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

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

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

Container Stowage Planning - k-shift instances - Roberti-Parenno

This dataset includes all the instances for the k-shift container stowage planning problem from the papers: Parreño-Torres, C., Çalık, H., Alvarez-Valdes, R., & Ruiz, R. (2021). Solving the generalized multi-port container stowage planning problem by a matheuristic algorithm. Computers and Operations Research, 133, 105383. https://doi.org/10.1016/j.cor.2021.105383 Roberti, R., & Pacino, D. (2018). A decomposition method for finding optimal container stowage plans. Transportation Science, 52(6), 1444–1462. https://doi.org/10.1287/trsc.2017.0795 </p

Minimizing crane times in pre-marshalling problems

[EN] The pre-marshalling problem has been extensively studied in recent years with the aim of minimizing the number of movements needed to rearrange a bay of containers. Time is a more realistic objective for measuring process efficiency, and we show that it does not correlate with the number of movements. As a result, we study the problem of minimizing crane times and develop two exact approaches to solve it: an integer linear model, and a branch and bound algorithm, with new upper and lower bounds, dominance criteria, and a heuristic procedure, to provide optimal solutions for problems of practical sizeThis work has been partially supported by the Spanish Ministry of Science, Innovation, and Universities, FPU Grant A-2015-12849 and under the project "OPTEP-Port Terminal Operations Optimization" (No. RTI2018-094940-B-I00) financed with FEDER funds.Parreño-Torres, C.; Álvarez-Valdés, R.; Ruiz García, R.; Tierney, K. (2020). Minimizing crane times in pre-marshalling problems. Transportation Research Part E Logistics and Transportation Review. 137:1-20. https://doi.org/10.1016/j.tre.2020.101917120137Bacci, T., Mattia, S., & Ventura, P. (2019). The bounded beam search algorithm for the block relocation problem. Computers & Operations Research, 103, 252-264. doi:10.1016/j.cor.2018.11.008Bortfeldt, A., & Forster, F. (2012). A tree search procedure for the container pre-marshalling problem. European Journal of Operational Research, 217(3), 531-540. doi:10.1016/j.ejor.2011.10.005van Brink, M., van der Zwaan, R., 2014. A branch and price procedure for the container premarshalling problem. In: Schulz, A., Wagner, D. (Eds.), Algorithms - ESA 2014. Springer, Berlin Heidelberg. volume 8737 of Lecture Notes in Computer Science, pp. 798–809. https://doi.org/10.1007/978-3-662-44777-2_66.Caserta, M., Schwarze, S., Voß, S., 2011. Container rehandling at maritime container terminals, in: Böse, J. (Ed.), Handbook of Terminal Planning. Springer, New York. volume 49 of Operations Research/Computer Science Interfaces Series, pp. 247–269. https://doi.org/10.1007/978-1-4419-8408-1_13.Expósito-Izquierdo, C., Melián-Batista, B., & Moreno-Vega, M. (2012). Pre-Marshalling Problem: Heuristic solution method and instances generator. Expert Systems with Applications, 39(9), 8337-8349. doi:10.1016/j.eswa.2012.01.187Hottung, A., Tanaka, S., & Tierney, K. (2020). Deep learning assisted heuristic tree search for the container pre-marshalling problem. Computers & Operations Research, 113, 104781. doi:10.1016/j.cor.2019.104781Jovanovic, R., Tanaka, S., Nishi, T., & Voß, S. (2018). A GRASP approach for solving the Blocks Relocation Problem with Stowage Plan. Flexible Services and Manufacturing Journal, 31(3), 702-729. doi:10.1007/s10696-018-9320-3Jovanovic, R., Tuba, M., & Voß, S. (2015). A multi-heuristic approach for solving the pre-marshalling problem. Central European Journal of Operations Research, 25(1), 1-28. doi:10.1007/s10100-015-0410-yJovanovic, R., Tuba, M., & Voß, S. (2019). An efficient ant colony optimization algorithm for the blocks relocation problem. European Journal of Operational Research, 274(1), 78-90. doi:10.1016/j.ejor.2018.09.038Lee, Y., & Chao, S.-L. (2009). A neighborhood search heuristic for pre-marshalling export containers. European Journal of Operational Research, 196(2), 468-475. doi:10.1016/j.ejor.2008.03.011Lee, Y., & Hsu, N.-Y. (2007). An optimization model for the container pre-marshalling problem. Computers & Operations Research, 34(11), 3295-3313. doi:10.1016/j.cor.2005.12.006Lee, Y., & Lee, Y.-J. (2010). A heuristic for retrieving containers from a yard. Computers & Operations Research, 37(6), 1139-1147. doi:10.1016/j.cor.2009.10.005Lehnfeld, J., & Knust, S. (2014). Loading, unloading and premarshalling of stacks in storage areas: Survey and classification. European Journal of Operational Research, 239(2), 297-312. doi:10.1016/j.ejor.2014.03.011Lin, D.-Y., Lee, Y.-J., & Lee, Y. (2015). The container retrieval problem with respect to relocation. Transportation Research Part C: Emerging Technologies, 52, 132-143. doi:10.1016/j.trc.2015.01.024Parreño-Torres, C., Alvarez-Valdes, R., & Ruiz, R. (2019). Integer programming models for the pre-marshalling problem. European Journal of Operational Research, 274(1), 142-154. doi:10.1016/j.ejor.2018.09.048Prandtstetter, M., 2013. A dynamic programming based branch-and-bound algorithm for the container pre-marshalling problem. Technical Report. Technical report, AIT Austrian Institute of Technology.Quispe, K. E. Y., Lintzmayer, C. N., & Xavier, E. C. (2018). An exact algorithm for the Blocks Relocation Problem with new lower bounds. Computers & Operations Research, 99, 206-217. doi:10.1016/j.cor.2018.06.021De Melo da Silva, M., Toulouse, S., & Wolfler Calvo, R. (2018). A new effective unified model for solving the Pre-marshalling and Block Relocation Problems. European Journal of Operational Research, 271(1), 40-56. doi:10.1016/j.ejor.2018.05.004Da Silva Firmino, A., de Abreu Silva, R. M., & Times, V. C. (2018). A reactive GRASP metaheuristic for the container retrieval problem to reduce crane’s working time. Journal of Heuristics, 25(2), 141-173. doi:10.1007/s10732-018-9390-0Tanaka, S., & Mizuno, F. (2018). An exact algorithm for the unrestricted block relocation problem. Computers & Operations Research, 95, 12-31. doi:10.1016/j.cor.2018.02.019Tanaka, S., & Tierney, K. (2018). Solving real-world sized container pre-marshalling problems with an iterative deepening branch-and-bound algorithm. European Journal of Operational Research, 264(1), 165-180. doi:10.1016/j.ejor.2017.05.046Tanaka, S., Tierney, K., Parreño-Torres, C., Alvarez-Valdes, R., & Ruiz, R. (2019). A branch and bound approach for large pre-marshalling problems. European Journal of Operational Research, 278(1), 211-225. doi:10.1016/j.ejor.2019.04.005Tanaka, S., & Voß, S. (2019). An exact algorithm for the block relocation problem with a stowage plan. European Journal of Operational Research, 279(3), 767-781. doi:10.1016/j.ejor.2019.06.014Tierney, K., Pacino, D., & Voß, S. (2016). Solving the pre-marshalling problem to optimality with A* and IDA*. Flexible Services and Manufacturing Journal, 29(2), 223-259. doi:10.1007/s10696-016-9246-6UNCTAD, 2018. United Nations Conference on Trade and Development (UNCTAD) Review of Maritime Transport. United Nations. .Wang, N., Jin, B., & Lim, A. (2015). Target-guided algorithms for the container pre-marshalling problem. Omega, 53, 67-77. doi:10.1016/j.omega.2014.12.002Wang, N., Jin, B., Zhang, Z., & Lim, A. (2017). A feasibility-based heuristic for the container pre-marshalling problem. European Journal of Operational Research, 256(1), 90-101. doi:10.1016/j.ejor.2016.05.061Zhang, R., Liu, S., & Kopfer, H. 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El pecio de Binissafúller. Estado de las investigaciones

En este artículo se presentan los resultados de los estudios derivados de la campaña de excavación llevada a cabo en 2011, junto con los de intervenciones anteriores y los trabajos de clasiicación y revisión de los materiales extraídos en los años setenta del pasado siglo. Considerando que actualmente aún queda casi un cuarenta por ciento del yacimiento por excavar, los resultados obtenidos dan una visión global que varía, en parte, algunas de las conclusiones recogidas en la bibliografía generada tras las primeras excavaciones. Actualmente un equipo multidisciplinar de investigación está estudiando los restos hallados, materiales cerámicos, inscripciones en ánforas, arquitectura naval y analíticas de restos orgánicos e inorgánicos, resultados que se presentan en el siguiente artículo.This article presents the results of the studies derived from the excavation campaign carried out in 2011, along with those of previous interventions and the classiication work and review of the materials removed in the 70s of the last century. Considering that currently almost fourty per cent of the shipwreck remains to be excavated, the results give a global view that changes, in part, some of the conclusions of the studies of this wreck which derived from the literature generated after the irst excavations. Currently,a multidisciplinary research team is studying the remains found: ceramics, inscriptions on amphorae, naval architecture and analyses of organic and inorganic residues. The results are presented in the following article