Solution approaches for the soft drink integrated production lot sizing and scheduling problem

In this paper we present a mixed integer programming model that integrates production lot sizing and scheduling decisions of beverage plants with sequence-dependent setup costs and times. The model considers that the industrial process produces soft drink bottles in different flavours and sizes, and it is carried out in two production stages: liquid preparation (stage I) and bottling (stage II). The model also takes into account that the production bottleneck may alternate between stages I and II, and a synchronisation of the production between these stages is required. A relaxation approach and several strategies of the relax-and-fix heuristic are proposed to solve the model. Computational tests with instances generated based on real data from a Brazilian soft drink plant are also presented. The results show that the solution approaches are capable of producing better solutions than those used by the company.     

Hermitian Curvature and Plurisubharmonicity of Energy on Teichmüller Space

Let M be a closed Riemann surface, N a Riemannian manifold of Hermitian non-positive curvature, f : M → N a continuous map, and E the function on the Teichmüller space of M that assigns to a complex structure on M the energy of the harmonic map homotopic to f. We show that E is a plurisubharmonic function on the Teichmüller space of M. If N has strictly negative Hermitian curvature, we characterize the directions in which the complex Hessian of E vanishes.     

Convergence of distributed optimal control problems governed by elliptic variational inequalities

First, let u _g be the unique solution of an elliptic variational inequality with source term g. We establish, in the general case, the error estimate between $u_{3}(\mu)=\mu u_{g_{1}}+ (1-\mu)u_{g_{2}}$ and $u_{4}(\mu)=u_{\mu g_{1}+ (1-\mu) g_{2}}$ for ????[0,1]. Secondly, we consider a family of distributed optimal control problems governed by elliptic variational inequalities over the internal energy g for each positive heat transfer coefficient h given on a part of the boundary of the domain. For a given cost functional and using some monotony property between u ₃(??) and u ₄(??) given in Mignot (J.?Funct. Anal. 22:130?C185, 1976), we prove the strong convergence of the optimal controls and states associated to this family of distributed optimal control problems governed by elliptic variational inequalities to a limit Dirichlet distributed optimal control problem, governed also by an elliptic variational inequality, when the parameter h goes to infinity. We obtain this convergence without using the adjoint state problem (or the Mignot??s conical differentiability) which is a great advantage with respect to the proof given in Gariboldi and Tarzia (Appl. Math. Optim. 47:213?C230, 2003), for optimal control problems governed by elliptic variational equalities.     

Measurement of the neutron F2 structure function via spectator tagging with CLAS

We report on the first measurement of the F(2) structure function of the neutron from the semi-inclusive scattering of electrons from deuterium, with low-momentum protons detected in the backward hemisphere. Restricting the momentum of the spectator protons to ?100 MeV/c and their angles to ?100° relative to the momentum transfer allows an interpretation of the process in terms of scattering from nearly on-shell neutrons. The F(2)(n) data collected cover the nucleon-resonance and deep-inelastic regions over a wide range of Bjorken x for 0.65相似文献   

One-dimensional metal–organic frameworks built by coordinating 2,4,6-tris(4-pyridyl)-1,3,5-triazine linker with copper nodes: CO2 adsorption properties

The reaction between 2,4,6-tris(4-pyridyl)-1,3,5-triazine (4-tpt) and copper(II) hexafluoroacetylacetone (Cu(hfa)₂) yields two different 1D metal–organic frameworks (MOFs), [(Cu(hfa)₂)₂(4-tpt)]_n ( 1 ) and [Cu(hfa)₂(4-tpt)]_n ( 2 ). The Cu:4-tpt ratio in the new MOFs is determined by the reaction medium, particularly, the solvent used. The two compounds have been fully characterized, including crystal structure elucidation. [(Cu(hfa)₂)₂(4-tpt)]_n ( 1 ), with a 2:1 Cu:4-tpt ratio, could be precipitated in either 1,1,2-trichloroethane or supercritical CO₂. In ( 1 ), 4-tpt shows a tritopic coordination mode, but only half of the Cu(hfa)₂ subunits act as a node, thus connecting two 4-tpt and giving a 1D network. The other half of Cu(hfa)₂ subunits are connected only to one pyridine and thus protrude along the chains. The later Cu(hfa)₂ fragments show a labile character and can be dissolved in diethyl ether to give the second MOF [Cu(hfa)₂(4-tpt)]_n ( 2 ), with a 1:1 Cu:4-tpt ratio. The compound ( 2 ) has also a 1D structure, with all the incorporated copper atoms acting as nodes. In this case, the packing of the chains defines accessible channels, which are perpendicular to the chain axis. After activation, N₂ adsorption/desorption measurements at 77 K confirm the microporous character of ( 2 ) with an apparent surface area of 190 m² g⁻¹. Besides, at 273 K this material clearly shows a significant adsorption of CO₂ prompted by noncoordinated nitrogen in the triazine linker.     

Spline quasi-interpolation in the Bernstein basis and its application to digital elevation models

A nonstandard low-cost spline approximation method for approximating bivariate functions is constructed. It is applied for Digital Elevation approximation and then its accuracy in the downscaling process is studied.