Multi-resource allocation in stochastic project scheduling

We propose a resource allocation model for project scheduling. Our model accommodates multiple resources and decision-dependent activity durations inspired by microeconomic theory. First, we elaborate a deterministic problem formulation. In a second stage, we enhance this model to account for uncertain problem parameters. Assuming that the first and second moments of these parameters are known, the stochastic model minimises an approximation of the value-at-risk of the project makespan. As a salient feature, our approach employs a scenario-free formulation which is based on normal approximations of the activity path durations. We extend our model to situations in which the moments of the random parameters are ambiguous and describe an iterative solution procedure. Extensive numerical results are provided.     

Robust portfolio optimization: a conic programming approach

The Markowitz Mean Variance model (MMV) and its variants are widely used for portfolio selection. The mean and covariance matrix used in the model originate from probability distributions that need to be determined empirically. It is well known that these parameters are notoriously difficult to estimate. In addition, the model is very sensitive to these parameter estimates. As a result, the performance and composition of MMV portfolios can vary significantly with the specification of the mean and covariance matrix. In order to address this issue we propose a one-period mean-variance model, where the mean and covariance matrix are only assumed to belong to an exogenously specified uncertainty set. The robust mean-variance portfolio selection problem is then written as a conic program that can be solved efficiently with standard solvers. Both second order cone program (SOCP) and semidefinite program (SDP) formulations are discussed. Using numerical experiments with real data we show that the portfolios generated by the proposed robust mean-variance model can be computed efficiently and are not as sensitive to input errors as the classical MMV??s portfolios.     

Global optimization of multi-parametric MILP problems

In this paper, we present a novel global optimisation approach for the general solution of multi-parametric mixed integer linear programs (mp-MILPs). We describe an optimisation procedure which iterates between a (master) mixed integer nonlinear program and a (slave) multi-parametric program. Moreover, we explain how to overcome the presence of bilinearities, responsible for the non-convexity of the multi-parametric program, in two classes of mp-MILPs, with (i) varying parameters in the objective function and (ii) simultaneous presence of varying parameters in the objective function and the right-hand side of the constraints. Examples are provided to illustrate the solution steps.     

A smoothing algorithm for finite min–max–min problems

We generalize a smoothing algorithm for finite min–max to finite min–max–min problems. We apply a smoothing technique twice, once to eliminate the inner min operator and once to eliminate the max operator. In mini–max problems, where only the max operator is eliminated, the approximation function is decreasing with respect to the smoothing parameter. Such a property is convenient to establish algorithm convergence, but it does not hold when both operators are eliminated. To maintain the desired property, an additional term is added to the approximation. We establish convergence of a steepest descent algorithm and provide a numerical example.     

Tributylphosphine catalyzed addition of diphenylphosphine oxide to unsubstituted and substituted electron-deficient alkenes

The PBu₃-catalyzed conjugate addition of diphenylphosphine oxide to unsubstituted and substituted electron-deficient alkenes is reported. β-Substituted α,β-unsaturated esters, trans-methyl crotonate and trans-methyl cinnamate, known for their reluctance to participate in phosphine-catalyzed transformations, also react well under the developed conditions. Mild reaction conditions, simple work-up and the ease of catalyst recovery make the proposed methodology useful for the preparation of functionalized tertiary phosphine oxides. The utility of this method was demonstrated by the gram-scale reactions of diphenylphosphine oxide with electron-deficient alkenes.     

Reaction of Halidemethyldithio- and Selenothiophosphonic Acids with Alkylthiocyanates – A Novel Method of Synthesizing P,N, S (Se) – Containing Heterocycles

Abstract

Novel heterocyclic derivatives - 1,3,4-thiazaphospholines and 1,3,4-selenoazaphospolines 7, were obtained passing hydrogen sulfide or hydrogen selenide 2 through the solution of 0-phenylchloromethyl (chloro)thiophosphonate 1 and alkylthiocyanate followed by addition of triethylamine. It is assumed that 0-phenylchloromethylthiophosphonic and -selenophosphonic acids 3 are formed at the first stage, which further add to CN triple bond of alkylthiocyanates 4 to produce S- or Se-thiophosphonyldithio- or selenothioiminocarbonates 5. The latter undergo phosphorotropic rearrangement into appropriate S-thiophosphonyl dithio- or selenothiocarbamates 6.     

Semi-Infinite Programming and Applications to Minimax Problems

A minimisation problem with infinitely many constraints – semi-infinite programming problem (SIP) is considered. The problem is solved using a two stage procedure that searches for global maximum violation of the constraints. A version of the algorithm that searches for any violation of constraints is also considered, and the performance of the two algorithm is compared. An application to solving minimax problem (with and without coupled constraints) is given and a comparison with the algorithm for continuous minimax of Rustem and Howe (2001) is included. Finally, we consider an application to chemical engineering problems.