Branch-and-price approach for the multi-skill project scheduling problem

This work introduces a procedure to solve the multi-skill project scheduling problem (MSPSP) (Néron and Baptista, International symposium on combinatorial, optimization (CO’2002), 2002). The MSPSP mixes both the classical resource constrained project scheduling problem and the multi-purpose machine model. The aim is to find a schedule that minimizes the completion time (makespan) of a project, composed of a set of activities. In addition, precedence relations and resources constraints are considered. In this problem, resources are staff members that master several skills. Thus, a given number of workers must be assigned to perform each skill required by an activity. Practical applications include the construction of buildings, as well as production and software development planning. We present a column generation approach embedded within a branch-and-price (B&P) procedure that considers a given activity and time-based decomposition approach. Obtained results show that the proposed B&P procedure is able to reach optimal solutions for several small and medium sized instances in an acceptable computational time. Furthermore, some previously open instances were optimally solved.     

Ketopiperazines: Conformationally Constrained Peptidomimetic of Arginine Amides

We have synthesized guanidine‐containing ketopiperazines designed to be conformational mimics of peptidomimetic arginine amides. D‐Allylglycine was converted by an efficient approach to give enantiopure ketopiperazines in which the trans stereochemistry of the C‐substituents resulted from stereospecific enolate alkylation.     

Algorithmes stochastiques à bruit dépendant

We introduce different ways of modeling the dependency of the input noise of stochastic algorithms. We are aimed to prove that such innovations allow us to use the ODE (ordinary differential equation) method. Illustrations in the linear regression framework and in the law of the large number for triangular arrays of weighted dependent random variables are also given. We have aimed to provide results easy to check in practice. To cite this article: P. Doukhan, O. Brandière, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Structural Aspects of 5‐methylthio‐1‐oxa‐6,6a δIV‐dithia‐2‐azapentalenes

Alkylation of 5‐[1‐hydroxyiminoalkyl]‐1,2‐dithiole‐3‐thiones using methyl iodide in the presence of sodium hydroxide gives derivatives which may be considered as being 5‐methylthio‐1‐oxa‐6,6a δ^IV‐dithia‐2‐azapentalenes with quantitative yields. The structure of oxadithiazapentalene attributed to the alkylation products is founded on X‐ray analysis and NMR and IR data.     

Etude en RMN du carbone 13 de dicoumarols substitués

The ¹³C n.m.r. spectrum of the bridge substituted dicoumarols are interpreted in order to obtain structural information for quantitative structure-activity relationships. The results are in agreement with those obtained by ¹H n.m.r. These dicoumarols exhibit double restricted rotation around both bridge bonds.     

Détermination des constantes thermodynamiques d'équilibres en solution par calorimétrie à conduction et flux de réactif: I. Description de la méthode

An injection apparatus attached to the two elements of a conduction microcalorimeter allows measurement of the thermal change arising from displacement of the equilibria in the liquid phase.Analysis of the thermograms obtained leads to the simultaneous determination of the enthalpy increase and the equilibrium constants. The high sensitivity of the thermal fluxmeter used, a calorimeter of the Calvet type, its excellent temperature stability allows, under certain conditions, the observation of successive equilibria and thus facilitates the interpretation of the phenomena.     

The diameter of domination k-critical graphs

A graph is k-domination-critical if γ(G) = k, and for any edge e not in G, γ(G + e) = k ? 1. In this paper we show that the diameter of a domination k-critical graph with k ≧ 2 is at most 2k ? 2. We also show that for every k ≧ 2, there is a k-domination-critical graph having diameter [(3/2)k ? 1]. We also show that the diameter of a 4-domination-critical graph is at most 5.