Predetermined intervals for start times of activities in?the?stochastic project scheduling problem

This paper proposes a new methodology to schedule activities in projects with stochastic activity durations. The main idea is to determine for each activity an interval in which the activity is allowed to start its processing. Deviations from these intervals result in penalty costs. We employ the Cross-Entropy methodology to set the intervals so as to minimize the sum of the expected penalty costs. The paper describes the implementation of the method, compares its results to other heuristic methods and provides some insights towards actual applications.     

Robust multi-echelon multi-period inventory control

We consider the problem of minimizing the overall cost of a supply chain, over a possible long horizon, under demand uncertainly which is known only crudely. Under such circumstances, the method of choice is Robust Optimization, in particular the Affinely Adjustable Robust Counterpart (AARC) method which leads to tractable deterministic optimization problems. The latter is due to a recent re-parametrization technique for discrete time linear control systems. In this paper we model, analyze and test an extension of the AARC method known as the Globalized Robust Counterpart (GRC) in order to control inventories in serial supply chains. A simulation study demonstrates the merit of the methods employed here, in particular, it shows that a good control law that minimizes cost achieves simultaneously good control of the bullwhip effect.     

A theoretical analysis of topography and molecular parameters of the CFCl3···O3 complex: Linear and bifurcate halogen‐oxygen bonding interactions

A theoretical analysis of linear and bifurcate halogen‐oxygen bonds is presented in this work. B3LYP/6‐311++G(d,p) and MP2/6‐311++G(d,p) calculations were used to determine the optimized geometries of intermolecular systems formed by CFCl₃ and O₃. Molecular properties often analyzed in hydrogen‐bonded complexes were used here to describe the interaction between chlorine (CFCl₃) and oxygen (O₃). The halogen‐oxygen bond in the CFCl₃···O₃ complex was characterized using the topological parameters derived from the quantum theory of atoms in molecules. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

A modified lead–matrix separation procedure shown for lead isotope analysis in Trojan silver artefacts as an example

A modified Pb–matrix separation procedure using NH₄HCO₃ solution as eluent has been developed and validated for determination of Pb isotope amount ratios by thermal ionization mass spectrometry. The procedure is based on chromatographic separation using the Pb·Spec resin and an in-house-prepared NH₄HCO₃ solution serving as eluent. The advantages of this eluent are low Pb blanks (<40 pg?mL^?1) and the property that NH₄HCO₃ can be easily removed by use of a heating step (>60 °C). Pb recovery is >95 % for water samples. For archaeological silver samples, however, the Pb recovery is reduced to approximately 50 %, but causes no bias in the determination of Pb isotope amount ratios. The validated procedure was used to determine lead isotope amount ratios in Trojan silver artefacts with expanded uncertainties (k?=?2) <0.09 %.     

Sphere-separable partitions of multi-parameter elements

We show the optimality of sphere-separable partitions for problems where n vectors in d-dimensional space are to be partitioned into p categories to minimize a cost function which is dependent in the sum of the vectors in each category; the sum of the squares of their Euclidean norms; and the number of elements in each category. We further show that the number of these partitions is polynomial in n. These results broaden the class of partition problems for which an optimal solution is guaranteed within a prescribed set whose size is polynomially bounded in n. Applications of the results are demonstrated through examples.     

A generalization of the Hall–Witt identity

Let Y → X be a finite normal cover of a wedge of n ≥ 3 circles. We prove that for any nonzero v ∈ H ₁(Y; Q) there exists a lift \(\widetilde F\) to Y of a basepoint-preserving homotopy equivalence F: X → X such that the set of iterates \(\left\{ {{{\widetilde F}^d}\left( v \right)} \right\}:d \in \mathbb{Z} \subseteq {H_1}\left( {Y,\mathbb{Q}} \right)\) is infinite. The main achievement of this paper is the use of representation theory to prove the existence of a purely topological object that seems to be inaccessible via topology.     

Selective CH Functionalization of Methane,Ethane, and Propane by a Perfluoroarene Iodine(III) Complex

Direct partial oxidation of methane, ethane, and propane to their respective trifluoroacetate esters is achieved by a homogeneous hypervalent iodine(III) complex in non‐superacidic (trifluoroacetic acid) solvent. The reaction is highly selective for ester formation (>99 %). In the case of ethane, greater than 0.5 M EtTFA can be achieved. Preliminary kinetic analysis and density functional calculations support a nonradical electrophilic CH activation and iodine alkyl functionalization mechanism.     

Setting gates for activities in the stochastic project scheduling problem through the cross entropy methodology

This paper addresses the problem of scheduling activities in projects with stochastic activity durations. The aim is to determine for each activity a gate—a time before it the activity cannot begin. Setting these gates is analogous to setting inventory levels in the news vendor problem. The resources required for each activity are scheduled to arrive according to its gate. Since activities’ durations are stochastic, the start and finish time of each activity is uncertain. This fact may lead to one of two outcomes: (1) an activity is ready to start its processing as all its predecessors have finished, but it cannot start because the resources required for it were scheduled to arrive at a later time. (2) The resources required for the activity have arrived and are ready to be used but the activity is not ready to start because of precedence constraints. In the first case we will incur a “holding” cost while in the second case, we will incur a “shortage” cost. Our objective is to set gates so as to minimize the sum of the expected holding and shortage costs. We employ the Cross-Entropy method to solve the problem. The paper describes the implementation of the method, compares its results to various heuristic methods and provides some insights towards actual applications.     

Voronoi Diagrams of Lines in 3-Space Under Polyhedral Convex Distance Functions

The combinatorial complexity of the Voronoi diagram ofnlines in three dimensions under a convex distance function induced by a polytope with a constant number of edges is shown to beO(n²α(n)log n), where α(n) is a slowly growing inverse of the Ackermann function. There are arrangements ofnlines where this complexity can be as large as Ω(n²α(n)).     

Multiple proton donors on BeH2···2HCl trimolecular dihydrogen-bonded complex: some theoretical insights

In this theoretical work, the characterization of multiple proton donors in three isomers of BeH₂···2HCl trimolecular dihydrogen-bonded complex was developed through the analysis of structural parameters, electronic criteria, and analysis of vibrational harmonic spectrum, where all these data were obtained from the B3LYP/6-311++G(3d,3p) calculations. As dihydrogen bonds are formed by the interaction between two hydrogen atoms, proton donors and hydride hydrogen, the isomers of BeH₂···2HCl trimolecular dihydrogen-bonded complexes are stabilized by two, three, and four centers of proton donors. By analyzing the charge density integrations calculated by the theory of Atoms in Molecules, these multiple centers of proton donors were identified by quantification of the intermolecular electronic density, Laplacian operators, and charge transfers.