Network Optimization

The pinch design method creates a network structure based on the assumption that no heat exchanger should have a temperature difference smaller than ATmin. Having now created a structure for the heat exchanger network, the structure can now be subjected to continuous optimization. The constraint that no exchanger should have a temperature 

Given a network structure, it is possible to identify loops and paths for it, as in Section 17.1. Within the context of optimization, only those paths that connect two different utilities need to be considered. This could be a path from steam to cooling water or a path from high-pressure steam used as hot utility to low-pressure steam also used as hot utility. These paths between two different utilities will be termed to be utility paths. Loops and utility paths both provide degrees of freedom in the optimization1,2. 

utility paths and stream splits offer the degrees of freedom for manipulating the network cost. The objective function in new design is usually to minimize total cost, that is, combined operating and annualized capital cost. The annualization period chosen for the capital cost will have a direct influence on the optimization. A longer annualization period will lead to more energy-efficient designs. 

In practice, rather than manipulate loops and paths explicitly, the optimization is normally formulated such that the individual duties on each match are varied in the multivariable optimization, subject to  

In a network, some of the duties on the matches will not be able to be varied because they are not in a loop or a utility path. This simplifies the optimization. The problem is one of multivariable nonlinear continuous optimization6. 

The design method used so far, the pinch design method, creates an 

However, the assumption is that no unit should have a temperature 

Thus loops, utility paths, and stream splits offer the degrees of freedom for manipulating the network cost. The problem is one of multivariable nonlinear optimization. The constraints are only those of feasible heat transfer positive temperature difference and nonnegative heat duty for each exchanger. Furthermore, if stream splits exist, then positive bremch flow rates are additional constraints. 

If the network is optimized at fixed energy consumption, then only loops and stream splits are used. When energy consumption is allowed to vary, utility paths also must he included. As the network energy consumption increases, the overall capital cost decreases. 

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Thus the hot and cold utility consumption both need to be increased by 1.6 MW to restore the Arm to the original 10°C. In fact there is no justification to restore the Arm back to the original 10°C. The amount of additional energy shifted along the utility path is a degree of freedom that should be set by cost optimization. However, the example illustrates how the degrees of freedom can be manipulated in network optimization. 

Several simulation-based optimization models in the context of supply chain management can be found e.g. in the area of supply chain network optimization (Preusser et al. 2005) or to simulate rescheduling of production facing demand uncertainty or unplanned shut-downs (Tang/Grubbstrom 2002 Neuhaus/Giinther 2006). A basic approach of simulation-based optimization is presented by Preusser et al. 2005, p. 98 illustrated in fig. 24. 

Joseph and Wu used a simulation to show that an ANN could be used to optimize the cure cycle for variations in raw material properties. The results were encouraging an 89 percent decrease in standard deviation for thickness and a 96 percent reduction in void size. The mean thickness was also closer to the target thickness for the neural network-optimized processes. They also used the ANN for in-process adjustment of the cure cycle [22]. 

Remark 2 Since the target of minimum number of matches is not used as a heuristic to determine the matches and heat loads with either the MILP transshipment model or the vertical MILP transshipment model, the above problem statement addresses correctly the simultaneous matches-network optimization. 

In the following section, we will discuss the approach proposed by Floudas and Ciric (1989) for simultaneous matches-network optimization. 

The basic idea in the simultaneous matches-network optimization approach of Floudas and Ciric... 

Remark 1 The above statement corresponds to the simultaneous consideration of all steps shown in Figure 8.20, including the optimization loop of the HRAT. We do not decompose based on the artificial pinch-point which provides the minimum utility loads required, but instead allow for the appropriate trade-offs between the operating cost (i.e., utility loads) and the investment cost (i.e., cost of heat exchangers) to be determined. Since the target of minimum utility cost is not used as heuristic to determine the utility loads with the LP transshipment model, but the utility loads are treated as unknown variables, then the above problem statement eliminates the last part of decomposition imposed in the simultaneous matches-network optimization presented in section 8.5.1. 

Remark 3 For (ii)-(iv), the hyperstructure approach presented in the section of simultaneous matches-network optimization will be utilized. 

Note that the binaries yij multiply Aij in the objective function for the same reasons that we wrote the objective function of case I of the simultaneous matches-network optimization (see section 8.5.1.4). 

A. R. Ciric and C. A. Floudas. Application of the simultaneous match-network optimization approach to the pseudo-pinch problem. Comp. Chem. Eng., 14 241,1990. 

An application case study of the production network optimization model is reported in Chapter 5. In this context the integration of the optimization model into a planning tool to support interactive explorations of the solution space is demonstrated and guidance on how to develop the data required for quantitative strategic network design analyses is provided. Additionally, important analyses that can be performed using the proposed optimization model are introduced and improvement potentials identified in the course of a pilot application in industry are explained. 

In the following chapters the individual phases of the planning process and the major activities taking place in each phase are outlined. The decision support tools proposed for the production network optimization phase and the site selection phase will be developed in Chapters 3 and 4 respectively. 

Table 4. Classification of supply network optimization models...

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