Constructive procedures to solve 2-dimensional bin packing problems with irregular pieces and guillotine cuts

This paper presents an approach for solving a new real problem in cutting and packing. At its core is an innovative mixed integer programme model that places irregular pieces and defines guillotine cuts. The two-dimensional irregular shape bin packing problem with guillotine constraints arises in the glass cutting industry, for example, the cutting of glass for conservatories. Almost all cutting and packing problems that include guillotine cuts deal with rectangles only, where all cuts are orthogonal to the edges of the stock sheet and a maximum of two angles of rotation are permitted. The literature tackling packing problems with irregular shapes largely focuses on strip packing i.e. minimizing the length of a single fixed width stock sheet, and does not consider guillotine cuts. Hence, this problem combines the challenges of tackling the complexity of packing irregular pieces with free rotation, guaranteeing guillotine cuts that are not always orthogonal to the edges of the stock sheet, and allocating pieces to bins. To our knowledge only one other recent paper tackles this problem. We present a hybrid algorithm that is a constructive heuristic that determines the relative position of pieces in the bin and guillotine constraints via a mixed integer programme model. We investigate two approaches for allocating guillotine cuts at the same time as determining the placement of the piece, and a two phase approach that delays the allocation of cuts to provide flexibility in space usage. Finally we describe an improvement procedure that is applied to each bin before it is closed. This approach improves on the results of the only other publication on this problem, and gives competitive results for the classic rectangle bin packing problem with guillotine constraint

Experimental and topological determination of the pressure-temperature phase diagram of morniflumate, a pharmaceutical ingredient with anti-inflammatory properties

The pressure-temperature phase diagram of morniflumate (niflumic acid ß-morpholinoethyl ester) has been obtained by high-pressure thermal analysis. In addition, calorimetric melting data (TI¿L = (348.1 ± 0.4) K and ¿HI¿L = (89 ± 2) J·g-1) and the specific volumes of the solid and the liquid state have been obtained under normal pressure. Comparison of the measured high-pressure melting data with the equilibrium curve obtained through the Clapeyron equation indicates that the initial slopes are the same (dP/dT = (2.96 ± 0.06) MPa·K-1) at the melting point under normal pressure. The fact that the Clapeyron equation can be used to construct topological phase diagrams may be of interest for the food and pharmaceutical industries.Peer ReviewedPostprint (author's final draft

Shortest paths on systems with power-law distributed long-range connections

We discuss shortest-path lengths $\ell(r)$ on periodic rings of size L supplemented with an average of pL randomly located long-range links whose lengths are distributed according to P_l \sim l^{-\xpn}. Using rescaling arguments and numerical simulation on systems of up to $10^7$ sites, we show that a characteristic length $\xi$ exists such that $\ell(r) \sim r$ for $r>\xi$. For small p we find that the shortest-path length satisfies the scaling relation \ell(r,\xpn,p)/\xi = f(\xpn,r/\xi). Three regions with different asymptotic behaviors are found, respectively: a) \xpn>2 where $\theta_s=1$, b) 1<\xpn<2 where 0<\theta_s(\xpn)<1/2 and, c) \xpn<1 where $\ell(r)$ behaves logarithmically, i.e. $\theta_s=0$. The characteristic length $\xi$ is of the form $\xi \sim p^{-\nu}$ with \nu=1/(2-\xpn) in region b), but depends on L as well in region c). A directed model of shortest-paths is solved and compared with numerical results.Comment: 10 pages, 10 figures, revtex4. Submitted to PR

Varieties of modules and pp-blocks of finite groups (Cohomology of Finite Groups and Related Topics)

We present a number of variants of a constructive algorithm able to solve a wide variety of variants of the Two-Dimensional Irregular Bin Packing Problem (2DIBPP). The aim of the 2DIBPP is to pack a set of irregular pieces, which may have concavities, into stock sheets (bins) with fixed dimensions in such a way that the utilization is maximized. This problem is inspired by a real application from a ceramic company in Spain. In addition, this problem arises in other industries such as the garment industry or ship building. The constructive procedure presented in this paper allows both free orientation for the pieces, as in the case of the ceramic industry, or a finite set of orientations as in the case of the garment industry. We explicitly model the assignment of pieces to bins and compare with the more common strategy of packing bins sequentially. There are very few papers in the literature that address the bin packing problem with irregular pieces and to our knowledge this is the first to additionally consider free rotation of pieces with bin packing. We propose several Integer Programing models to determine the association between pieces and bins and then we use a Mixed Integer Programing model for placing the pieces into the bins. The computational results show that the algorithm obtains high quality results in sets of instances with different properties. We have used both industry data and the available data in the literature of 2D irregular strip packing and bin packing problems

Experiencias de utilización del método de búsqueda TABU en la resolución de problemas de organización universitaria

A lo largo de los 10 últimos años hemos trabajado en problemas de organización académica de grandes dimensiones. En problemas universitarios hemos tratado la confección de calendarios de exámenes, la asignación de estudiantes a grupos vinculada al problema de la automatrícula y también la confección de horarios. Todos estos problemas son difíciles (NP-hard) por lo que en todos los casos los algoritmos de resolución implementados han sido complejos y basados en procedimientos adaptados a cada problema. Sin embargo, en todos ellos el método de Búsqueda Tabú (Tabu Search) ha constituído el elemento esencial en la obtención de buenas soluciones. En el presente trabajo exponemos algunas enseñanzas de estas experiencias. Tanto aquellos elementos que se han mostrado útiles en el conjunto de los problemas como los que han mostrado una validez diferente en los diversos casos planteados. Asimismo se examinan diferentes posibilidades de uso de los elementos del Tabú y se exponen conclusiones

Minimizing weighted earliness-tardiness on parallel machines using hybrid metaheuristics

We consider the problem of scheduling a set of jobs on a set of identical parallel machines where the objective is to minimize the total weighted earliness and tardiness penalties with respect to a common due date. We propose a hybrid heuristic algorithm for constructing good solutions, combining priority rules for assigning jobs to machines and a local search with exact procedures for solving the one-machine subproblems. These solutions are then used in two metaheuristic frameworks, Path Relinking and Scatter Search, to obtain high quality solutions for the problem. The algorithms are tested on a large number of test instances to assess the efficiency of the proposed strategies. The results show that our algorithms consistently outperform the best reported results for this problem.This study has been partially supported by the Spanish Ministry of Science and Technology, DPI2011-24977, and by Generalitat Valenciana, PROMETEO/2013/049.Alvarez Valdes, R.; Tamarit, J.; Villa Juliá, MF. (2015). Minimizing weighted earliness-tardiness on parallel machines using hybrid metaheuristics. Computers and Operations Research. 54:1-11. doi:10.1016/j.cor.2014.08.020S1115

GRASP and path relinking for project scheduling under partially renewable resources

Recently, in the field of project scheduling problems the concept of partially renewable resources has been introduced. Theoretically, it is a generalization of both renewable and non-renewable resources. From an applied point of view, partially renewable resources allow us to model a large variety of situations that do not fit into classical models, but can be found in real problems in timetabling and labor scheduling. In this paper, we develop some preprocessing techniques and several heuristic algorithms for the problem. Preprocessing significantly reduces the dimension of the problems, therefore improving the efficiency of solution procedures. Heuristic algorithms based on GRASP and Path relinking are then developed and tested on existing test instances, obtaining excellent results.

GRASP and path relinking for project scheduling under partially renewable resources

[EN] Recently, in the field of project scheduling problems the concept of partially renewable resources has been introduced. Theoretically, it is a generalization of both renewable and non-renewable resources. From an applied point of view, partially renewable resources allow us to model a large variety of situations that do not fit into classical models, but can be found in real problems in timetabling and labor scheduling. In this paper, we develop some preprocessing techniques and several heuristic algorithms for the problem. Preprocessing significantly reduces the dimension of the problems, therefore improving the efficiency of solution procedures. Heuristic algorithms based on GRASP and Path relinking are then developed and tested on existing test instances, obtaining excellent results.This work has been partially supported by the Spanish Ministry of Education and Science DPI2005-04796Alvarez-Valdes, R.; Crespo, E.; Tamarit, J.; Villa Juliá, MF. (2008). GRASP and path relinking for project scheduling under partially renewable resources. European Journal of Operational Research. 189(3):1153-1170. https://doi.org/10.1016/j.ejor.2006.06.073S11531170189

HORARIS: un paquete informático para confeccionar horarios de universidad

El problema de confeccionar un horario que permita atender todos los requerimientos docentes con los medios materiales de los que se dispone es un problema al que se enfrentan todos los administradores de los centros universitarios cada año. Un equipo de la Universitat de València ha desarrollado un sistema informático para confeccionar horarios de universidad, preparado para funcionar en ordenadores personales. El núcleo del sistema lo forman un conjunto de algoritmos basados en técnicas metaheurísticas que intentan asignar a cada lección un período temporal y una aula de manera que se consiga un buen valor para una función objetivo. Dicha función ha sido definida mediante criterios seleccionados por el usuario entre una amplia gama formada por los que son habituales en las universidades españolas. El interfase de comunicación usuario-programa es de fácil manejo, funciona en Windows y permite al usuario introducir los datos, elegir los criterios que considera importantes para su horario y obtener las soluciones en un formato sencillo que pueda ser interpretado por la gran cantidad de personas implicadas en el proceso