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.     

The determination of pd,pt, au,ag and ir in copper by neutron activation analysis

The determination of palladium, platinum and gold in copper metal by neutron activation analysis is described. The matrix activity was separated from the noble metals by cation-exchange adsorption. Gold was extracted; palladium and platinum were precipitated. The precipitates were counted with a low-energy photon detector. The gold results were checked by instrumental neutron activation analysis. Silver, iridium, selenium, antimony and arsenic were also determined simultaneously.     

Mass spectrometric study to characterize thioisoindole derivatives of aminoglycoside antibiotics

Aminoglycoside antibiotics are widely used to treat serious Gram-negative and Gram-positive bacterial infections. The lack of a UV chromophore presents a problem in the analysis of aminoglycosides. Derivatization with 1,2-phthalic dicarboxaldehyde (OPA) in the presence of a thiol made it possible to introduce a UV chromophoric thioisoindole moiety. A qualitative mass spectrometry study was carried out to confirm the molecular identity of the products formed. The conditions described earlier to derivatize gentamicin and kanamycin yielded products in which all primary amino groups are fully derivatized. On the other hand, with tobramycin and amikacin, there was also formation of incompletely derivatized products that contained one thioisoindole group less than the fully derivatized product. This study has therefore brought an additional insight into the nature of the OPA-aminoglycoside derivatives studied.     

Investigation of unknown related substances in commercial erythromycin samples with liquid chromatography/mass spectrometry

A selective reversed phase liquid chromatography/mass spectrometry (LC/MS(n)) method is described for the identification of erythromycin impurities and related substances in commercial erythromycin samples. Mass spectral data are acquired on a LCQ ion trap mass spectrometer equipped with an electrospray interface operated in positive ion mode. The LCQ is ideally suited for identification of impurities and related substances because it provides on-line LC/MS(n) capability. Compared with UV detection, this hyphenated LC/MS(n) technique provides as a main advantage efficient identification of novel substances without time-consuming isolation and purification procedures. Using this method four novel related substances were identified in commercial samples.     

The determination of platinum and palladium in copperbased standard reference materials by neutron activation analysis

The determination of palladium and platinum by n.a.a. in 100-1 μg g^?1 Pd-Cu and Pt-Cu alloys is described. To avoid systematic errors, standards with approximately the same shape and composition as the samples were prepared by quantitative deposition of the noble metals from dilute hydrochloric acid medium on copper powder; after ignition in hydrogen, the powder was pressed to standard pellets. Platinum was determined by i.n.a.a. via ¹⁹⁹Au. For palladium an instrumental analysis via ¹¹¹Ag was possible only for the 100 μg g^?1 samples. For the lower concentrations copper was removed by cation exchange and palladium was determined via the ¹⁰⁹Pd-^109mAg isotopes. The precision for each analysis was 2–3 % relative. The accuracy was checked by comparison with results from other laboratories.     

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.