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Optimization of the modernization of the technological system in a mine by means application of a mu |
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Optimization of the modernization of the technological system in a mine by means application of a multiplicative function Author: K. Czopek
A number of technical and economic problems are concerned with the proprieties of distinguishing the different economic factors. These may be materials, money, people, machines etc. The assignment of these factors to a specific activity cannot be arbitrary, since depending on the objective and quantity to which they are assigned, the outcome will produce a correspondingly diversified result. The paper deals with the above problem, since these factors should be allotted to individual elements of the system in such a way as to increase the efficiency of the system to optimize profitability, the financial means for modernization of the exploitation-processing system of a mine being limited. The essence of the problem presented is that the efficiency of the exploitation?processing system as a whole is the product of the efficiencies of individual elements included in the system. It means that the function of the objective is, in this case, of multiplicative character. Since it is a rather rare case in practice, it requires the application of dynamic programming with the multiplicative function of the objective. Dynamic programming helps to plan optimum solutions for the processes that can be steered, i.e., we can influence their course as they are being realized. The applied method requires the division of the realized process into successive stages, which may be achieved by conventional division of the realized process or by means of autonomous divisions. Optimum programming depends, then, on the hierarchical establishment of successive stages of the realization of the whole operation. The concept of a "stage" should be understood in a conventional way since it may embrace different activities. In the paper the illustrative example of the exploitation-processing system comprising 4 elements has been divided into 2 stages. In dynamic programming then, there are, n stages and at the beginning of each stage we must make a decision about the value of the decision variable xn. Thus a system of decisions x1, x2, ..., xn is chosen in such a way as to satisfy an optimum condition, for the established function of the objective Z(x1, x2, ..., xn), i.e. the function of the objective Z(x1, x2, ..., xn) ought to have an optimum value (maximum or minimum). The advantage of the method presented is the fact that it optimizes the process at each of the assumed stages. Regardless of a decision made at a given stage, the remaining decisions must be optimized by taking into account the results of the decision undertaken previously.
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2011