Model Extensions

In order to maximize the net present value of after-tax cash flows the model proposed in Chapter 3.4.2 has to be extended to determine the taxes payable in each country. To this end, pre-tax country profits comprising profits realized at both production and distribution entities have to be calculated. While the pre-tax profit of distribution entities can be calculated easily by subtracting all costs incurred from revenues realized, additional adjustments are required for production entities. Instead of cash flows associated with capital investments, depreciation costs have to be considered to identify pre-tax profits. The following assumptions are made to simplify the calculation  

COGSa Costs of goods sold in country c in period t 

Pre-tax profits from sales are calculated by subtracting all costs allocated to the selling country from net revenues. The costs of goods are calculated based on the transfer prices in equation (3.83). 

Profits at the site level are calculated in equation (3.84) by subtracting all costs incurred at the site from the revenues realized at the site from finished and intermediate products as calculated by equation (3.85). In addition to the cost items already contained in the basic model formulation, the costs of intermediates received from other sites have to be allocated to the receiving site for tax purposes and the depreciation costs have to be subtracted instead of investment expenditures. Equation (3.86) defines that depreciation costs are calculated by adding to the depreciation plan of old assets (which has to be determined outside the model) depreciation incurred from new investments. Based on the assumption of straight-line depreciation and a depreciation period that exceeds the planning horizon these costs can be calculated as a fixed percentage of the total investments incurred at a site. 

The resulting taxes payable per country are calculated in equation 

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Cisneros GA, Piquemal J-P, Darden TA (2006) Generalization of the Gaussian electrostatic model extension to arbitrary angular momentum, distributed multipoles and speedup with reciprocal space methods. J Chem Phys 125 184101... 

KL Model Extension to First-Order Complex Reactions... 

Let s look at a general framework for modeling extensible structures (see Figure 14.6). For a tree, set np to be 0,1 for a directed graph (with shared children), set np to. ... 

Finally, the model needs to prove its applicability in reality and its performance in an industry case study. The model is evaluated with comprehensive industry case data and the relevance of the end-to-end value chain planning approach is evaluated. Opportunities for model extensions are outlined at the end. 

The model is implemented and evaluated with an industry case. The technical implementation is described first. Then, the industry case is introduced and model-relevant case data are presented. Model reaction tests are conducted for various industry case data sets to analyze model applicability, sensitivity and model planning results. Model performance tests are conducted to analyze technical parameters such as solution time or approximation methods quality. The case evaluation inspired several model extension possibilities presented at the end of the chapter. 

In the considered value chain planning problem, the uncertainty of spot sales prices impacts the profitability of the overall value chain plan, since volume decisions can lead to profit-suboptimal plans, if the average sales price cannot be realized as planned. Therefore, price volatility is considered as an external (stochastic) influence in the considered value chain planning problem. The following model extensions account for this uncertainty and try to derive methods to achieve more robust plans with respect to profit results with contributions from Habla (2006). The objective of the proposed modeling approach is to maximize profit for the entire value chain network. It is assumed that the company behaves risk-averse in face of the price uncertainty. 

This model extension is tested with ILOG OPL Studio 3.71 using ILOG CPLEX 9.1 and examined industry case test data on an Intel Pentium 4 Processor with 1,598 Mhz and 256 MB RAM. The extension is tested for an excerpt of the value chain network including nine sales locations, one procurement location and one production and having one multi-purpose and one continuous production resource as shown in fig. 101. 

A good fit will give n s on the order of a, and the summation in Eq. (4.8b) then roughly equals N. For a reasonable N (>50) v is approximately N and x2 is about 1. Thus, a X2 much greater than 1 suggests a faulty model. Extensive tables of /r2 s versus v are available to determine if the models were reasonable. 58 For our discussion, it is sufficient to recognize that a. x2 much above 1 would indicate a poor model. 

As the chemical models mentioned here refer to some fundamental thermochemical and electronic effects of molecules, their application is not restricted to the prediction of chemical reactivity data. In fact, in the development of the models extensive comparisons were made with physical data, and thus such data can also be predicted from our models. Furthermore, some of the mechanisms responsible for binding substrates to receptors are naturally enough founded on quite similar electronic effects to those responsible for chemical reactivity. This suggest the use of the models developed here to calculate parameters for quantitative structure-activity relationships (QSAR). 

Due to the biochemical importance of porphyrine systems their metal complexes have been modeled extensively. Metalloporphyrines are assumed to be planar but there is a relatively high degree of flexibility, and six low energy distortion modes have been described (Figure 3).127 MM with a variety of force fields has been used to compute the structural and dynamic properties,65 66 128-131 and these studies also include information on the orientation of the axial donors.132 133 Reaction dynamics related to the interaction of substrates with the metal site have also been modeled,134-136 and MM has been used to correlate structural and spectroscopic properties (primarily Raman frequencies).137 138... 

While the above simulations describe how the disease pattern vary as a function of the disease state, the following simulations show that our model can also account for kindling phenomena and autonomous progression. This needs some model extensions which were made in reference to the above-mentioned assumption of episode sensitization which are assumed to be due to residues (memory traces) of previous disease episodes. For simplicity, and because the real mechanisms are unknown, we introduced an additional, positive feedback loop which is implemented exactly in the same way as the other feedback variables [4—7, 25]. The model now also includes a dynamic disease variable Sp (Fig. 7.4a). The specialities are that it only activates when a disease episode occurs (episode sensitization) and that it has long relaxation times (memory trace). 

To this point we have discussed recent model extensions in the context of oxide CMP. As illustrated schematically in Fig. 1, dishing and erosion concerns in copper damascene processing also... 

Equation (6), with the boundary condition at Eq. (7), can be solved analytically for a number of admittedly simple models. Extensive use will be made of these solutions throughout this section. 

The set of atomic orbitals Xk is called a basis set, and the quality of the basis set will usually dictate the accuracy of the calculations. For example, the interaction energy between an active site and an adsorbate molecule might be seriously overestimated because of excessive basis set superposition error (BSSE) if the number of atomic orbitals taken in Eq. [4] is too small. Note that Hartree-Fock theory does not describe correlated electron motion. Models that go beyond the FiF approximation and take electron correlation into account are termed post-Flartree-Fock models. Extensive reviews of post-HF models based on configurational interaction (Cl) theory, Moller-Plesset (MP) perturbation theory, and coupled-cluster theory can be found in other chapters of this series. ... 

NaX is a Faujasite type zeolite used industrially as a cracking catalyst. Its structure is depicted in the inset of Fig. 1. Benzene in NaX zeolite has been modeled extensively and found to bind strongly in a facially coordinated orientation above four Na cations (Sn sites) and weakly in four sites near Na(III ) cations (W sites). 

The original Danckwerts model has later been extended to relate the renewal rate s to many flow parameters, and to account for the existence of the micro scale flow of the fluid within the individual eddies. Further modifications relate to the fact that not all the penetrating eddies reach the whole way to the interface. Many model extensions have thus been developed based on the basic surface-renewal concept. A review of these models is given by Sideman and Pinczewski [135]. The various extensions are motivated by the inherent assumptions regarding, the governing equations, the boundary conditions, the age distribution function and/or the mean contact time. 

Around these fundamental and domain-independent models, extension points are placed that can be used to add the models of a specific application domain or other specializations. The concrete data are then stored as instances of the appropriate ontological concepts. This allows modifications and extensions of the partial models used, even during project execution. 

Monolith reactors have been modeled extensively for combustion applications, with most of the models relating to the combustion of pollutants in exhaust gases. Details of the various models for combustion in monolith reactors can be found in the review by Cybulski and Moulijn [16]. The models have been important tools in the design of catalysts for the control of pollutants, especially automobile exhaust catalysts. Many of the insights obtained through modeling the combustion of pollutants are transferable to fuel-combustion catalysts. 

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