The Design Problem

In the first step of the control strategy, a SC design problem is solved. The scheduling model is taken into consideration in the first month for the integrated approach. As shown in Fig. 9.5, the E[CV and financial risk for the traditional sequential approach seem to yield better values. Financial risk is defined as the probability of not meeting a certain CV level. For this case study, the integrated approach results in a solution 2.05 % lower than the sequential one. However, it should be emphasized that the 

9 Considerations of Planning and Scheduling into the Design of Supply Chains 

The Optimal Condition Decomposition (OCD), which is a particular case of the Lagrangian relaxation procedure, is applied to overcome the computational cost of solving the monolithic problem which integrates the design, planning, and scheduling formulations. Further details about this decomposition strategy can be found in Sect. A.7.1 of the Appendix A. 

The variables which are complicating the integrated mathematical model are the first stage, design variables () These two variables are duplicated so that one copy exists for every combination of events (hi). The following constraints have been added in order to do so. 

the affected Eqs. 9.2 and 9.3 are rewritten in terms of the proper duplicated variables. 

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Desorption with Chemical Reaction When chemical reactions are involved in a stripping operation, the design problem can become extremely complex. In fact, much less is known about this very important process than is known about absorption. A classic work on this subject is that of Shah and Sharma [Trans. In.st. Chem. Tng., 54, 1 (1976)], which is recommended to those in need of more details. 

Thus equation 4.45 is an ordinary differential equation (ODE) which can easily be solved for filter area, A (in the design problem) or filtrate collected, V (for performance mode calculation). 

Note that different thicknesses result from Equation (7.14) for different materials with their characteristic values of E and eauov abie- s, the design problem has only one answer if the material is specified, but many answers exist if the material is not specified. 

The design problem of a TMB consists on setting the flow rates in each section to obtain the desired separation. Some constraints have to be met to recover the less-adsorbed component A in the raffinate and the more retained component B in the extract. These constraints are expressed in terms of the net fluxes of components in each section (see Fig. 9-1). In section I, both species must move upwards, in sections II and III the light species must move upwards, while the net flux of the more retained component must be downwards, and in section IV the net flux of both species have to be downwards, i.e.. 

The latest tw o-phase flow research and design studies have broadened the interpretation of some of the earlier flow patterns and refined some design accuracy for selected situations. The method presented here serves as a fundamental reference source for further studies. It is suggested that the designer compare several design concept results and interpret which best encompasses the design problem under consideration. Some of the latest references are included in the Reference Section. No one reference has a solution to all two-phase flow problems. 

A large majority of the systems have operating lines and equilibrium curves which can be assumed as straight over the range covered by the design problem. For the conditions of a straight line equilibrium curve, y = mx, Colburn [10, 11] has integrated the relation above to obtain ... 

Refer to a plot of KaV/L versus L /G as in Figures 126A-G or in References 15 and 19. This saves the integration step, as this has been performed and calculated for a selection of reasonable wet bulb temperatures and temperature ranges. The curve to fit the design problem must be used. 

If the wire is to be used to carry much higher frequency currents, the design problem in geometry and plastic selection becomes more complicated. The dielectric constant and dielectric loss values for the plastics become important in the design. At a frequency of one megahertz the effect of the dielectric on the power transmission behavior of the wire is substantial and, even at frequencies of 10 to 100 kilohertz, the insulation on the wire must be considered in the design as a major electrical element in the circuit. More on the subject of insulation will be following this section. 

The following example provides information on designing of plastic structural products to take static loads. It is a structural problem common to a number of different structures to show how the different structural requirements will affect the choice architectural designers has to make. The design problem will be a roof section which may be used for anything from a work shed,... 

This type of design problem is somewhat different from others in that the unit is made from standardized sections that have specific physical properties and are available in only a limited number of thicknesses and configurations. The design problem now consists of trying the available materials in the structure... 

Another approach to the design problem is to determine empirical correlations based on experimental work and to adopt these correlations for scale-up. In many of the published works the latter approach is investigated. The correlations are such that the volumetric mass-transfer coefficient is generally reported as a function of one or more of the equipment, system, or operating variables cited above. Empirical correlations can be used confidently for scale-up only for equipment that has complete geometrical similarity to the... 

Loonkar and Robinson (1972) extended the design problem to the optimal selection of semi-continuous equipment for pre-selected batch equipment that was fixed by the recipe. 

Postscript The design problems given in Appendix F provide more problems in flow-sheeting. 

Plant parameter inputs, their use within the model, and appropriateness for the design problem. 

If the design problem in the absence of significant constraints can be decoupled in this way, there must be some mechanism behind this. Take two different sequences for the separation of a four-component mixture, Figure 21.103. Summing the feed flowrates of the key components (see Chapter 9) to each column in the sequence, the total flowrate is the same in both cases, Figure 21.10. However, the flow of nonkey components is different, Figure 21.10. 

The design problem usually fits into the spectrum ranging from (1) the rational design of a completely new reactor for a new process, to (2) the analysis of performance of an existing reactor for an existing process. A common situation, between these extremes, even for a new plant, is the modification of an existing type of reactor, the design of which has evolved over time. 

Having presented the pertinent equations and the procedure for computing the optimum, let us check the approach by computing the degrees of freedom in the design problem. 

You can now see why for line A a branch-and-bound technique is not required to solve the design problem. Because of the way the objective function is formulated, if the ratio (pd ps) = 1, the term involving compressor i vanishes from the first summation in the objective function. This outcome is equivalent to the deletion of compressor i in the execution of a branch-and-bound strategy. (Of course the pipeline segments joined at node i may be of different diameters.) But when... 

This case study is based upon the senior design report by Brass and Lee [5], which was prepared at the University of Pennsylvania in the Spring 2003. The design problem statement was formulated by the first author, who served as the faculty advisor. 

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