A Comparison of Mixed-Integer Programming Models for Non-Convex Piecewise Linear Cost Minimization Problems

We study a generic minimization problem with separable non-convex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed integer programming formulations each approximates the cost function by its lower convex envelope. We also show a relationship between this result and classical Lagrangian duality theory

Models and Methods for Merge-In-Transit Operations

We develop integer programming formulations and solution methods for addressing operational issues in merge-in-transit distribution systems. The models account for various complex problem features including the integration of inventory and transportation decisions, the dynamic and multimodal components of the application, and the non-convex piecewise linear structure of the cost functions. To accurately model the cost functions, we introduce disaggregation techniques that allow us to derive a hierarchy of linear programming relaxations. To solve these relaxations, we propose a cutting-plane procedure that combines constraint and variable generation with rounding and branch-and-bound heuristics. We demonstrate the effectiveness of this approach on a large set of test problems with instances with up to almost 500,000 integer variables derived from actual data from the computer industry. Key words : Merge-in-transit distribution systems, logistics, transportation, integer programming, disaggregation, cutting-plane method

Chemometric study on the forensic discrimination of soil types using their infrared spectral characteristics

Soil has been utilized in criminal investigations for some time because of its prevalence and transferability. It is usually the physical characteristics that are studied, however the research carried out here aims to make use of the chemical profile of soil samples. The research we are presenting in this work used sieved (2mm) soil samples taken from the top soil layer (about 10cm) that were then analysed using mid infrared spectroscopy. The spectra obtained were pre-treated and then input into two chemometric classification tools: Nonlinear iterative partial least squares followed by linear discriminant analysis (NIPALS-LDA) and partial least squares discriminant analysis (PLS-DA). The models produced show that it is possible to discriminate between soil samples from different land use types and both approaches are comparable in performance. NIPALS-LDA performs much better than PLS-DA in classifying samples to locatio