Functional cost, minimizing

After fitting the parameters of the model to the data, the the best tuning constants were found. The cost functional to minimize was the integral of the absolute value of the error (lAE) ... 

A rigorous approach to the discretization of equipment sizes involves the use of standard equipment sizes already at the start of the cost minimization problem, i.e. Eqn. 7.4-31 is solved but with Vj chosen for each stage from a set of standard equipment units DSVj of type j. The objective function then is formulated as ... 

We can then conclude that while the discrete time STN and RTN models are quite general and effective in monitoring the level of limited resources at the fixed times, their major weakness in terms of capability is the handling of relatively small processing and changeover times. Regarding the objective function, these models can easily handle profit maximization (cost minimization) for a fixed time horizon. Intermediate due dates can be easily modeled. Other objectives such as makespan minimization are more complex to implement since the time horizon and, in consequence, the number of time intervals, are unknown a priori (see [11]). 

From the different planning methods available within SNP, SNP optimization is selected because it offers the best fit to the customer requirements outlined above. The main reasons for this decision are the multisourcing characteristics of the supply network as well as the fact that the objective functions used by the SNP optimizer, profit maximization or cost minimization, correspond to the planning philosophy favored by the customer. In addition to SNP optimization with its cost-based approach, SNP offers several heuristic-based planning methods which follow a rule-based logic. 

A common problem encountered in large chemical companies involves the distribution of a single product (30 manufactured at several plant locations. Generally, the product needs to be delivered to several customers located at various distances from each plant. It is, therefore, desirable to determine how much Y must be produced at each of m plants (Yv Y2,..., Ym) and how, for example, Ym should be allocated to each of n demand points (YmV Ym2,. Ymnl The cost-minimizing solution to this problem not only involves the transportation costs between each supply and demand point but also the production cost versus capacity curves for each plant. The individual plants probably vary with respect to their nominal production rate, and some plants may be more efficient than others, having been constructed at a later date. Both of these factors contribute to a unique functionality between production cost and production rate. Because of the particular distribution of transportation costs, it may be... 

The economic objective in the model can either be represented as operating cost minimization or added-value maximization. In the case of added-value maximization, product prices are subtracted from the cost of feedstocks for each process. If PrCpet is the price of chemical cp, the added-value objective function can be represented as ... 

Here, L2 represents the chemical property space corresponding to the VCL, d(x, rf) represents an appropriate distance metric between the lead compound ry and the compound , p xf is the relative weight that can be attached to compound (if all compounds are of equal importance, then the weights p(xy) = for each i), and Mis typically much smaller than N. That is, this problem seeks a subset of M lead compounds ry in a descriptor space such that the average distance of a compound from its nearest lead compound is minimized. Alternatively, this problem can also be formulated as finding an optimal partition of the descriptor space co into M clusters Ay and assigning to each cluster a lead compound rj such that the following cost function is minimized ... 

The objective function of a supply network design model can either minimize costs or maximize profits. In practice the production function is often required to assume that all forecasted demands have to be met. In this constellation cost minimization and profit maximization lead to identical results and consequently cost minimization models are used. From an economic perspective this simplification can be justified in cases where a high share of fixed costs allows the assumption that any product sale con-... 

A detailed SMBR model was used in order to optimize the unit with the objective function of minimal eluent requirement under the constraints of full conversion and complete product separation. Due to the reduced cost of these resins, the cost of this process is in fact controlled by the cost of the solvent recovery from the extract and raffinate streams. 

In the formulation of this problem, it is supposed that in addition to the usual specifications, two purity specifications (bt/dt and bh/dh) are made, and that it is required to find the feed-plate location [plate number (kt + 1)], the total number of plates k2, and the corresponding values of the operating variables Li/D and D that minimize the operating costs and capital costs per mole of the most valuable product (D or B). Since only two of the four additional variables required to define the column are specified, many solutions may be obtained by making different choices for two of the four remaining variables. The best choice for the remaining variables has been made when the objective function is minimized. 

The production and supply side is analysed mainly using the MOREHyS model (Ball, 2006 Seydel, 2008). MOREHyS is a technology-based (bottom-up), mixed-integer, linear optimization model. The objective function used for the optimization, which is carried out sequentially, is yearly cost minimization for the whole country and the complete supply chain (production to dispensing) in each snapshot. 

Search for optimal solution through cost minimization functions... 

The objective function of minimizing the procurer s cost completes the mathematical model ... 

The objective functions discussed above take a cost minimization perspective and are appropriate when the jobs to be served are exogenously determined. When order acceptance is also a decision (or equivalently, if the demand depends on quoted lead times), then the objective is to maximize profit ... 

Therefore, the target function of cost minimization of the whole supply chain within period T is ... 

In this section the 2 performance problem in the time domain is studied. The following quadratic cost function is minimized... 

The maximum spaiming tree found by the j-th method of graph costing minimizes the objective function defined by... 

The above cost function considers minimization norm) of the ratio of base displacement (Xj) with controller and base displacement j... 

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