The Sample Average Approximation Method Applied to Stochastic Routing Problems: A Computational Study

The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. The process is repeated with different samples to obtain candidate solutions along with statistical estimates of their optimality gaps.We present a detailed computational study of the application of the SAA method to solve three classes of stochastic routing problems. These stochastic problems involve an extremely large number of scenarios and first-stage integer variables. For each of the three problem classes, we use decomposition and branch-and-cut to solve the approximating problem within the SAA scheme. Our computational results indicate that the proposed method is successful in solving problems with up to 2¹⁶⁹⁴ scenarios to within an estimated 1.0% of optimality. Furthermore, a surprising observation is that the number of optimality cuts required to solve the approximating problem to optimality does not significantly increase with the size of the sample. Therefore, the observed computation times needed to find optimal solutions to the approximating problems grow only linearly with the sample size. As a result, we are able to find provably near-optimal solutions to these difficult stochastic programs using only a moderate amount of computation time.     

Jack van Lint (1932-2004): A survey of his scientific work

When Jack van Lint was appointed as full professor at the Eindhoven University of Technology at the age of 26 he combined a PhD in number theory with a very open scientific mind. It took a sabbatical visit to Bell Laboratories in 1966 to make him understand that a new and fascinating field of applied mathematics was emerging: discrete mathematics. It fascinated and inspired him for the rest of his life. When he passed away on September 28, 2004, he left behind a legacy of 18 books and 177 articles, covering many aspects of coding theory, combinatorics, and finite geometry.van Lint was also a strong international advocate of the role that discrete mathematics ought to play in modern applied mathematics curricula. Quite a few departments sought his advice. Years later, four different universities showed their appreciation by awarding him an honorary degree.This overview is an homage to van Lint's academic achievements and can serve as an introduction to his work for younger generations.     

Enolates de l'acetylacetate d'ethyle. Structure et reactivite du sel de potassium en presence d'ether couronne et de cryptand

It is shown that, through the addition of 18-crown-6 or cryptand (2.2.2) to potassium ethyl acetoacetate enolate solutions in tetrahydrofuran, 1:1 complexes are formed. A single crystal of the 1:1 potassium énolate-18-crown-6 complex has been obtained. Its structure has been determined by X-ray diffraction. The crystal includes entities formed from an enolate anion chelating a potassium cation externally complexed by the crown-ether. The vibrational spectrometry shows that the structure of the entity is kept in solution. In the species formed through the addition of cryptand (2.2.2), the enolate anion has a structure (IR spectroscopy) and a reactivity very close to that of the free anion, observed in a dissociating solvent (DMSO, HMPA). When crown ether is added, a contact ion pair is formed, in which the cation is externally solvated by the crown. On the other hand, the cation encapsulation by the cryptand leads to a released anion with an “ S-trans” or “W” structure. The reactivity and the orientation of the alkylation reactions of these entities have been measured in THF solutions. They are discussed in relation to the structure of the species present in the reaction medium.     

Organic Syntheses Without Solvent: Preparation of Alkoxyphthalimides and of Alkoxylamines

Alkoxyphthalimides are prepared by alkylation of N-hydroxyphthalimide under solid-liquid phase transfer catalysis without solvent. When conversion of alkoxyphthalimides into alkoxylamines is nearly complete, neat hydrazine hydrate is added at room temperature.     

Identification and quantification of the antipsychotics risperidone,aripiprazole, pipamperone and their major metabolites in plasma using ultra‐high performance liquid chromatography–mass spectrometry

The antipsychotics risperidone, aripiprazole and pipamperone are frequently prescribed for the treatment in children with autism. The aim of this study was to validate an ultra‐high performance liquid chromatography–mass spectrometry method for the quantification of these antipsychotics in plasma. An ultra‐high performance liquid chromatography–mass spectrometry assay was developed for the determination of the drugs and metabolites. Gradient elution was performed on a reversed‐phase column with a mobile phase consisting of ammonium acetate, formic acid in methanol or in Milli‐Q ultrapure water at a flow rate of 0.5 mL/min. The method was validated according to the US Food and Drug Administration guidelines. The analytes were found to be stable enough after reconstitution and injection of only 5 μL improved the accuracy and precision in combination with the internal standard. Calibration curves of all five analytes were linear. All analytes were stable for at least 72 h in the autosampler and the high quality control of 9‐OH‐risperidone was stable for 48 h. The method allows quantification of all analytes. The advantage of this method is the combination of a minimal injection volume, a short run‐time, an easy sample preparation method and the ability to quantify all analytes in one run. Copyright © 2015 John Wiley & Sons, Ltd.     

A new level‐dependent coarse grid correction scheme for indefinite Helmholtz problems

In this paper, we construct and analyze a level‐dependent coarse grid correction scheme for indefinite Helmholtz problems. This adapted multigrid (MG) method is capable of solving the Helmholtz equation on the finest grid using a series of MG cycles with a grid‐dependent complex shift, leading to a stable correction scheme on all levels. It is rigorously shown that the adaptation of the complex shift throughout the MG cycle maintains the functionality of the two‐grid correction scheme, as no smooth modes are amplified in or added to the error. In addition, a sufficiently smoothing relaxation scheme should be applied to ensure damping of the oscillatory error components. Numerical experiments on various benchmark problems show the method to be competitive with or even outperform the current state‐of‐the‐art MG‐preconditioned Krylov methods, for example, complex shifted Laplacian preconditioned flexible GMRES. Copyright © 2013 John Wiley & Sons, Ltd.