Objective function with operating costs

Here, the objective is to minimize operating cost followed by trading off with fixed cost as discussed in Ou ner IWo. If needed, one can diteclly minimize total annualized cost by adding a fixed-cost term to the objective function. This fixed-cost term is ex(nessed in terms of as described in Chapter TWo. 

The system shown in Figure El 1.4 may be modeled as linear constraints and combined with a linear objective function. The objective is to minimize the operating cost of the system by choice of steam flow rates and power generated or purchased, subject to the demands and restrictions on the system. The following objective function is the cost to operate the system per hour, namely, the sum of steam produced HPS, purchased power required PP, and excess power EP ... 

The investigation of the object functions showed optimum costs and optiminn profits associated with machine operation, at an age of 10-15 years for both object functions. The object functions representing costs and profits in the successive years of service are shown in respectively Fig. 3 and 4. The vertical lines delimit the age/operating hours range for which full cost data are available. The region before the lines (the earlier one) is based on incomplete cost data. The region after the second line (the later one) represents the objective function obtained under the assumption that from the reliabihty point of view, an older machine is not better than a younger machine. 

Secondly, the minimum amount of intermediate storage is determined with and without the PIS operational philosophy. In both cases the production goal was set to that which was achieved when the model was solved with infinite intermediate storage. In the illustrative example a 20% reduction in the amount of intermediate storage is achieved. The design model is an MINLP model due to the non-linear capital cost objective function. This model is applied to an illustrative problem and results in the flowsheet as well as determining the capacities of the required units. 

Finally, the objective function to be minimized with respect to Th, the working fluid temperature, is the sum of the operating cost and surface area costs ... 

With respect to the objective function for a filter, the total annual cost of filtration / is assumed to be the sum of the annualized capital costs fc and the annual operating costs/0. The annualized capital cost is related to the cross-sectional area of the filter by the relation... 

Optimisation may be used, for example, to minimise the cost of reactor operation or to maximise conversion. Having set up a mathematical model of a reactor system, it is only necessary to define a cost or profit function and then to minimise or maximise this by variation of the operational parameters, such as temperature, feed flow rate or coolant flow rate. The extremum can then be found either manually by trial and error or by the use of numerical optimisation algorithms. The first method is easily applied with MADONNA, or with any other simulation software, if only one operational parameter is allowed to vary at any one time. If two or more parameters are to be optimised this method becomes extremely cumbersome. To handle such problems, MADONNA has a built-in optimisation algorithm for the minimisation of a user-defined objective function. This can be activated by the OPTIMIZE command from the Parameter menu. In MADONNA the use of parametric plots for a single variable optimisation is easy and straight-forward. It often suffices to identify optimal conditions, as shown in Case A below. 

Objective function a profit maximization function over the time horizon is considered as the difference between the revenue due to product sales and the overall costs, with the latter consisting of the cost of raw materials, operating cost, investment cost, and inventory cost ... 

The economic objective function to be minimized is the cost, which combines the capital costs associated with building the column and the utility costs associated with operating the column. The form for the capital cost of the column depends upon the vapor boilup, the number of trays, and the column diameter... 

The objective function F is a function of the variables within the unified reactor model and the heating and cooling utility loads. The cost model for separation presented in the previous section is incorporated within F as Cjep. The operating costs for the separation profile (for example, heat loads in the case of distillation) are directly incorporated into the energy minimization formulation. Note that this formulation combines the energy target in (PIO) with the separation target in (PI2). 

Proactive and reactive scheduling approaches are two different strategies aimed at dealing with unexpected events in the plant. In this work, an evaluation criterion is established in order to make feasible the aforementioned comparison. The proposed metric consists of a combination of the already stated objective function, OF, plus a rescheduling cost, weighted by the plant operational cost. Therefore, the evaluation criterion metric is given by Eq.(20). 

Because it is difficult to make any reasonable estimates of the costs of aU the different contributions to the production cost, we can consider in a general discussion only some simple scenarios and their possible combinations. Since the feed cost depends essentially on the value of the recovery yield, it can be minimized by either considering optimization procedures with a constraint of min-imrun recovery yield or maximizing the product of the production rate and the recovery yield. Another possibility is to minimize the operating costs, or the fixed costs. Most practical cases are intermediate between these two extremes and can be taken care of by a proper mixing of the two objective functions (see Section 18.4.4). 

Table 5.5 Temperature Optimization Based on a Cost-Objective Function of Multiple Staggered CPBER with Chitin-Immobilized P-Galactosidase Under Biocatalyst Replacement at 25% of Initial Activity. Operation Conditions Are Those in Table 5.3...

Fig. 5.22 Surface of response for temperature optimization of continuous staggered CPBR with chitin-immobilised P-galactosidase, based on data in Table 5.3, considering the annual cost of reactor operation as the objective function...

Minimization of the time demand or cost of analyses might also constitute an objective function. To optimize an entire analytical procedure, methods of operational research might be needed in addition to the systematic approaches considered in this section. This is especially important in cases where risk assessment is required in connection with the analytical procedure. 

We may have size options for the new facilities and associated operating costs. These costs are fixed (f ) and variable costs (v,) that can be reflected on the model. Hence, our selection variables are modified as Xj o- The value of the variable is equal to one if facihty on site i is to be opened with size option o. Variable costs are added to transportation costs. So, objective function becomes ... 

The greatest potential for this system is as part of a program of preventive maintenance. Currently, in most operating rooms, endoscopes are removed from service and sent for repair when they fail in clinical use. This causes operative delay with attendant risk to the patient and an increase in cost to the institution. The problem is difficult because an endoscope maybe adequate in one procedure but fail in the next which is more exacting due to clinical variables such as large patient size or bleeding. Objective assessment of endoscope function with the EndoTester may eliminate some of these problems. 

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