A continuous-time MILP model for short-term scheduling of make-and-pack production processes

In process industries, make-and-pack production is used to produce food and beverages, chemicals, and metal products, among others. This type of production process allows the fabrication of a wide range of products in relatively small amounts using the same equipment. In this article, we consider a real-world production process (cf. Honkomp et al. 2000. The curse of reality – why process scheduling optimization problems are diffcult in practice. Computers & Chemical Engineering, 24, 323–328.) comprising sequence-dependent changeover times, multipurpose storage units with limited capacities, quarantine times, batch splitting, partial equipment connectivity, and transfer times. The planning problem consists of computing a production schedule such that a given demand of packed products is fulfilled, all technological constraints are satisfied, and the production makespan is minimised. None of the models in the literature covers all of the technological constraints that occur in such make-and-pack production processes. To close this gap, we develop an efficient mixed-integer linear programming model that is based on a continuous time domain and general-precedence variables. We propose novel types of symmetry-breaking constraints and a preprocessing procedure to improve the model performance. In an experimental analysis, we show that small- and moderate-sized instances can be solved to optimality within short CPU times.

A hybrid method for large-scale short-term scheduling of make-and-pack production processes

Due to the ongoing trend towards increased product variety, fast-moving consumer goods such as food and beverages, pharmaceuticals, and chemicals are typically manufactured through so-called make-and-pack processes. These processes consist of a make stage, a pack stage, and intermediate storage facilities that decouple these two stages. In operations scheduling, complex technological constraints must be considered, e.g., non-identical parallel processing units, sequence-dependent changeovers, batch splitting, no-wait restrictions, material transfer times, minimum storage times, and finite storage capacity. The short-term scheduling problem is to compute a production schedule such that a given demand for products is fulfilled, all technological constraints are met, and the production makespan is minimised. A production schedule typically comprises 500–1500 operations. Due to the problem size and complexity of the technological constraints, the performance of known mixed-integer linear programming (MILP) formulations and heuristic approaches is often insufficient. We present a hybrid method consisting of three phases. First, the set of operations is divided into several subsets. Second, these subsets are iteratively scheduled using a generic and flexible MILP formulation. Third, a novel critical path-based improvement procedure is applied to the resulting schedule. We develop several strategies for the integration of the MILP model into this heuristic framework. Using these strategies, high-quality feasible solutions to large-scale instances can be obtained within reasonable CPU times using standard optimisation software. We have applied the proposed hybrid method to a set of industrial problem instances and found that the method outperforms state-of-the-art methods.

Bone Volume Fraction and Fabric Anisotropy Are Better Determinants of Trabecular Bone Stiffness than Other Morphological Variables

As our population ages, more individuals suffer from osteoporosis. This disease leads to impaired trabecular architecture and increased fracture risk. It is essential to understand how morphological and mechanical properties of the cancellous bone are related. Morphologyelasticity relationships based on bone volume fraction (BV/TV) and fabric anisotropy explain up to 98% of the variation in elastic properties. Yet, other morphological variables such as individual trabeculae segmentation (ITS) and trabecular bone score (TBS) could improve the stiffness predictions. A total of 743 micro-computed tomography reconstructions of cubic trabecular bone samples extracted from femur, radius, vertebrae and iliac crest were analysed. Their morphology was assessed via 25 variables and their stiffness tensor (inline image) was computed from six independent load cases using micro finite element analyses. Variance inflation factors were calculated to evaluate collinearity between morphological variables and decide upon their inclusion in morphology-elasticity relationships. The statistically admissible morphological variables were included in a multi-linear regression modelling the dependent variable inline image. The contribution of each independent variable was evaluated (ANOVA). Our results show that BV/TV is the best determinant of inline image (inline image=0.889), especially in combination with fabric (inline image=0.968). Including the other independent predictors hardly affected the amount of variance explained by the model (inline image=0.975). Across all anatomical sites, BV/TV explained 87% of the variance of the bone elastic properties. Fabric further described 10% of the bone stiffness, but the improvement in variance explanation by adding other independent factors was marginal (<1%). These findings confirm that BV/TV and fabric are the best determinants of trabecular bone stiffness and show, against common belief, that other morphological variables do not bring any further contribution. These overall conclusions remain to be confirmed for specific bone diseases and post-elastic properties.

Decision Support Models for Composing and Navigating through e-Learning Objects

Libraries of learning objects may serve as basis for deriving course offerings that are customized to the needs of different learning communities or even individuals. Several ways of organizing this course composition process are discussed. Course composition needs a clear understanding of the dependencies between the learning objects. Therefore we discuss the metadata for object relationships proposed in different standardization projects and especially those suggested in the Dublin Core Metadata Initiative. Based on these metadata we construct adjacency matrices and graphs. We show how Gozinto-type computations can be used to determine direct and indirect prerequisites for certain learning objects. The metadata may also be used to define integer programming models which can be applied to support the instructor in formulating his specifications for selecting objects or which allow a computer agent to automatically select learning objects. Such decision models could also be helpful for a learner navigating through a library of learning objects. We also sketch a graph-based procedure for manual or automatic sequencing of the learning objects.

SNA--a toolbox for the stoichiometric analysis of metabolic networks

BACKGROUND: Despite recent algorithmic and conceptual progress, the stoichiometric network analysis of large metabolic models remains a computationally challenging problem. RESULTS: SNA is a interactive, high performance toolbox for analysing the possible steady state behaviour of metabolic networks by computing the generating and elementary vectors of their flux and conversions cones. It also supports analysing the steady states by linear programming. The toolbox is implemented mainly in Mathematica and returns numerically exact results. It is available under an open source license from: http://bioinformatics.org/project/?group_id=546. CONCLUSION: Thanks to its performance and modular design, SNA is demonstrably useful in analysing genome scale metabolic networks. Further, the integration into Mathematica provides a very flexible environment for the subsequent analysis and interpretation of the results.

Fully Automatic Segmentation of Hip CT Images

Automatic segmentation of the hip joint with pelvis and proximal femur surfaces from CT images is essential for orthopedic diagnosis and surgery. It remains challenging due to the narrowness of hip joint space, where the adjacent surfaces of acetabulum and femoral head are hardly distinguished from each other. This chapter presents a fully automatic method to segment pelvic and proximal femoral surfaces from hip CT images. A coarse-to-fine strategy was proposed to combine multi-atlas segmentation with graph-based surface detection. The multi-atlas segmentation step seeks to coarsely extract the entire hip joint region. It uses automatically detected anatomical landmarks to initialize and select the atlas and accelerate the segmentation. The graph based surface detection is to refine the coarsely segmented hip joint region. It aims at completely and efficiently separate the adjacent surfaces of the acetabulum and the femoral head while preserving the hip joint structure. The proposed strategy was evaluated on 30 hip CT images and provided an average accuracy of 0.55, 0.54, and 0.50 mm for segmenting the pelvis, the left and right proximal femurs, respectively.

Retinal slit lamp video mosaicking

Purpose To this day, the slit lamp remains the first tool used by an ophthalmologist to examine patient eyes. Imaging of the retina poses, however, a variety of problems, namely a shallow depth of focus, reflections from the optical system, a small field of view and non-uniform illumination. For ophthalmologists, the use of slit lamp images for documentation and analysis purposes, however, remains extremely challenging due to large image artifacts. For this reason, we propose an automatic retinal slit lamp video mosaicking, which enlarges the field of view and reduces amount of noise and reflections, thus enhancing image quality. Methods Our method is composed of three parts: (i) viable content segmentation, (ii) global registration and (iii) image blending. Frame content is segmented using gradient boosting with custom pixel-wise features. Speeded-up robust features are used for finding pair-wise translations between frames with robust random sample consensus estimation and graph-based simultaneous localization and mapping for global bundle adjustment. Foreground-aware blending based on feathering merges video frames into comprehensive mosaics. Results Foreground is segmented successfully with an area under the curve of the receiver operating characteristic curve of 0.9557. Mosaicking results and state-of-the-art methods were compared and rated by ophthalmologists showing a strong preference for a large field of view provided by our method. Conclusions The proposed method for global registration of retinal slit lamp images of the retina into comprehensive mosaics improves over state-of-the-art methods and is preferred qualitatively.