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Demographic projection models describe the development over time of the population in terms of events. A consistency problem arises if projected numbers of events are required to satisfy certain constraints: the consistency problem can be seen as a generalization of the well-known two-sex problem in nuptiality models. This paper presents a very general characterization of consistency problems, using matrix notation, as well as a slightly less general algorithm to solve them. The preferred specification of the objective function to be minimized by the algorithm leads to a solution that can be interpreted as a generalization of the harmonic-mean approach. [ABSTRACT FROM AUTHOR]

Cross-docking is a technique firstly proposed to reduce the storage space and flow time, simultaneously. This paper addresses a truck scheduling problem, in which a position-based learning effect is taken into consideration for unloading and loading tasks done by human labors in many related environments. The goal of the given problem is to minimize the mean completion time of outbound trucks. Therefore, a mathematical model is proposed inspired by an available model in the literature of this field. Furthermore, four heuristic algorithms are developed along with a simulated annealing (SA) algorithm in order to overwhelm the complexity of large-sized problems. The performance of the proposed algorithms is compared with the optimal solutions obtained by a complete enumeration method. [ABSTRACT FROM AUTHOR]

A sparse layout problem for clusters formed by irregular 3D objects is introduced. The shape of a 3D cluster is represented as a convex hull of the objects inside the cluster. The objects in the cluster may have different irregular shapes, can be freely translated and rotated and must be placed in the cluster without mutual overlapping. Each irregular 3D object in the cluster is composed by a union of basic convex 3D objects. The clusters must be placed in a container without mutual overlapping. The objective is to maximize the distance between the 3D clusters. New geometric tools to describe analytically nonoverlapping, containment and distance constraints for 3D clusters are introduced. The sparse layout problem is formulated as a nonlinear nonconvex continuous programming problem. A solution algorithm is proposed, and computational results are provided. [ABSTRACT FROM AUTHOR]

BackgroundDiscontinuity of spirometry reference values from childhood into adulthood has been a problem with traditional reference values, thus modern modelling approaches using smoothing spline functions to better depict the transition during growth and ageing have been recently introduced. Following the publication of the new international Global Lung Initiative (GLI2012) reference values also new national Finnish reference values have been calculated using similar GAMLSS-modelling, with spline estimates for mean (Mspline) and standard deviation (Sspline) provided in tables. The aim of this study was to produce polynomial estimates for these spline functions to use in lieu of lookup tables and to assess their validity in the reference population of healthy non-smokers.MethodsLinear regression modelling was used to approximate the estimated values for Mspline and Sspline using similar polynomial functions as in the international GLI2012 reference values. Estimated values were compared to original calculations in absolute values, the derived predicted mean and individually calculated z-scores using both values.ResultsPolynomial functions were estimated for all 10 spirometry variables. The agreement between original lookup table-produced values and polynomial estimates was very good, with no significant differences found. The variation slightly increased in larger predicted volumes, but a range of −0.018 to +0.022 litres of FEV1 representing ± 0.4% of maximum difference in predicted mean.ConclusionsPolynomial approximations were very close to the original lookup tables and are recommended for use in clinical practice to facilitate the use of new reference values. [ABSTRACT FROM PUBLISHER]