A model of JIT make-to-stock inventory with stochastic demand

We consider a firm that manages its internal manufacturing operations according to a just-in-time (JIT) system but maintains an inventory of finished goods as a buffer against random demands from external customers. We formulate a model in which finished goods are replenished by a small fixed quantity each time period. In the interest of schedule stability, the size of the replenishment quantity must remain fixed for a predetermined interval of time periods. We analyse the single-interval problem in depth, showing how to compute a cost-minimising value of the replenishment quantity for a given interval length, and characterising the optimal cost, inventory levels and service as functions of the interval length and initial inventory. The model displays significant cost and service penalties for schedule stability. A dynamic version of the problem is also formulated, and shown to be convex in nature with relatively easily computed optima.     

Bivariate Free Knot Splines

We consider the least squares approximation of gridded 2D data by tensor product splines with free knots. The smoothing functional to be minimized—a generalization of the univariate Schoenberg functional—is chosen in such a way that the solution of the bivariate problem separates into the solution of a sequence of univariate problems in case of fixed knots. The resulting optimization problem is a constrained separable least squares problem with tensor product structure. Based on some ideas developed by the authors for the univariate case, an efficient method for solving the specially structured 2D problem is proposed, analyzed and tested on hand of some examples from the literature.     

ROBUSTNESS OF AN UPWIND FINITE DIFFERENCE SCHEME FOR SEMILINEAR CONVECTION-DIFFUSION PROBLEMS WITH BOUNDARY TURNING POINTS

We consider a singularly perturbed semilinear convection-diffusion problem with a boundary layer of attractive turning-point type. It is shown that its solution can be decomposed into a regular solution component and a layer component. This decomposi-tion is used to analyse the convergence of an upwinded finite difference scheme on Shishkin meshes.     

Analysis of a finite-difference scheme for a singularly perturbed problem with two small parameters

We study a model linear convection-diffusion-reaction problem where both the diffusion term and the convection term are multiplied by small parameters ε_d and ε_c, respectively. Depending on the size of the parameters the solution of the problem may exhibit exponential layers at both end points of the domain. Sharp bounds for the derivatives of the solution are derived using a barrier-function technique. These bounds are applied in the analysis of a simple upwind-difference scheme on Shishkin meshes. This method is established to be almost first-order convergent, independently of the parameters ε_d and ε_c.     

Synthesis,Vibrational Spectrum and Structure of the Tetracyanoborate K[B(CN)4]·CH3CN

The new tetracyanoborate K[B(CN)₄]·CH₃CN was synthesized by dissolution of the solvent‐free K[B(CN)₄] in acetonitrile and subsequent careful crystallization. The crystal structure has been determined by single‐crystal X‐ray diffraction. It crystallizes in the orthorhombic space group P2₁2₁2₁ with Z = 4. Some comparisons with related structures are made, and the vibrational spectrum is discussed.     

Near threshold absolute TDCS: first results

A new method, and first results for an impact energy 2 eV above the threshold of ionisation of helium, are presented for the measurement of absolute triple differential cross sections (TDCS) in a crossed beam experiment. The method is based upon measurement of beam/target overlap densities using known absolute total ionisation cross sections and of detection efficiencies using known absolute double differential cross sections (DDCS). For the present work the necessary absolute DDCS for 1 eV electrons had also to be measured. Results are presented for several different coplanar kinematics and are compared with recent DWBA calculations.     

Rhodium and palladium β-diketonate determination with on-line supercritical fluid extraction-high performance liquid chromatography via solid phase extraction

 An on-line system of supercritical fluid extraction (SFE) and high performance liquid chromatography (HPLC) via solid phase extraction (SPE) is described for the determination of palladium and rhodium 2,2,6,6-tetramethyl-3,5-heptanedione-(thd) as well as rhodium-acetylacetonate-(acac) and benzylacetonate-(bzac) chelates. The chelates were extracted with supercritical CO₂ from sand and humic acid, concentrated on SPE cartridges and analysed with HPLC. Two cartridge materials were tested and compared to off-line trapping. The percentage of the breakthrough and cartridge retained material were measured in liquid dichloromethane. The SFE conditions could be optimized to separate metal chelates during the extraction. The supercritical fluid (SF) behaviour of different ligands on rhodium were investigated. Received: 19 July 1996/Revised: 11 December 1996/Accepted: 14 December 1996     

Synthesis and properties of crosslinked polyvinylformamide and polyvinylamine hydrogels in conjunction with silica particles

Polyvinylamine hydrogels with silica particles encapsulated (PVAm/silica) were produced by a two‐step synthesis. In the first step, polyvinylformamide/silica (PVFA/silica) hybrids were synthesized from vinylformamide (VFA) and 1,3‐divinylimidazolidin‐2‐one (1,3‐bisvinylethyleneurea, BVU), as the crosslinker, by radical copolymerization in silica/water suspensions using different compositions of VFA/BVU. The target product PVAm/silica was obtained by acidic hydrolysis of the PVFA/silica hydrogels in a second step. The chemical structures of both hydrogels, PVFA/silica and PVAm/silica, respectively, were revealed by solid‐state ¹³C(¹H) cross‐polarity/magic‐angle spinning NMR spectroscopy. Both hydrogels swelled significantly in water. The swelling capacity of the two systems was characterized by the correlation length ξ (or hydrodynamic blob size) of the network meshes with small‐angle neutron scattering experiments. ξ is significantly larger for PVAm/silica than for PVFA/silica, which corresponds to the observed higher swelling capacity of this polyelectrolyte material. Furthermore, the swelling behavior of the hybrid hydrogels was quantitatively described in terms of free swell capacity, centrifuge‐retention capacity, adsorption against pressure, and free swell rate as compared with values of the corresponding copolymer hydrogels. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3144–3152, 2002