Bid Evaluation in Procurement Auctions with Piecewise Linear Supply Curves

Consider a marketplace operated by a buyer who wishes to procure large quantities of several heterogeneous products. Suppliers submit price curves for each of the commodities indicating the price charged as a function of the supplied quantity. The total amount paid to a supplier is the sum of the prices charged for the individual commodities. It is assumed that the submitted supply curves are piecewise linear as they often are in practice. The bid evaluation problem faced by the procurer is to determine how much of each commodity to buy from each of the suppliers so as to minimize the total purchase price. In addition to meeting the demand, the buyer may impose additional business requirements that restrict which contracts suppliers may be awarded. These requirements may result in interdependencies between the commodities which lead to suboptimal results if the commodities are traded in independent auctions rather than simultaneously. Even without the additional business constraints the bid evaluation problem is NP-hard. The main contribution of our study is a flexible column generation based heuristics that provides near-optimal solutions to the procurer’s bid evaluation problem. Our method scales very well due to the Branch-and-Price technology it is built on. We employ sophisticated rounding and local improvement heuristics to obtain quality solutions. We also developed a test data generator that produces realistic problems and allows control over the difficulty level of the problems using parameters.     

On the Existence of a Generalized Solution to a Three-Dimensional Elliptic Equation with Radiation Boundary Condition

For a second order elliptic equation with a nonlinear radiation-type boundary condition on the surface of a three-dimensional domain, we prove existence of generalized solutions without explicit conditions (like ) on the trace of solutions. In the boundary condition, we admit polynomial growth of any fixed degree in the unknown solution, and the heat exchange and emissivity coefficients may vary along the radiating surface. Our generalized solution is contained in a Sobolev space with an exponent q which is greater than for the fourth power law.     

The Hilbert Kernel Regression Estimate

Let (X, Y) be an ^d× -valued regression pair, whereXhas a density andYis bounded. Ifni.i.d. samples are drawn from this distribution, the Nadaraya–Watson kernel regression estimate in ^dwith Hilbert kernelK(x)=1/x^dis shown to converge weakly for all such regression pairs. We also show that strong convergence cannot be obtained. This is particularly interesting as this regression estimate does not have a smoothing parameter.     

Nonlinear effects of electrolyte diodes and transistors in a polymer gel medium

The polarization curve of an acid-base interface in a hydrogel medium has a diode characteristic. Two of each such electrolyte diodes can be combined to give an electrolyte transistor. When a salt is added to the alkaline or to the acidic part of a reverse biased electrolyte diode, the current response is highly nonlinear. If the salt is added to the acidic side, even bistability can be observed. This bistability can generate complex oscillations in a base-acid-base electrolyte transistor. These nonlinear effects are studied experimentally and theoretically. While the nonlinear salt effect can be explained with the Nernst-Planck equations, to understand the bistable behavior further investigations are necessary. (c) 1999 American Institute of Physics.     

Selective and shape-selective Baeyer-Villiger oxidations of aromatic aldehydes and cyclic ketones with Sn-beta zeolites and H2O2

Sn-Beta is used as a heterogeneous catalyst for the Baeyer-Villiger reaction with hydrogen peroxide. Cyclic ketones are transformed into the corresponding lactones, while unsaturated ketones are oxidized to the corresponding unsaturated lactones with very high chemoselectivity. The catalyst is also selective for the oxidation of aromatic aldehydes with H2O2, producing the formate ester or the corresponding hydrolyzed product, that is the alcohol. Shape-selective oxidations are observed for isomeric reactants with different molecular shapes. The catalytic Sn sites have been characterized by 119Sn MAS-NMR spectroscopy, and tetrahedral incorporation into the zeolite framework has been demonstrated. In situ IR spectroscopy and 18O labeling experiments have shown that the oxidation mechanism involves an intermediate of the Criegee type.     

Intermediates of the borane reduction of some imidazolidines: An AM1 study

Amine(N? B)-aminoborane internal complexes and 1,3,2-diazaborolidines were recently identified as intermediates of the borane reduction of imidazolidino[1,2-d]dithiazepines. Theoretical Mo calculations were used to obtain the structural, conformational, and electronic properties and heats of formation of the boron compounds in the framework of the semiempirical AM 1 approximation. Internal constraints in the bicyclic system were analyzed through comparisons with the calculated molecular geometries, electron distribution of monocyclic, and open-chain models. The geometry of the five-membered diazaborolidine systems becomes distorted upon building up the complex bicyclic structure, compared to the nearly planar monocycles. The weak coordinative nitrogen–boron bond (calculated bond order around 0.5) in the internal complexes exerts less conformational strains in the adjoining nine-membered ring containing the disulfide than does the covalent N? B bond in the corresponding 1,2,3-diazaborolidine. Thus, the internal constraints of the bicyclic system is taken up by the five-membered ring to a lesser degree in the 1,3,2diazaborolidine than in the internal complex. © 1992 John Wiley & Sons, Inc.     

Chelation of Na+ cations in nonaqueous solvents. Structural requirements and methodological considerations

Intrinsic formation constants for complexes of Na⁺ ions with a series of polyamines have been determined from²³Na NMR measurements in binary mixtures of tetrahydrofuran (THF) and amines. The results show in a totally unambiguous manner a regular decrease in the magnitude of the chelate effect with the number of atoms intervening between the nitrogen ligators. The key assumption, tetracoordination of the cation, is critically examined, and experimental evidence is adduced in its support.     

Komplexkatalyse : VI. Ir-spektroskopische untersuchung der reaktion von nitrosylmolybdänkomplexen mit C2H5AlCl2, (C2H5)3Al,AlCl3 und kohlenmonoxid,ein beitrag zur klärung der struktur des katalytisch aktiven komplexes für die olefinmetathese

The reaction of di- and mono-nitrosylmolybdenum complexes with C₂H₅-AlCl₂, AlCl₃ and Al(C₂H₅)₃ under argon and CO was followed IR-spectroscopically. Some conclusions were reached concerning the nature of the catalyticactivity of the complex in olefin metathesis.     

Intranasal irradiation with the xenon chloride ultraviolet B laser improves allergic rhinitis

We earlier reported that the 308 nm xenon chloride (XeCl) ultraviolet B (UVB) laser is highly effective for the treatment of inflammatory skin diseases. Since UVB irradiation has been shown to exert both local and systemic immunosuppression, we investigated the clinical efficacy of UVB irradiation in allergic rhinitis. In an open study, groups of patients with severe allergic rhinitis received intranasal irradiation with a 308 nm XeCl UVB excimer laser for two weeks. In the low-dose group (n=10), treatment was given twice weekly, starting with 0.25x the individual minimal erythema dose (MED), whereas patients in the medium-dose group (n=8) were treated four times weekly, starting with 0.4x MED. In each group, the dosage was gradually increased. Evaluation was based on the symptom scores. The effect of the XeCl laser on the skin prick test reaction was also studied. In the low-dose group, seven patients completed the study, and there was no improvement in the nasal symptoms. In the medium-dose group, the XeCl UVB irradiation significantly inhibited the rhinorrhoea, the sneezing, the nasal obstruction and the total nasal score (p<0.05). The XeCl UVB excimer laser also inhibited the allergen-induced skin prick test in a dose-dependent manner. These results suggest that the XeCl UVB excimer laser might serve as a new therapeutic tool in the treatment of allergic rhinitis.