A Fuzzy Optimization Model for the Berth Allocation Problem and Quay Crane Allocation Problem (BAP + QCAP) with n Quays

Edwar Lujan,Carlos Sabino-Escobar,Flabio Gutierrez,Edmundo Vergara,Miguel Jiménez-Carrión,Jose Rodriguez-Melquiades

doi:10.3390/jmse9020152

Abstract

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.

Highlights

Maritime container terminals (MCTs) are vital elements in the global supply chain.The essential objective of an MCT is to provide the resources and organization to the transport of containers between the landside and maritime mediums
The quay crane allocation problem (QCAP) tries to assign a number of quay cranes (QC) to each berth vessel, aiming to perform all the necessary unload or load movements of the containers in the vehicles
We present a fuzzy optimization model for the berth allocation problem (BAP) + QCAP with two quays, continuous and dynamic, which considers the vessels’ imprecise arrival times, meaning they can arrive early or late of an allowed time

Summary

Introduction

Maritime container terminals (MCTs) are vital elements in the global supply chain. The essential objective of an MCT is to provide the resources and organization to the transport of containers between the landside and maritime mediums. A reactive strategy for the BAP + QCAP with discrete berths is proposed in [8], a mixed integer linear programming (MILP) model with practical constraints, is formulated to obtain a basic planning when uncertainty problems appear (deviation of vessels’ arrival times, deviation of vessels’ loading and unloading operation times, unscheduled vessel calls, quay breakdowns, etc.), and a moving horizon heuristic is used to obtain good feasible solutions. We present a fuzzy optimization model for the BAP + QCAP with two quays, continuous and dynamic, which considers the vessels’ imprecise arrival times, meaning they can arrive early or late of an allowed time. In order to analyze the behavior and efficiency, the model is applied to a small, medium, and large instances respectively

Fuzzy Arithmetic

Problem Description

Limitations

Fuzzy Optimization Model Solution

Results

Study Case