020152
DO - 10.3390/jmse9020152
M3 - Article
AN - SCOPUS:85100815126
SN - 2077-1312
VL - 9
SP - 1
EP - 15
JO - Journal of Marine Science and Engineering
JF - Journal of Marine Science and Engineering
IS - 2
M1 - 152
ER -