Handling uncertainty in the quay crane scheduling problem: a unified distributionally robust decision model

Abstract

Quay cranes are among the most important resources in port terminals, and their efficient use is crucial for port terminals to remain competitive in the market. The problem of determining the sequence of tasks performed by the quay cranes that minimizes the turnaround time of a vessel is an NP‐hard problem known as the quay crane scheduling problem (QCSP).In this paper, we consider the unidirectional QCSP under uncertain processing times, where the cranes are only allowed to move in a specific direction. We start by presenting the first distributionally robust optimization (DRO) model for this problem and an exact decomposition algorithm to solve it. The proposed DRO model makes it possible to derive a stochastic programming model and a robust optimization model for the unidirectional QCSP by an appropriate choice of the risk‐averse parameter of the model. Through extensive numerical results, we compare these three approaches—stochastic programming, robust optimization, and DRO—to investigate whether significant differences among the solutions obtained exist. Finally, we propose a new method for helping practitioners to determine a representative set of different DRO solutions.

Just‐in‐time scheduling problem with due windows and release dates for precast bridge girders

“…It is well known that there are likely to be some unexpected situations in the manufacturing process, such as machine failure. Thus, in this case, it is necessary to develop a robust scheduling scheme (Rodrigues and Agra, 2024). In addition, the adoption of matheuristic methods (Boschetti et al, 2023) and metaheuristics (Sarhani et al, 2023) to exploit the model formulation are also valuable studies when faced with large-scale problems.…”

Quay partitioning problem

“…Still, the number of ships and their types, arrival frequencies, and the number of containers they will load/unload are necessary for dimensioning the terminal. Second, evaluating the efficiency of a given terminal layout, for a given traffic model, is already Kastner et al (2022) Review of container terminal design studies, regarding equipment choice, layout design for seaside, storage, hinterland areas, and evaluation methods, SL seaside scheduling Meisel (2010, 2015) BAP, QCAP literature reviews, TL, OL Rodrigues and Agra (2022) Review and taxonomy for BAP with uncertainty, TL, OL Imai et al (2014) Berth schedule templates in time × space, TL, obj: cost and flow time Bouzekri et al (2021) Laycan allocation problem -assigning berthing time windows to new vessels to charter, +BAP, +QCAP, TL, OL, obj: cost, alternatively, flow time Nam et al (2002) Evaluation by simulation of four scenarios of sharing berths and quay cranes between four terminal operators of a quay, TL, OL, multicriteria Chen et al (2021) Evaluation by simulation of two alternative bulk and container terminal locations, SL, obj:(average waiting time)/(average service time) Rodrigues and Agra (2023) Distributionally robust optimization for QCSP, obj: makespan yard (storage) layout Petering (2009) Evaluation by simulation of storage block width impact on quay crane rate and terminal performance, SL, obj: gross crane rate (lifts/hour) Wiese et al (2011) Storage block width and length bi-criteria optimization by mathematical programming, SL, obj: cost, alternatively, makespan Gupta et al (2017) Integrated queuing network model for container unloading process with ALVs, SL, obj: expected time to unload a container Alcalde et al (2015) A probabilistic model to predict storage space requirements, SL, obj: cost Lee et al (2018) Deterministic performance analysis of single-/double-lane storage blocks, SL, bi-obj: container throughput and number of equipment units Zhou et al (2016) Two-stage stochastic programming model for storage blocks layout, with terminal operations simulations providing container transfer timing, SL, obj: investment, and operational costs Tan et al (2022) PSO algorithm planning transition from diesel to green yard cranes, SL, obj: combined cost…”

Improved sequential insertion heuristics for berth allocation problems

“…The problem of assigning berthing positions and berthing times to vessels is known as the berth allocation problem (BAP), and it has been studied for decades (Lim, 1998). The berth allocation process impacts all subsequent operations in a port, such as the assignment/scheduling of quay cranes (Rodrigues and Agra, 2023), 1586 F. Rodrigues / Intl. Trans.…”

“…The problem of assigning berthing positions and berthing times to vessels is known as the berth allocation problem (BAP), and it has been studied for decades (Lim, 1998). The berth allocation process impacts all subsequent operations in a port, such as the assignment/scheduling of quay cranes (Rodrigues and Agra, 2023), the scheduling/deployment of yard cranes (Tan et al., 2022), the scheduling/routing of internal and external vehicles (Mhiri et al., 2023), etc. Therefore, it is crucial to make such a process as efficient as possible.…”