Abstract
We present an exact method, based on an arc-flow formulation with side constraints, for solving bin packing and cutting stock problems-including multi-constraint variants-by simply representing all the patterns in a very compact graph. Our method includes a graph compression algorithm that usually reduces the size of the underlying graph substantially without weakening the model. Our formulation is equivalent to Gilmore and Gomory's, thus providing a very strong linear relaxation. However, instead of using column-generation in an iterative process, the method constructs a graph, where paths from the source to the target node represent every valid packing pattern. The same method, without any problem-specific parameterization, was used to solve a large variety of instances from several different cutting and packing problems. In this paper, we deal with vector packing, bin packing, cutting stock, cardinality constrained bin packing, cutting stock with cutting knife limitation, bin packing with conflicts, and other problems. We report computational results obtained with many benchmark test datasets, some of them showing a large advantage of this formulation with respect to the traditional ones.

Abstract
This paper presents a class of packing problems where circles may be placed either inside or outside other circles, the whole set being packed in a rectangle. This corresponds to a practical problem of packing tubes in a container. Before being inserted in the container, tubes may be put inside other tubes in a recursive fashion. A variant of the greedy randomized adaptive search procedure is proposed for tackling this problem, and its performance is assessed in a set of benchmark instances.

Abstract
SCIP is a solver for a wide variety of mathematical optimization problems. It is written in C and extendable due to its plug-in based design. However, dealing with all C specifics when extending SCIP can be detrimental to development and testing of new ideas. This paper attempts to provide a remedy by introducing PySCIPOPT, a Python interface to SCIP that enables users to write new SCIP code entirely in Python. We demonstrate how to intuitively model mixed-integer linear and quadratic optimization problems and moreover provide examples on how new Python plug-ins can be added to SCIP.

Abstract

Abstract
This research aims at tackling a real-world long-haul freight transportation problem where tractors are allowed to exchange semi-trailers through several transshipment points until a request reaches its destiny. The unique characteristics of the considered logistics network allow for providing long-haul services by means of short-haul jobs, drastically reducing empty truck journeys. A greater flexibility is achieved with faster responses. Furthermore, the planning goals as well as the nature of the considered trips led to the definition of a new problem, the long-haul freight transportation problem with multiple transshipment locations. A novel mathematical formulation is developed to ensure resource synchronization while including realistic features, which are commonly found separately in the literature. Considering the complexity and dimension of this routing and scheduling problem, a mathematical programming heuristic (matheuristic) is developed with the objective of obtaining good quality solutions in a reasonable amount of time, considering the logistics business context. We provide a comparison between the results obtained for 79 real-world instances. The developed solution method is now the basis of a decision support system of a Portuguese logistics operator (LO).

Abstract
With rising healthcare costs, using health personnel and resources efficiently and effectively is critical. International cross-country and simple worker-to-population ratio comparisons are frequently used for improving the efficiency of health systems, planning of health human resources and guiding policy changes. These comparisons are made between countries typically of the same continental region. However, if used imprudently, inconsistencies arising from frail comparisons of health systems may outweigh the positive benefits brought by new policy insights. In this work, we propose a different approach to international health system comparisons. We present a methodology to group similar countries in terms of mortality, morbidity, utilisation levels, and human and physical resources, which are all factors that influence health gains. Instead of constructing an absolute rank or comparing against the average, the method finds countries that share similar ground, upon which more reliable comparisons can then be conducted, including performance analysis. We apply this methodology using data from the World Health Organization's Health for All database, and we present some interesting empirical relationships between indicators that may provide new insights into how such information can be used to promote better healthcare planning and policy guidance.