Integrated Berth Allocation and Quay Crane Assignment Problem: Set partitioning models and computational results

Abstract

Most of the operational problems in container terminals are strongly interconnected. In this paper, we study the integrated berth allocation and quay crane assignment problem in seaport container terminals. We will extend the current stateof-the-art by proposing novel set partitioning models. To improve the performance of the set partitioning formulations, a number of variable reduction techniques are proposed. Furthermore, we analyze the eects of dierent discretization schemes and the impact of using a time-variant/invariant quay crane allocation policy. Computational experiments show that the proposed models signicantly improve the benchmark solutions of the current state-of-art optimal approaches.

The matching relaxation for a class of generalized set partitioning problems

“…It is worth remarking that, since this technique is applied prior to the model optimization, such a proposal can be integrated with any approach based on enumerating the variables of the GSPP formulation and solving the resulting model with an integer linear programming algorithm. This strategy has already been adopted by Iris et al (2015), using lower bounds implied by probing the selection of a single assignment or a pair of assignments for two different tasks.…”

“…This section extends our key idea, the matching relaxation of the GSPP structure, into algorithmic results. First, we derive in Section 4.1 a preprocessing method to probe and discard assignments that imply a suboptimal solution, as it is done in the work of Iris et al (2015) in the context of a port logistics problem. Next, we present in Section 4.2 a matheuristic algorithm to find approximate solutions to the problem in reduced computational time.…”

Berth allocation and quay crane assignment in a container terminal for the trade-off between time-saving and energy-saving

“…However, this policy can either reduce large setup losses due to reallocation of quay cranes, or reduce computational complexity. The comparison between the two policies was addressed by Iris et al [16]. Their conclusion is that timeinvariant QC assignment policy may result in an additional cost.…”

“…Constraints (16)- (21) ensure that there is no overlap among all vessels in the 2-dimensional berth-time plane. Constraints (16) ensure that Vessel j must be moored at the berth after Vessel i departs if Vessel i is located below Vessel j in the berth-time plane. Constraints (17) ensure that the left side position of Vessel j must be greater than the right side position Vessel i if Vessel i is located in the left of Vessel j in the berth-time plane.…”

“…Thus, we calculate the lower bounds corresponding to the instances by relaxing some complex constraints. Since Constraints (16) and (17) include big-M and significantly impacts the CPU time based on the preliminary tests, two new valid inequalities are set to substitute them: 8 600 6 3742 94 0 3742 a 47 8 600 6 4286 97 0 4286 a 51 8 600 6 3936 101 0 3936 a 61 8 600 6 3952 96 0 3952 a 44 8 600 6 4202 100 0 4202 a 54 10 800 8 5525 133 0 5525 a 103 10 800 8 4946 141 0 4946 a 116 10 800 8 5237 144 0 5237 a 95 10 800 8 4854 137 0 4854 a 104 10 800 8 5613 134 0 Based on the preliminary tests, the probability of crossover, the probability of mutation, and the maximum generations of the GA are set as 60, 0.6, 0.1 and 80, respectively. Based on the preliminary tests, the parameters of the SA, i.e., the initial temperature T, cooling rate a, the number of nested loops R, and the threshold are set as 40, 0.6, 40 and 1, respectively.…”