Robust optimization of uncertain multistage inventory systems with inexact data in decision rules

In production-inventory problems customer demand is often subject to uncertainty. Therefore, it is challenging to design production plans that satisfy both demand and a set of constraints on e.g. production capacity and required inventory levels. Adjustable robust optimization (ARO) is a technique to solve these dynamic (multistage) production-inventory problems. In ARO, the decision in each stage is a function of the data on the realizations of the uncertain demand gathered from the previous periods. These data, however, are often inaccurate; there is much evidence in the information management literature that data quality in inventory systems is often poor. Reliance on data “as is” may then lead to poor performance of “data-driven” methods such as ARO. In this paper, we remedy this weakness of ARO by introducing a model that treats past data itself as an uncertain model parameter. We show that computational tractability of the robust counterparts associated with this extension of ARO is still maintained. The benefits of the new model are demonstrated by a numerical test case of a well-studied production-inventory problem. Our approach is also applicable to other ARO models outside the realm of production-inventory planning.     

Heat and brine transport in porous media: the Oberbeck-Boussinesq approximation revisited

This paper discusses the Oberbeck-Boussinesq approximation for heat and solute transport in porous media. In this commonly used approximation all density variations are neglected except for the gravity term in Darcy’s law. However, in the limit of vanishing density differences this gravity term disappears as well. The main purpose of this paper is to give the correct limits in which the gravity term is retained, while other density effects can be neglected. We show that for isothermal brine transport, fluid volume changes can be neglected when a condition is fulfilled for a dimensionless number, which is independent of the density difference and specific discharge. For heat transfer an additional condition is required. One-dimensional examples of simultaneous heat and brine transport are given for which similarity solutions are constructed. These examples are included to elucidate the volume effects and the corresponding induced specific discharge variations. Finally, a two-dimensional example illustrates the relative effects of volume changes and gravity.     

A general,recursive, and open‐ended response code

We present a new implementation of a recent open‐ended response theory formulation for time‐ and perturbation‐dependent basis sets (Thorvaldsen et al., J. Chem. Phys. 2008, 129, 214108) at the Hartree–Fock and density functional levels of theory. A novel feature of the new implementation is the use of recursive programming techniques, making it possible to write highly compact code for the analytic calculation of any response property at any valid choice of rule for the order of perturbation at which to include perturbed density matrices. The formalism is expressed in terms of the density matrix in the atomic orbital basis, allowing the recursive scheme presented here to be used in linear‐scaling formulations of response theory as well as with two‐ and four‐component relativistic wave functions. To demonstrate the new code, we present calculations of the third geometrical derivatives of the frequency‐dependent second hyperpolarizability for HSOH at the Hartree–Fock level of theory, a seventh‐order energy derivative involving basis sets that are both time and perturbation dependent. © 2014 Wiley Periodicals, Inc.     

Relativistic four-component calculations of Buckingham birefringence using London atomic orbitals

We present the first relativistic study of the electric-field-gradient induced birefringence (Buckingham birefringence), with application to the series of molecules CX₂ (X?=?O, S, Se, Te). A recently developed atomic-orbital-driven scheme for the calculation of time-dependent molecular properties using one-, two- and four-component relativistic wave functions (Bast et?al. in Chem Phys 356:177, 2009) is extended to first-order frequency-dependent magnetic-field perturbations, using London atomic orbitals to ensure gauge-origin independent results and to improve basis-set convergence. Calculations are presented at the Hartree?CFock and Kohn?CSham levels of theory and results for CO₂ and CS₂ are compared with previous high-level coupled-cluster calculations. Except for the heaviest member of the series, relativistic effects are small??in particular for the temperature-independent contribution to the birefringence. By contrast, the effects of electron correlation are significant. However, the reliability of standard exchange-correlation functionals in describing Buckingham birefringence remains unclear based on the comparison with high-level coupled-cluster singles-and-doubles calculations.     

Experimental and four‐component relativistic DFT studies of tungsten carbonyl complexes

We present a theoretical and experimental study of the structure and nuclear magnetic resonance (NMR) parameters of the pentacarbonyltungsten complexes of η¹‐2‐(trimethylstannyl)‐4,5‐dimethylphosphinine, η²‐norbornene, and imidazolidine‐2‐thione. The three complexes have a pseudo‐octahedral molecular structure with the six ligands bonded to the tungsten atom. The η¹‐2‐(trimethylstannyl)‐4,5‐dimethylphosphinine‐pentacarbonyl tungsten complex was synthesized for the first time. For all compounds, we present four‐component relativistic calculations of the NMR parameters at the Dirac–Kohn–Sham density functional level of theory using hybrid functionals. These large‐scale relativistic calculations of NMR chemical shifts and spin–spin coupling constants were compared with available experimental data, either taken from the literature or measured in this work. The inclusion of solvent effects modeled using a conductor‐like screening model was found to improve agreement between the calculated and experimental NMR parameters, and our best estimates for the NMR parameters are generally in good agreement with available experimental results. The present work demonstrates that four‐component relativistic theory has reached a level of maturity that makes it a convenient and accurate tool for modeling and understanding chemical shifts and indirect spin–spin coupling constants of organometallic compounds containing heavy elements, for which conventional non‐relativistic theory breaks down. Copyright © 2015 John Wiley & Sons, Ltd.     

Characterisation and quantification of liposome-type nanoparticles in a beverage matrix using hydrodynamic chromatography and MALDI–TOF mass spectrometry

This paper describes the characterisation of liposome-type nanoparticles (NPs) dispersed in a beverage matrix. Characterisation is based on a two-step procedure: first, liposomes are separated on the basis of size in the nanometre range by use of hydrodynamic chromatography (HDC); second, chemical characterisation is performed by use of MALDI–TOF mass spectrometry (MS). Characterisation of three types of Coatsome liposome, a commercially available type of empty liposome, was investigated. All three liposome types, Coatsome A?=?anionic, N?=?neutral, and C?=?cationic, gave single peaks in HDC, reflecting diameters of 153, 187, and 205 nm, respectively. Subsequent MALDI–TOF MS in positive mode furnished major signals at m/z?=?734.5 ([M?+?H]⁺ adduct) and m/z?=?756.6 ([M?+?Na]⁺ adduct) of l-(α)-dipalmitoylphosphatidylcholine (DPPC) monomer and dimeric adducts at m/z?=?1468.1 and m/z?=?1490.1, respectively. MALDI–TOF MS in negative mode gave a signal at m/z?=?721.3 ([M???H]^? adduct) of l-(α)-dipalmitoylphosphatidylglycerol (DPPG), except for Coatsome C which lacks this phospholipid. After HDC separation of Coatsome A NPs the major DPPC and DPPG signals can be detected in the expected fractions by use of MALDI–TOF MS in positive and negative modes, respectively. Validation of the analytical strategy revealed linearity (R ²?>?0.99), repeatability (relative standard deviation <10 %), and reproducibility (relative standard deviation between days <10 %) were good, recovery was 61?±?5 %, and the limit of quantification was 1 mg?mL^?1 in this matrix. With 4 mg Coatsome A mL^?1 20 out of 20 samples furnished the 734.5 and 756.6 signals typical of DPPC in MALDI–TOF MS characterisation.     

Dynamic inventory rationing strategies for inventory systems with two demand classes,Poisson demand and backordering

We study inventory systems with two demand classes (critical and non-critical), Poisson demand and backordering. We analyze dynamic rationing strategies where the number of items reserved for critical demand depends on the remaining time until the next order arrives. Different from results in the literature, we do not discretize demand but derive a set of formulae that determine the optimal rationing level for any possible value of the remaining time. Moreover, we show that the cost parameters can be captured in a single relevant dimension, which allows us to present the optimal rationing levels in charts and lookup tables that are easy to implement. Numerical examples illustrate that the optimal dynamic rationing strategy outperforms all static strategies with fixed rationing levels.