Simulation Modeling and Hybrid Approaches

Simulation is perceived as an essential part of the supply chain configuration process. It complements findings made using mathematical programming and other modeling approaches. In view of the high costs associated with the implementation of configuration decisions, simulation provides the means for detailed evaluation of these decisions before their physical implementation. 

Section 9.2 discusses the purpose of using simulation and hybrid modeling in supply chain configuration. The development of supply chain configuration discrete event simulation models is discussed in Sect. 9.3. The development approach 

Utilizes the concept of generic supply chain unit as the main building block of the simulation model. Section 9.4 defines the type of hybrid models and elaborates a meta-modeling based method for development of the hybrid models. The method allows for computationally efficient integration between the optimization and simulation models. An example illustrating the hybrid modeling is provided. 

Referring back to the definition of the supply chain configuration scope (Chap. 2), simulation is particularly well suited to address managerial concerns, such as  

Some important performance measures provided by simulation are  

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Chapter 9 Simulation Modeling Approaches and Chap. 10 Hybrid Approaches in the hrst edition have been combined into Chap. 9 Simulation Modeling and Hybrid Approaches in the second edition, where techniques for simultaneous and integrated application of simulation and optimization approaches have been described. 

Finally, within the ideality hypothesis oj k) can always be obtained for any model from computer simulation of an isolated chain, which is now feasible for fairly long chains. For the rotational isomeric state model, a hybrid approach has been shown to be quite accurate. In this method the distribution function is calculated from exact enumeration for sites separated by five bonds or less and approximately using the Koyama distribution for sites separated by more than five bonds. 

For one specific set of discharge parameters, in a comparison between the hybrid approach and a full PIC/MC method, the spectra and the ion densities of the hybrid model showed some deviations from those of the full particle simulation. Nevertheless, due to its computational advantages, the hybrid model is appropri-... 

The approaches based on explicit representations of the environment molecules include full quantum mechanical (QM) and hybrid QM/MM methods. In the former, the supramolecular system that is the object of the calculations cannot be very large for instance, it can be composed of the chromophore and a few solvent molecules ( cluster or microsolvation approach). A full QM calculation can be combined with PCM to take into account the bulk of the medium [5,13], which is also a way to test the accuracy of the PCM and of its parameterization, by comparing PCM only and PCM+microsolvation results. The full QM microsolvation approach is recommended when dealing with chromophore-environment interactions that are not easily modelled in the standard ways, such as those involving Rydberg states. An example is the simulation of the absorption spectrum of liquid water, by calculations on water clusters (all QM), clusters + PCM, and a single molecule + PCM only the cluster approach (with or without PCM) yielded results in agreement with experiment [13] (but we note that this example does not conform to the above requirement for a clear distinction between chromophore and environment). 

The empirical and fully mechanistic models reflect the extreme of both situations, either a huge reductionism or a complex description of the biological system. As each approach has its strengths and weaknesses, a hybrid of both (the so-called semi-mechanistic approach) was introduced into the field of clinical modeling and simulation. Within the area of M S these models are also often just referred to as mechanistic models . 

Wan and Isayev (1996) examined a hybrid approach of control-volume finite-element and finite-difference modelling of injection moulding of rubber compounds. The effect of vulcanization on viscosity and yield stress during cavity filling is reported. On comparing two versions of the modified Cross viscosity models - with and without the effect of cure - the use of a viscosity model that accounts for the cure was found to improve the accuracy of the cavity-pressure-prediction models. When the modified Cross model was further extended to include the yield stress and was implemented in the simulation program a significant improvement in the prediction of cavity pressure was obtained in the case of low injection speed. 

In summary, ab initio and hybrid QM/MM molecular dynamics studies provide a valuable tool for the investigation of photoinduced CTI. Excited-state MD simulations of two small organic molecules, PSB5 and formaldimine, were carried out in order to assess the performance of different excited-state methods for the description of cis-trans isomerization reactions. In contrast to the majority of previous studies of the same model systems, our approach has the advantage to allow a completely unconstrained and unbiased relaxation of the excited molecule on its (3N-6)-dimensional PES. 

One of the biggest limitations of current molecular dynamics calculations is that trajectories can only be followed for around 100 ps with reasonable computation times. This short time scale complicates the observation of activated phenomena and makes the method sensitive to the choice of initial conditions, since the simulation may not run long enough to adequately sample configuration space. 100 ps is far too short to model dynamics that affect the NMR lineshape, for which the time scale is typically on the order of a ms. As demonstrated by Thomas and coworkers 132 and others, hybrid approaches employing Monte Carlo methods and other methods in addition to molecular dynamics can extend these simulations to longer effective time scales. 

Going beyond the mean-field level, several "hybrid" approaches are now being explored in MD simulations. Examples include a recent model [70] in which the immediate hydration of the solute is modeled explicitly by a layer of water molecules, and the GB model is used to treat the bulk continuum solvent outside the explicit simulation volume. A similar idea was recently found very effective in the context of replica-exchange simulations [71]. An explicit ion/implicit water (PB) solvation model for molecular dynamics of nucleic acids has recently been tested [72]. 

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