Improving container terminal efficiency: New models and algorithms for Premarshalling and Stowage Problems

El desarrollo del contenedor ha revolucionado el comercio marítimo de mercancías, permitiendo la manipulación de carga de diversos tipos y dimensiones con un costo reducido y disminuyendo el costo de importación de muchos productos, En la actualidad, aproximadamente el 90\% de la carga no a granel en todo el mundo se transporta en buques portacontenedores, cuyas capacidades han llegado a sobrepasar los 20000 TEUs (\emph{Twenty-foot Equivalent Unit}, unidad de medida correspondiente a un contenedor normalizado de 20 pies). Las terminales de contenedores tienen que hacer frente al creciente volumen de carga transportada, al aumento del tamaño de las naves y a las alianzas de las navieras. En este contexto, deben competir por menos servicios de barcos cada vez más grandes. Para ello, deben aumentar su eficiencia, optimizando los recursos existentes. En esta tesis se estudian dos problemas de optimización combinatoria, el problema de premarshalling y el problema de la estiba, que surgen en el patio y en el muelle de las terminales de contenedores, antes y durante las operaciones de carga y descarga de los buques, y cuya resolución deriva en una disminución del tiempo de atraque y, por lo tanto, en un aumento de la eficiencia de las terminales. El problema de premarshalling prepara el patio de contenedores antes de la llegada del buque, usando las grúas de patio cuando la carga de trabajo es mínima, con el fin de evitar un mayor número de recolocaciones a la llegada del buque y así acelerar los tiempos de servicio. El objetivo clásico de este problema ha sido reducir al mínimo el número de movimientos necesarios para eliminar los contenedores que bloquean la retirada de otros dentro de una bahía. De este modo, el número de movimientos se ha tomado como un indicador del tiempo de grúa. No obstante, en esta tesis se prueba que considerando como objetivo el tiempo real que la grúa emplea en realizar los movimientos, se puede reducir hasta un 24\% el tiempo total empleado. Para la resolución de ambos problemas, el premarshalling con función objetivo clásica y el premarshalling con la nueva función objetivo, se han desarrollado diversos modelos matemáticos y algoritmos Branch and Bound con nuevas cotas superiores e inferiores, reglas de dominancia y algoritmos heurísticos integrados en el proceso de ramificación. Por lo que respecta al problema de la estiba, se ha estudiado el problema multi-puerto que busca obtener un plan de estiba del barco de modo que se reduzca al mínimo el número total de movimientos improductivos en las operaciones de carga y descarga a lo largo de la ruta en la que presta servicio. Comenzamos estudiando el problema simplificado, en el que no se consideran restricciones de tamaño ni de peso de los contenedores, y progresivamente se van introducido restricciones más realistas, desarrollando modelos matemáticos, heurísticas, metaheurísticas y mateheurísticas. Estos procedimientos son capaces de resolver instancias de gran tamaño correspondientes a los barcos de mayor capacidad que se encuentran actualmente en el sector.The development of containers has revolutionized maritime trade by making it possible to handle various types and sizes of cargo at a reduced cost, lowering the import cost of many products to such an extent that it is sometimes cheaper to transport goods to the other side of the world than to produce them locally. Nowadays, about 90 per cent of non-bulk cargo worldwide is carried on container ships with capacities exceeding 20,000 TEUs (Twenty-foot Equivalent Units). Container terminals have to cope with the increase in the volumes of cargo transported, the ever-larger ships, and the consolidation of shipping companies. In this context, they have to compete for fewer calls of larger ships. Since they cannot simply increase the number of cranes indefinitely, they have to improve efficiency by optimizing the available resources. This thesis studies two combinatorial optimization problems, the premarshalling problem and the stowage problem. These problems arise in the yard and the seaside of container terminals, before and during the loading and unloading operations of the ships, and make it possible to reduce the berthing time and thus to increase container terminal efficiency. The premarshalling problem prepares the container yard before the arrival of the ship, using the yard cranes when the workload at the terminal is at a minimum to rearrange the yard in order to avoid container relocations when the vessel arrives and to speed up the service times. The classic objective of this problem is to minimize the number of movements required to remove containers blocking the retrieval of others within a bay. Thus, the number of movements has been used as an indicator of crane time. However, this thesis shows that considering the real time that the crane takes to perform the movements as the target, the total time spent by the crane can be cut down up to 24 per cent. To solve both problems, premarshalling with the classic objective function and premarshalling with the new objective function, this thesis develops several mathematical models and branch and bound algorithms with new upper and lower bounds, dominance rules and heuristic algorithms integrated in the branching process. With regard to the stowage problem, the multi-port problem is addressed, seeking to obtain a stowage plan for the ship so as to minimize the total number of unproductive moves in the loading/unloading operations along the trade route of the ship. We start with a simplified problem, in which no size and weight constraints are considered, and progressively introduce more realistic constraints, developing mathematical models, metaheuristics, and matheuristics. These procedures are able to solve very large instances, corresponding to the largest ships in service

A beam search algorithm for minimizing crane times in premarshalling problems

The premarshalling problem consists of sorting the containers placed in a bay of the container yard so that they can be retrieved in the order in which they will be required. We study the premarshalling problem with crane time minimization objective and develop a beam search algorithm, with some new elements adapted to the characteristics of the problem, to solve it. We propose various evaluation criteria, depending on the type of container movement, for its local evaluation; a new heuristic algorithm including local search for blue its global evaluation; and several new dominance rules. The computational study shows the contribution of each new element. The performance of the complete algorithm is tested on well-known benchmarks. The beam search algorithm matches all known optimal solutions, improves on the known suboptimal solutions, and obtains solutions for the largest instances, for which no solution had previously been found

A branch and bound approach for large pre-marshalling problems

[EN] The container pre-marshalling problem involves the sorting of containers in stacks so that there are no blocking containers and retrieval is carried out without additional movements. This sorting process should be carried out in as few container moves as possible. Despite recent advancements in solving real world sized problems to optimality, several classes of pre-marshalling problems remain difficult for exact approaches. We propose a branch and bound algorithm with new components for solving such difficult instances. We strengthen existing lower bounds and introduce two new lower bounds that use a relaxation of the pre-marshalling problem to provide tight bounds in specific situations. We introduce generalized dominance rules that help reduce the search space, and a memoization heuristic that finds feasible solutions quickly. We evaluate our approach on standard benchmarks of pre-marshalling instances, as well as on a new dataset to avoid overfitting to the available data. Overall, our approach optimally solves many more instances than previous work, and finds feasible solutions on nearly every problem it encounters in limited CPU times.The authors thank the Paderborn Center for Parallel Computation (PC2) for the use of the Arminius cluster for the computational study in this work. This work has been partially supported by the Spanish Ministry of Science, Innovation, and Universities FPU Grant A-2015-12849 and by the Spanish Ministry of Economy and Competitiveness, under projects DPI2014-53665-P and DPI2015-65895-R, partially financed with FEDER funds.Tanaka, S.; Tierney, K.; Parreño-Torres, C.; Alvarez-Valdes, R.; Ruiz García, R. (2019). A branch and bound approach for large pre-marshalling problems. European Journal of Operational Research. 278(1):211-225. https://doi.org/10.1016/j.ejor.2019.04.005S211225278

Integer programming models for the pre-marshalling problem

[EN] The performance of shipping companies greatly depends on reduced berthing times. The trend towards bigger ships and shorter berthing times places severe stress on container terminals, which cannot simply increase the available cranes indefinitely. Therefore, the focus is on optimizing existing resources. An effective way of speeding up the loading/unloading operations of ships at the container terminal is to use the idle time before the arrival of a ship for sorting the stored containers in advance. The pre-marshalling problem consists in rearranging the containers placed in a bay in the order in which they will be required later, looking for a sequence with the minimum number of moves. With sorted bays, loading/unloading operations are significantly faster, as there is no longer a need to make unproductive moves in the bays once ships are berthed. In this paper, we address the pre-marshalling problem by developing and testing integer linear programming models. Two alternative families of models are proposed, as well as an iterative solution procedure that does not depend on a difficult to obtain upper bound. An extensive computational analysis has been carried out over several well-known datasets from the literature. This analysis has allowed us to test the performance of the models, and to conclude that the performance of the best proposed model is superior to that of previously published alternatives.This study has been partially supported by the Spanish Ministry of Education, Culture, and Sport, FPU Grant A-2015-12849 and by the Spanish Ministry of Economy and Competitiveness, under projects DPI2014-53665-P and DPI2015-65895-R, partially financed with FEDER funds.Parreño-Torres, C.; Alvarez-Valdes, R.; Ruiz García, R. (2019). Integer programming models for the pre-marshalling problem. European Journal of Operational Research. 274(1):142-154. https://doi.org/10.1016/j.ejor.2018.09.048S142154274

The Stochastic Container Relocation Problem

The Container Relocation Problem (CRP) is concerned with finding a sequence of moves of containers that minimizes the number of relocations needed to retrieve all containers, while respecting a given order of retrieval. However, the assumption of knowing the full retrieval order of containers is particularly unrealistic in real operations. This paper studies the stochastic CRP (SCRP), which relaxes this assumption. A new multi-stage stochastic model, called the batch model, is introduced, motivated, and compared with an existing model (the online model). The two main contributions are an optimal algorithm called Pruning-Best-First-Search (PBFS) and a randomized approximate algorithm called PBFS-Approximate with a bounded average error. Both algorithms, applicable in the batch and online models, are based on a new family of lower bounds for which we show some theoretical properties. Moreover, we introduce two new heuristics outperforming the best existing heuristics. Algorithms, bounds and heuristics are tested in an extensive computational section. Finally, based on strong computational evidence, we conjecture the optimality of the “Leveling” heuristic in a special “no information” case, where at any retrieval stage, any of the remaining containers is equally likely to be retrieved next

The synergistic effect of operational research and big data analytics in greening container terminal operations: a review and future directions

Container Terminals (CTs) are continuously presented with highly interrelated, complex, and uncertain planning tasks. The ever-increasing intensity of operations at CTs in recent years has also resulted in increasing environmental concerns, and they are experiencing an unprecedented pressure to lower their emissions. Operational Research (OR), as a key player in the optimisation of the complex decision problems that arise from the quay and land side operations at CTs, has been therefore presented with new challenges and opportunities to incorporate environmental considerations into decision making and better utilise the ‘big data’ that is continuously generated from the never-stopping operations at CTs. The state-of-the-art literature on OR's incorporation of environmental considerations and its interplay with Big Data Analytics (BDA) is, however, still very much underdeveloped, fragmented, and divergent, and a guiding framework is completely missing. This paper presents a review of the most relevant developments in the field and sheds light on promising research opportunities for the better exploitation of the synergistic effect of the two disciplines in addressing CT operational problems, while incorporating uncertainty and environmental concerns efficiently. The paper finds that while OR has thus far contributed to improving the environmental performance of CTs (rather implicitly), this can be much further stepped up with more explicit incorporation of environmental considerations and better exploitation of BDA predictive modelling capabilities. New interdisciplinary research at the intersection of conventional CT optimisation problems, energy management and sizing, and net-zero technology and energy vectors adoption is also presented as a prominent line of future research

Matheuristics: using mathematics for heuristic design

Matheuristics are heuristic algorithms based on mathematical tools such as the ones provided by mathematical programming, that are structurally general enough to be applied to different problems with little adaptations to their abstract structure. The result can be metaheuristic hybrids having components derived from the mathematical model of the problems of interest, but the mathematical techniques themselves can define general heuristic solution frameworks. In this paper, we focus our attention on mathematical programming and its contributions to developing effective heuristics. We briefly describe the mathematical tools available and then some matheuristic approaches, reporting some representative examples from the literature. We also take the opportunity to provide some ideas for possible future development