Hybrid next-fit algorithm for the two-dimensional rectangle bin-packing problem

We present a new approximation algorithm for the two-dimensional bin-packing problem. The algorithm is based on two one-dimensional bin-packing algorithms. Since the algorithm is of next-fit type it can also be used for those cases where the output is required to be on-line (e. g. if we open an new bin we have no possibility to pack elements into the earlier opened bins). We give a tight bound for its worst-case and show that this bound is a parameter of the maximal sizes of the items to be packed. Moreover, we also present a probabilistic analysis of this algorithm.worst-case analysis;probabilistic analysis;bin-packing;heuristic algorithm;on-line algorithm;two-dimensional packing

Hybrid next-fit algorithm for the two-dimensional rectangle bin-packing problem

We present a new approximation algorithm for the two-dimensional bin-packing problem. The algorithm is based on two one-dimensional bin-packing algorithms. Since the algorithm is of next-fit type it can also be used for those cases where the output is required to be on-line (e. g. if we open an new bin we have no possibility to pack elements into the earlier opened bins). We give a tight bound for its worst-case and show that this bound is a parameter of the maximal sizes of the items to be packed. Moreover, we also present a probabilistic analysis of this algorithm

Rediseño de un embalaje de material automotriz que permite disminución de costos para el transporte e inventario

Los eslabones para una cadena de suministro pueden ser el origen, el transporte y el destino. El rediseño de embalaje de cajas de cartón que contiene autopartes es transportado vía marítima desde un país asiático (origen) a un país de América Latina (destino). En el origen se desean reducir costos de transporte e inventario, en la práctica se consideran cajas de cartón con idénticas dimensiones y pesos y sin posibilidad de rotación de ellas. El problema se modela mediante programación no lineal entero mixta para encontrar la máxima cantidad de piezas que pueden transportarse en un contenedor High Cube seco de 40”. Se consideraron en este caso de estudio los únicos seis escenarios factibles para realizar el cambio del embalaje que actualmente se utiliza para transportar el material. Para cada uno de ellos se consideraron especificaciones, dimensiones del contenedor, montacargas, resistencia del cartón para su peso con estiba a tres niveles, así como las necesidades del cliente. Con esos escenarios alimentamos al modelo mencionado, cuyo resultado proporciona el escenario que aumenta el número de piezas alojadas en el contenedor. El resultado logra un 10% en la reducción de costos sin verse afectados los gastos de inventario

Efficient Heuristic Solutions to Scheduling Online Courses

The demand for efficient algorithms to automate (near-)optimal timetables has motivated many well-studied scheduling problems in operational research. With most of the courses moving online during the recent pandemic, the delivery of quality education has raised many new technical issues, including online course scheduling. This thesis considers the problem of yielding a near-optimal schedule of the real-time courses in an educational institute, taking into account the conflict among courses, the constraint on the simultaneous consumption of the bandwidth at the hosting servers of the courses, and the maximum utilization of the prime time for the lectures. We propose three approaches for solving the online course scheduling problem; Integer Linear Programming technique, Construction Heuristic using Graph Coloring, and a Hybrid approach using Column Generation technique in combination with Dynamic Programming, and K-coloring. The column generation technique is adopted along with the ILP approach to handling the exponentially increasing number of decision variables in the set-covering problem formulation. This empirical study demonstrates the impact of the input parameters on each approach’s efficiency, including internet bandwidth, number of conflicts, number of connected components. Our results prove the Hybrid approach’s scalability with the change in input parameters and confirm its efficiency in producing near-optimal schedules in a reasonable tim

Solving the two-dimensional bin packing problem

Das ”two-dimensional bin packing” Problem mit orientierten Elementen und freiem Schneiden (2BP|O|F) wurde in dieser Arbeit diskutiert. Für dieses Problem müssen ein Set kleiner, rechteckiger Elemente in ein unbegrenztes Set von einheitlichen großen Objekten gepackt werden. Orientiert heißt, dass die Elemente nicht gedreht werden dürfen und freies Schneiden heißt, dass die Elemente überall im großen Objekt platziert werden können, solange sie innerhalb von diesem platziert werden und sich dabei nicht überlappen. Es gibt eine große Anzahl an Variationen für das Problem, wie zum Beispiel eine unterschiedliche Dimensionalität, unterschiedlich große Objekte, unregelmäßig geformte Elemente, rotierbare Elemente oder dass nur Guillotineschnitte vorgenommen werden können. Für diese Arbeit wurde ein neues ILP Modell entwickelt. Weiters wurde eine bereits existierende Heuristik (LGFi) verbessert, indem ein auf Wahrscheinlichkeiten basierender Ansatz verwendet wurde. Die Heuristik besteht aus einem Vorverarbeitungsschritt und einem zweiten Schritt in dem die Elemente gepackt werden. Das Ziel des Vorverarbeitungsschrittes ist es die Elemente zu sortieren und das Ziel des zweiten Schrittes ist es die sortierten Elemente zu packen. Was verändert wurde ist, dass die Elemente nicht mehr auf eine deterministische Weise sortiert werden sondern basierend auf Wahrscheinlichkeiten. Diese verbesserte Heuristik wurde mit Hilfe von drei verschiedenen Ansätzen auf 500 Instanzen, die von der Literatur zur Verfügung gestellt wurden, angewendet. Diese drei sind ein multi-start Ansatz, Beam Search und Variable Neighborhood Search. Alle drei übertreffen die bisher dagewesenen Ansätze, wobei Beam Search die schlechteste ist und der multi-start Ansatz und Variable Neighborhood Search am besten und etwa gleich gut sind. Außerdem wurden drei neue beste Lösungen für die 500 Instanzen gefunden

Design and evaluation of algorithms for dynamic resource management on SDN/NFV networks

Internet service providers and telecommunications operators have traditionally deployed networks installing various hardware appliances linked together using physical static links, these devices are configured through a broad set of tools to provide services. The aforementioned devices tend to be highly specialized and customized, usually having their operative system tightly coupled to the underlying hardware. Communication among devices is achieved through the implementation of strict protocols to achieve reliability. The aforementioned approach altogether with the exponential demand increase experienced in modern networks have proved that these networks are expensive to operate, are difficult to scale, require highly specialized maintenance and are not flexible. This has brought difficulties to service providers, since this increase in the demand of quality in their services is not accompanied by an increase in the service fees. Network Function Virtualization (NFV) was introduced by service operators as a new paradigm proposing to address these difficulties, looking to obtain similar benefits as those obtained in Information technology (IT) environments leveraging server virtualization. In the present document a brief review is done of the state of the art technologies involved in Service Function Chaining (SFC) in NFV environments, including a high-level description of the main components involved in open-source NFV and a detailed description of the open-source orchestrator Open Source MANO (OSM). Finally, an introduction to a framework for providing resource optimization assignment algorithms in orchestrators is done, providing preliminary results. Although the developed components do not achieve the requirements for acceptance into a production environment they provide a starting point for integration into production orchestration environments

"Rotterdam econometrics": publications of the econometric institute 1956-2005

This paper contains a list of all publications over the period 1956-2005, as reported in the Rotterdam Econometric Institute Reprint series during 1957-2005