A computational comparison of algorithms for the inventory routing problem

The inventory routing problem is a distribution problem in which each customer maintains a local inventory of a product such as heating oil and consumes a certain amount of that product each day. Each day a fleet of trucks is dispatched over a set of routes to resupply a subset of the customers. In this paper, we describe and compare algorithms for this problem defined over a short planning period, e.g. one week. These algorithms define the set of customers to be serviced each day and produce routes for a fleet of vehicles to service those customers. Two algorithms are compared in detail, one which first allocates deliveries to days and then solves a vehicle routing problem and a second which treats the multi-day problem as a modified vehicle routing problem. The comparison is based on a set of real data obtained from a propane distribution firm in Pennsylvania. The solutions obtained by both procedures compare quite favorably with those in use by the firm.Part of this work was performed while this author was visiting the University of Waterloo.     

Representations for the conductivity functions of multicomponent composites

The effective conductivity σ* of a multicomponent composite material is considered. Integral representations for σ* treated as a holomorphic function on a polydisk with values in a half-plane are analyzed. A representation for σ* is introduced which is symmetric in the component conductivities and for which the moments of the positive measure in the integral are directly related to the coefficients in a perturbation expansion of σ* around a homogeneous medium. This second feature, which is important for obtaining bounds on σ*, was previously available only in the two-component case. In addition, a bound valid for any holomorphic function of the above type is proven.     

Exploring the Role of Individual and Socially Constructed Knowledge Mobilization Tasks in Revealing Preservice Elementary Teachers' Understandings of a Triangle Fraction Task

This study compares the effectiveness of two forms of a knowledge mobilization task on preservice elementary teachers' (n= 65) performance in solving a triangle fraction problem. The study then identifies the source of the successful solutions by linking solutions to earlier activities. One group worked with the triangle fraction task individually; a second worked with the triangle fraction task in a social constructivist setting; a control group had no knowledge mobilization pretask. Although there was no significant difference in the frequency of successful solutions among treatment groups, a chi‐square analysis found that the social‐constructivist pretask group applied fewer ideas from the manipulative lessons as solutions to the posttask than did the comparison groups. The social constructivist group was, however, most successful at generating novel solutions to the triangle problem. The potential benefits of individual and socially constructed knowledge mobilization tasks are discussed.     

Amperometric detection of cationic neurotransmitters at nafion-coated glassy carbon electrodes in flow streams

Substantial improvements in amperometric monitoring of flowing streams are obtained by using Nafion-coated working electrodes. The charged coating tends to exclude anionic and neutral interferences, thus adding a new dimension of selectivity to electrochemical detection for flow-injection and liquid-chromatographic systems. A highly selective response is observed for cationic neurotransmitters in the presence of otherwise interfering substances (e.g., ascorbic acid, uric acid, bilirubin or chlorpromazine). The permselectivity and transport characteristics are evaluated with respect to solution pH, solvent, flow rate, film thickness, and other variables. The reduced flow-rate dependence results in low noise levels and detection limits of 0.04 and 0.10 ng of norepinephrine and epinephrine, respectively. A bilayer electrode coating, with a cellulose acetate film over the Nafion layer, offers a bifunctional (selectivity, protection) capability. Applicability to urine samples is demonstrated.     

Kinetics of the gas-phase reaction of acetone with iodine: Heat of formation and stabilization energy of the acetonyl radical

The kinetics of the gas-phase reaction CH₃COCH₃ + I₂ ? CH₃COCH₂I + HI have been measured spectrophotometrically in a static system over the temperature range 340–430°. The pressure of CH₃COCH₃ was varied from 15 to 330 torr and of I₂ from 4 to 48 torr, and the initial rate of the reaction was found to be consistent with \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_3 {\rm COCH}_3 + {\rm I}^{\rm .} \stackrel{1}{\rightarrow}{\rm CH}_{\rm 3} {\rm COCH} + {\rm HI} $\end{document} as the rate-determining step. An Arrhenius plot of the variation of k₁ with temperature showed considerable scatter of the points, depending on the conditioning of the reaction vessel. After allowance for surface catalysis, the best line drawn by inspection yielded the Arrhenius equation, log [k₁/(M^?1 sec^?1)] = (11.2 ± 0.8) – (27.7 θ 2.3)/θ, where θ = 2.303 R T in kcal/mole. This activation energy yields an acetone C? H bond strength of 98 kcal/mole and δH (CH₃CO?H₂) radical = ?5.7 ± 2.6 kcal/mole. As the acetone bond strength is the same as the primary C? H bond strength in isopropyl alcohol, there is no resonance stabilization of the acetonyl radical due to delocalization of the radical site. By contrast, the isoelectronic allyl resonance energy is 10 kcal/mole, and reasons for the difference are discussed in terms of the π-bond energies of acetone and propene.     

Kinetics of the gas-phase reaction of cyclopropylcarbinyl iodide and hydrogen iodide. Heat of formation and stabilization energy of the cyclopropylcarbinyl radical

The rate of the gas phase reaction has been measured spectrophotometrically over the range 480°–550°K. The rate constant fits the equation where θ = 2.303RT in kcal/mole. This result, together with the assumption that the activation energy for the back reaction is 0 ± 1 kcal/mole, allows calculation of DH (Δ? CH₂? H) = 97.4 ± 1.6 kcal/mole and ΔH (Δ? CH₂·) = 51.1 ± 1.6 kcal/mole. These values correspond to a stabilization energy of 0.4 ± 1.6 kcal/mole in the cyclopropylcarbinyl radical.     

Very Low-Pressure Pyrolysis (VLPP); A Versatile Kinetic Tool

The theory and applications of the very low-pressure pyrolysis technique to the study of the rates and mechanisms of unimolecular reactions, radical-radical, and radical-molecule bimolecular reactions, surface recombination of atoms, heterogeneous reactions, and vibrational energy transfer are reviewed.     

Kinetics and mechanism of chromate reduction with hydrogen peroxide in base

[Cr(VI)O(4)](2)(-) is reduced to [Cr(V)(O(2))(4)](3)(-) by hydrogen peroxide in strongly basic media where the acid dissociation of H(2)O(2) (pK(a) = 11.65) is appreciable. The reaction is first order in chromium(VI) and inhibited by hydroxide. The hydrogen peroxide dependence is defined by the form of the effective pseudo-first-order rate constant: k(eff) = [H(2)O(2)](3)/(K(1) + K(2)[H(2)O(2)] + K(3)[HO(2)(-)]) with K(1) = 175(43) s x M(3), K(2) = 403(18) s x M(2), and K(3) = 1422(34) s x M(2). Hydrogen peroxide anion initially attacks chromate, and subsequent equilibrium steps that exchange oxo groups for three peroxo groups precede a rate-determining, one-electron, intramolecular reduction step.     

Amino acid, fatty acid, and carbohydrate content of Artocarpus altilis (breadfruit)

A study is conducted to determine the amino acid, fatty acid, and carbohydrate content of breadfruit using high-performance liquid chromatography (HPLC) and gas chromatography (GC). An HPLC method is used for the determination of amino acids and fatty acids in breadfruit. Representative amino acid samples are derivatized with phenylisothiocianate and the resulting phenylthiocarbamyl derivatives are separated on a reversed-phase column by gradient elution with a 0.05M ammonium acetate buffer and 0.01M ammonium acetate in acetonitrile-methanol-water (44:10:46, v/v). Representative fatty acid samples are derivatized with phenacyl bromide and the resulting fatty acid phenacyl esters are separated on a reversed-phase column by gradient elution with acetonitrile and water. Amino acid and fatty acid derivatives are detected by ultraviolet detection at 254 nm. The analysis of the carbohydrates in breadfruit employs a GC method. Carbohydrates are derivatized using trimethylchlorosilane and hexamethyldisilazane to form trimethylsilyl ethers. Compounds in the samples are separated by the temperature programming of a GC using nitrogen as the carrier gas. Percent recoveries of amino acids, fatty acids, and carbohydrates are 72.5%, 68.2%, and 81.4%, respectively. The starch content of the breadfruit is 15.52 g/100 g fresh weight.