A Mathematical Model for Supermarket Order Picking

Order picking consists in retrieving products from storage locations to sat- isfy independent orders from multiple customers. It is generally recognized as one of the most significant activities in a warehouse (Koster et al, 2007). In fact, order picking accounts up to 50% (Frazelle, 2001) or even 80% (Van den Berg, 1999) of the total warehouse operating costs. The critical issue in today’s business environ- ment is to simultaneously reduce the cost and increase the speed of order picking. In this paper, we address the order picking process in one of the Portuguese largest companies in the grocery business. This problem was proposed at the 92nd European Study Group with Industry (ESGI92). In this setting, each operator steers a trolley on the shop floor in order to select items for multiple customers. The objective is to improve their grocery e-commerce and bring it up to the level of the best inter- national practices. In particular, the company wants to improve the routing tasks in order to decrease distances. For this purpose, a mathematical model for a faster open shop picking was developed. In this paper, we describe the problem, our proposed solution as well as some preliminary results and conclusions.info:eu-repo/semantics/publishedVersio

Ab Initio Evidence for the Formation of Impurity d(3z^2-r^2) Holes in Doped La_{2-x}Sr_xCuO_4

Using the spin unrestricted Becke-3-Lee-Yang-Parr density functional, we computed the electronic structure of explicitly doped La_{2-x}Sr_xCuO_4 (x = 0.125, 0.25, and 0.5). At each doping level, an impurity hole band is formed within the undoped insulating gap. This band is well-localized to CuO_6 octahedra adjacent to the Sr impurities. The nature of the impurity hole is A_{1g} in symmetry, formed primarily from the z^2 orbital on the Cu and p_z orbitals on the apical O's. There is a strong triplet coupling of this hole with the intrinsic B_{1g} Cu x^2-y^2/O1 p_{sigma} hole on the same site. Optimization of the c coordinate of the apical O's in the doped CuO_6 octahedron lead to an asymmetric anti-Jahn-Teller distortion of the O2 atoms toward the central Cu. In particular, the O2 atom between the Cu and Sr is displaced 0.26 A while the O2 atom between the Cu and La is displaced 0.10 A. Contrary to expectations, investigation of a 0.1 A enhanced Jahn-Teller distortion of this octahedron does not force formation of an x^2-y^2 hole, but instead leads to migration of the z^2 hole to the four other CuO_6 octahedra surrounding the Sr impurity. This latter observation offers a simple explanation for the bifurcation of the Sr-O2 distance revealed in x-ray absorption fine structure data.Comment: Submitted to Phys. Rev. B. See http://www.firstprinciples.com for more informatio

The Antiferromagnetic Band Structure of La2CuO4 Revisited

Using the Becke-3-LYP functional, we have performed band structure calculations on the high temperature superconductor parent compound, La2CuO4. Under the restricted spin formalism (rho(alpha) equal to rho(beta)), the R-B3LYP band structure agrees well with the standard LDA band structure. It is metallic with a single Cu x2-y2/O p(sigma) band crossing the Fermi level. Under the unrestricted spin formalism (rho(alpha) not equal to rho(beta)), the UB3LYP band structure has a spin polarized antiferromagnetic solution with a band gap of 2.0 eV, agreeing well with experiment. This state is 1.0 eV (per formula unit) lower than that calculated from the R-B3LYP. The apparent high energy of the spin restricted state is attributed to an overestimate of on-site Coulomb repulsion which is corrected in the unrestricted spin calculations. The stabilization of the total energy with spin polarization arises primarily from the stabilization of the x2-y2 band, such that the character of the eigenstates at the top of the valence band in the antiferromagnetic state becomes a strong mixture of Cu x2-y2/O p(sigma) and Cu z2/O' p(z). Since the Hohenberg-Kohn theorem requires the spin restricted and spin unrestricted calculations give exactly the same ground state energy and total density for the exact functionals, this large disparity in energy reflects the inadequacy of current functionals for describing the cuprates. This calls into question the use of band structures based on current restricted spin density functionals (including LDA) as a basis for single band theories of superconductivity in these materials.Comment: 13 pages, 8 figures, to appear in Phys. Rev. B, for more information see http://www.firstprinciples.co

Threshold electronic structure at the oxygen K edge of 3d transition metal oxides: a configuration interaction approach

It has been generally accepted that the threshold structure observed in the oxygen K edge X-ray absorption spectrum in 3d transition metal oxides represents the electronic structure of the 3d transition metal. There is, however, no consensus about the correct description. We present an interpretation, which includes both ground state hybridization and electron correlation. It is based on a configuration interaction cluster calculation using a MO6 cluster. The oxygen K edge spectrum is calculated by annihilating a ligand hole in the ground state and is compared to calculations representing inverse photoemission experiments in which a 3d transition metal electron is added. Clear differences are observed related to the amount of ligand hole created in the ground state. Two "rules" connected to this are discussed. Comparison with experimental data of some early transition metal compounds is made and shows that this simple cluster approach explains the experimental features quite well.Comment: 10 pages, submitted to Phys. Rev. B, tried to make a better PS file

Mathematical programming modelling tools for resource-poor countries and organisations

In recent years, powerful mathematical modelling languages have enabled Operational Research practitioners to rapidly develop prototype tools capable of modelling complex managerial decisions such as staff shift scheduling, or production and supply chain planning. However, such tools have often required expensive commercial optimisation solvers that are sometimes beyond the financial reach of small companies and organisations, particularly in the low-income and emerging economies. Fortunately, the worldwide scope of the internet has put powerful free optimisation tools within the reach of anyone with a modest PC and even a slow internet connection. This article will present examples showing just how beneficial such an approach can be for resource-poor organisations

Diabetes status and post-load plasma glucose concentration in relation to site-specific cancer mortality: findings from the original Whitehall study

ObjectiveWhile several studies have reported on the relation of diabetes status with pancreatic cancer risk, the predictive value of this disorder for other malignancies is unclear. Methods: The Whitehall study, a 25year follow-up for mortality experience of 18,006 men with data on post-challenge blood glucose and self-reported diabetes, allowed us to address these issues. Results: There were 2158 cancer deaths at follow-up. Of the 15 cancer outcomes, diabetes status was positively associated with mortality from carcinoma of the pancreas and liver, while the relationship with lung cancer was inverse, after controlling for a range of potential covariates and mediators which included obesity and socioeconomic position. After excluding deaths occurring in the first 10years of follow-up to examine the effect of reverse causality, the magnitude of the relationships for carcinoma of the pancreas and lung was little altered, while for liver cancer it was markedly attenuated. Conclusions: In the present study, diabetes status was related to pancreatic, liver, and lung cancer risk. Cohorts with serially collected data on blood glucose and covariates are required to further examine this area

Contribution of the first K-homology domain of poly(C)-binding protein 1 to its affinity and specificity for C-rich oligonucleotides

Poly-C-binding proteins are triple KH (hnRNP K homology) domain proteins with specificity for single stranded C-rich RNA and DNA. They play diverse roles in the regulation of protein expression at both transcriptional and translational levels. Here, we analyse the contributions of individual αCP1 KH domains to binding C-rich oligonucleotides using biophysical and structural methods. Using surface plasmon resonance (SPR), we demonstrate that KH1 makes the most stable interactions with both RNA and DNA, KH3 binds with intermediate affinity and KH2 only interacts detectibly with DNA. The crystal structure of KH1 bound to a 5′-CCCTCCCT-3′ DNA sequence shows a 2:1 protein:DNA stoichiometry and demonstrates a molecular arrangement of KH domains bound to immediately adjacent oligonucleotide target sites. SPR experiments, with a series of poly-C-sequences reveals that cytosine is preferred at all four positions in the oligonucleotide binding cleft and that a C-tetrad binds KH1 with 10 times higher affinity than a C-triplet. The basis for this high affinity interaction is finally detailed with the structure determination of a KH1.W.C54S mutant bound to 5′-ACCCCA-3′ DNA sequence. Together, these data establish the lead role of KH1 in oligonucleotide binding by αCP1 and reveal the molecular basis of its specificity for a C-rich tetrad

Insights into the function of silver as an oxidation catalyst by ab initio, atomistic thermodynamics

To help understand the high activity of silver as an oxidation catalyst, e.g., for the oxidation of ethylene to epoxide and the dehydrogenation of methanol to formaldehyde, the interaction and stability of oxygen species at the Ag(111) surface has been studied for a wide range of coverages. Through calculation of the free energy, as obtained from density-functional theory and taking into account the temperature and pressure via the oxygen chemical potential, we obtain the phase diagram of O/Ag(111). Our results reveal that a thin surface-oxide structure is most stable for the temperature and pressure range of ethylene epoxidation and we propose it (and possibly other similar structures) contains the species actuating the catalysis. For higher temperatures, low coverages of chemisorbed oxygen are most stable, which could also play a role in oxidation reactions. For temperatures greater than about 775 K there are no stable oxygen species, except for the possibility of O atoms adsorbed at under-coordinated surface sites Our calculations rule out thicker oxide-like structures, as well as bulk dissolved oxygen and molecular ozone-like species, as playing a role in the oxidation reactions.Comment: 15 pages including 9 figures, Related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm