A robust optimization model for multi-product two-stage capacitated production planning under uncertainty

Production planning (PP) is one of the most important issues carried out in manufacturing environments which seeks efficient planning, scheduling and coordination of all production activities that optimizes the company’s objectives. In this paper, we studied a two-stage real world capacitated production system with lead time and setup decisions in which some parameters such as production costs and customer demand are uncertain. A robust optimization model is developed to formulate the problem in which minimization of the total costs including the setup costs, production costs, labor costs, inventory costs, and workforce changing costs is considered as performance measure. The robust approach is used to reduce the effects of fluctuations of the uncertain parameters with regards to all the possible future scenarios. A mixed-integer programming (MIP) model is developed to formulate the related robust production planning problem. In fact the robust proposed model is presented to generate an initial robust schedule. The performance of this schedule could be improved against of any possible occurrences of uncertain parameters. A case from an Iran refrigerator factory is studied and the characteristics of factory and its products are discussed. The computational results display the robustness and effectiveness of the model and highlight the importance of using robust optimization approach in generating more robust production plans in the uncertain environments. The tradeoff between solution robustness and model robustness is also analyzed.     

Study of complex formation of 5,5′-(2E, 2′E)-2,2′-(ethane-1,2-diylidene)bis(hydrazine-1-yl-2-ylidene)bis(4-amino-4H-1,2,4-triazole-3-thiol) (HYT) macrocyclic ligand with Cd2+ cation in non-aqueous solution by spectroscopic and conductometric methods

In this paper the complexation reaction of the 5,5′-(2E,2′E)-2,2′-(ethane-1,2-diylidene)bis(hydrazine-1-yl-2-ylidene)bis(4-amino-4H-1,2,4-triazole-3-thiol) ligand (HYT) with Cd²⁺ education was studied in some binary mixtures of methanol (MeOH), n-propanol (PrOH) and dimethyl-formamide (DMF) at different temperatures using the conductometry and spectrophotometry. The stability constants of the complex was determined using a GENPLOT computer program. The conductance data and absorbance-mole ratio plots show that in all solvent systems, the stoichiometry of the complex formed between (HYT) and Cd²⁺ cation is 1: 1. The obtained results show that the stability of (HYT)-Cd complex is sensitive to the mixed solvents composition. The values of thermodynamic parameters (ΔG ^°, ΔH ^°, and ΔS ^°) for formation of (HYT)-Cd complex were obtained from temperature dependence of the stability constant using the van’t Hoff plots. The results show that in most cases, the complex are enthalpy destabilized but entropy stabilized and the complex formation is affected by pH, time, temperature and the nature of the solvent.     

The quantum theory of atoms in positronic molecules: The subsystem variational procedure

This contribution deals with the subsystem variational procedure within the context of the quantum theory of atoms in positronic molecules (QTAIPM). Before introducing the subsystem energy functional termed as joint subsystem energy functional, a novel notation and the combination strategy are disclosed in detail by restating the positronic subsystem hypervirial theorem. They are employed in proposing the proper subsystem energy functional, the validity of which is checked by various criteria. The zero flux surfaces of the joint density distribution are used to define the topological atoms in the positronic molecules, and they are incorporated into the subsystem variational procedure as proper real space boundary conditions. The variational procedure finally yields the flux of the joint current property density that also appears in the positronic subsystem hypervirial theorem. At every stage, the corresponding equations for the purely electronic systems within the context of the quantum theory of atoms in molecules (QTAIM) are presented to clearly reveal the analogy between these two formalisms and to emphasize the importance of combining the property density distributions in the QTAIPM. The presented material demonstrates the internal consistency of the whole framework and discloses the fact that the QTAIM must be regarded as a variant of the QTAIPM. Furthermore, this formalism promises an extended QTAIM, which is hoped to resolve the issue of molecular structure beyond the clamp nuclei approximation. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Revisiting the foundations of the quantum theory of atoms in molecules: Toward a rigorous definition of topological atoms

An explicit classification of consistent variational constraints within the context of the “quantum theory of proper open subsystems” as well as the “quantum theory of atoms in molecules” (QTAIM) it presented. It is demonstrated that the general variational procedure is not sensitive enough to discriminate between different mathematically consistent variational conditions. The uniqueness of the regional kinetic energy is employed to derive the net zero‐flux condition and the regions satisfying this condition are named as quantum divided basins. A modified form of the local zero‐flux is proposed in order to define topological atoms within the context of the orthodox QTAIM. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Tracing the Fingerprint of Chemical Bonds within the Electron Densities of Hydrocarbons: A Comparative Analysis of the Optimized and the Promolecule Densities

The equivalence of the molecular graphs emerging from the comparative analysis of the optimized and the promolecule electron densities in two hundred and twenty five unsubstituted hydrocarbons was recently demonstrated [Keyvani et al. Chem. Eur. J. 2016 , 22, 5003]. Thus, the molecular graph of an optimized molecular electron density is not shaped by the formation of the C?H and C?C bonds. In the present study, to trace the fingerprint of the C?H and C?C bonds in the electron densities of the same set of hydrocarbons, the amount of electron density and its Laplacian at the (3, ?1) critical points associated with these bonds are derived from both optimized and promolecule densities, and compared in a newly proposed comparative analysis. The analysis not only conforms to the qualitative picture of the electron density build up between two atoms upon formation of a bond in between, but also quantifies the resulting accumulation of the electron density at the (3, ?1) critical points. The comparative analysis also reveals a unified mode of density accumulation in the case of 2318 studied C?H bonds, but various modes of density accumulation are observed in the case of 1509 studied C?C bonds and they are classified into four groups. The four emerging groups do not always conform to the traditional classification based on the bond orders. Furthermore, four C?C bonds described as exotic bonds in previous studies, for example the inverted C?C bond in 1,1,1‐propellane, are naturally distinguished from the analysis.     

Mass attenuation coefficients of B<Subscript>2</Subscript>O<Subscript>3</Subscript>–Al<Subscript>2</Subscript>O<Subscript>3</Subscript>–SiO<Subscript>2</Subscript>–CaF<Subscript>2</Subscript> glass system at 0.662 and 1.25 MeV gamma energies

The total mass attenuation coefficients, partial interaction and the effective atomic numbers (Z_eff) of glass system (80−x)B₂O₃–10Al₂O₃–10SiO₂–xCaF₂ (where x = 5, 10, 20, 25, 30, 35 and 40 mol %) have been calculated at photon energies 0.662 and 1.25 MeV using the WinXCom software on the basis of mixture rule. Results indicated that the total mass attenuation coefficients showed a decrease with increasing the CaF₂ concentration, due to a decrease in Compton scattering probability, which gave a dominant contribution to the total mass attenuation coefficients for the studied glass samples at both energies. However, the photoelectric absorption and coherent scattering showed an increase with increasing the CaF₂, concentrations at same energies. For a comparison, the total mass attenuation coefficients of the glass system had lower values at the energy 1.25 MeV than that at 0.662 MeV. Z_eff was found to increase linearly with the increase of CaF₂ concentrations. It was concluded that low CaF₂ concentrations in glass system, under study, have Z_eff close to that of human tissue and have higher total absorption coefficients at energy of 0.662 MeV than that at 1.25 MeV. These results are very useful in designing gamma radiation detectors using thermoluminescence technique. Therefore, it is recommended to use low CaF₂ concentration of our glass system as good gamma detectors at energy of 1.25 MeV.     

Towards a complete basis set limit of Hartree–Fock method: correlation-consistent versus polarized-consistent basis sets

In this paper the convergence pattern of correlation-consistent (cc-pVxZ) and polarized-consistent (PC-n) hierarchies relative to the complete basis set limit have been considered in a small set of diatomic molecules. Using the sequence of these basis sets it was demonstrated that potential energy surfaces derived from basis-set-dependent solution of the Hartree–Fock equations achieves the exact numerical derived potential energy surfaces (PESs) in an ordered manner. So it was possible to compute the spectroscopic parameters in the complete basis set limit with considerable accuracy using the most extended members of both hierarchies. On the other hand, for the first time the detailed convergence patterns of total energies in three separate inter-nuclear distances have been considered in these molecules and it was demonstrated that the total energies arrive at microhartree accuracy at a considerable rate. Possible performance of extrapolation schemes is discussed and it was demonstrated that reliable extrapolation procedures indeed exist. A successful test of the proposed extrapolation method, using the three most extended members of polarized-consistent basis sets, has been accomplished on selected polyatomic molecules.