Tighter bounds of the First Fit algorithm for the bin-packing problem

AbstractIn this paper, we present improved bounds for the First Fit algorithm for the bin-packing problem. We prove CFF(L)≤1710C∗(L)+710 for all lists L, and the absolute performance ratio of FF is at most 127

Worst case bin packing for OTN electrical layer networks dimensioning

The OTN (Optical Transport Network) standard, defined by ITU-T Recommendation G.709 and G.872, contains a flexible digital hierarchy of ODU (Optical Data Unit) signals. The ODU hierarchy provides sub-wavelength grooming in OTN networks, which is necessary for efficient utilization of the high bit rates of optical channels. When dimensioning the links of a transport network consisting of ODU switches, the packing of lower order ODU signals into higher order ODU signals needs to be taken into account. These networks are expected to be controlled by GMPLS (Generalized MPLS) , which puts specific constraints on the dimensioning. We assume that there is no explicit label control and that the GMPLS control plane is using first-fit strategy for making reservations on a link . With these assumptions the link dimensioning problem is defined as deciding how many higher order ODU component links are required on an OTN GMPLS bundled link for first-fit packing of a given set of lower order ODU demands, in any order of arrival. The paper provides strict bounds for ODU hierarchy-specific item and bin sizes. Then, it introduces an extended variant of the dimensioning problem, when lower order ODU connections which are not controlled by GMPLS are also present

kk-times bin packing and its application to fair electricity distribution

Given items of different sizes and a fixed bin capacity, the bin-packing problem is to pack these items into a minimum number of bins such that the sum of item sizes in a bin does not exceed the capacity. We define a new variant called $k$-times bin packing ($k$BP), where the goal is to pack the items such that each item appears exactly $k$ times, in $k$ different bins. We generalize some existing approximation algorithms for bin-packing to solve $k$BP, and analyze their performance ratio. The study of $k$BP is motivated by the problem of fair electricity distribution. In many developing countries, the total electricity demand is higher than the supply capacity. We show that $k$-times bin packing can be used to distribute the electricity in a fair and efficient way. Particularly, we implement generalizations of the First-Fit and First-Fit-Decreasing bin-packing algorithms to solve $k$BP, and apply the generalizations to real electricity demand data. We show that our generalizations outperform existing heuristic solutions to the same problem.Comment: 30 pages, 5 figures, 3 table

Diseño de una estrategia para la sincronización del proceso logístico de distribución de aceites vegetales basado en la valoración de tiempos ociosos y planeación de cargues de Gracetales Ltda

El ambiente de competitividad global ha motivado que las organizaciones se vean en la necesidad de buscar, desarrollar e implementar nuevos y mejores métodos que les permita entregar sus productos al menor costo y la mayor brevedad posible, desarrollando así procedimientos que minimicen el tiempo de proceso, esperas, demoras, inspecciones, tiempos ociosos, reprocesos y en general todas aquellas actividades que no agregan valor. Este trabajo busca realizar una valoración de los tiempos ociosos que se presentan en la operación de cargue y transporte de producto terminado de la empresa GRACETALES LTDA., para conocer la cantidad de tiempo perdido durante la operación de cargue y que de ser recuperado puede convertirse en un mayor número de unidades cargadas y despachadas. Se procedió a caracterizar el proceso de cargue actual de vehículos, cuyo modelo (con desconsolidación de carga) consiste en arrumar las cajas de producto terminado dentro de los vehículos; una vez identificado y valorizados los tiempos ociosos del modelo actual, se procedió a plantear una nueva metodología de cargue (sin desconsolidación de carga -basado en los principios del Problema Bin Packing) en la cual la mercancía se ubique de manera paletizada dentro de los camiones y de esa manera se despache hacia los distintos destinos. Al simular ambos modelos de cargue utilizando como herramienta el software ARENA ®, se pudo encontrar que con el nuevo modelo planteado -sin desconsolidación de carga- el tiempo de cargue se reduce, se atienden más vehículos y se requieren menos recursos para el proceso de cargue.PregradoIngeniero Industria

Exact and evolutionary algorithms for the score-constrained packing problem

This thesis concerns the Score-Constrained Packing Problem (SCPP), a combinatorial optimisation problem related to the one-dimensional bin packing problem. The aim of the SCPP is to pack a set of rectangular items from left to right into the fewest number of bins such that no bin is overfilled; however, the order and orientation of the items in each bin affects the feasibility of the overall solution. The SCPP has applications in the packaging industry, and obtaining high quality solutions for instances of the SCPP has the ability to reduce the amount of waste material, costs, and time, which motivates the study in this thesis. The minimal existing research on the SCPP leads us to explore a wide range of approaches to the problem in this thesis, implementing ideas from related problems in literature as well as bespoke methods. To begin, we present an exact algorithm that can produce a feasible configuration of a subset of items in a single bin in polynomial-time. We then introduce a range of methods for the SCPP including heuristics, an evolutionary algorithm framework comprising a local search procedure and a choice of three distinct recombination operators, and two algorithms combining metaheuristics with an exact procedure. Each method is investigated to gain more insight into the characteristics that benefit or hinder the improvement of solutions, both theoretically and computationally, using a large number of problem instances with varying parameters. This allows us to determine the specific methods and properties that produce superior solutions depending on the type of problem instance