The object of research is a test network diagram, in relation to which the task of minimizing the objective function qmax/qmin→min is posed, which requires maximizing the uniformity of the workload of personnel when implementing an arbitrary project using network planning. The formulation of the optimization problem, therefore, assumed finding such times of the beginning of the execution of operations, taken as input variables, in order to ensure the minimum value of the ratio of the peak workload of personnel to the minimum workload. The procedure for studying the response surface proposed in the framework of RSM is described in relation to the problem of optimizing network diagrams. A feature of this procedure is the study of the response surface by a combination of two methods – canonical transformation and ridge analysis. This combination of methods for studying the response surface allows to see the difference between optimal solutions in the sense of "extreme" and in the sense of "best". For the considered test network diagram, the results of the canonical transformation showed the position on the response surface of the extrema in the form of maxima, which is unacceptable for the chosen criterion for minimizing the objective function qmax/qmin→min. It is shown that the direction of movement towards the best solutions with respect to minimizing the value of the objective function is determined on the basis of a parametric description of the objective function and the restrictions imposed by the experiment planning area. A procedure for constructing nomograms of optimal solutions is proposed, which allows, after its implementation, to purposefully choose the best solutions based on the real network diagrams of your project
The object of research is a model network schedule for performing a complex of operations. One of the most problematic areas is the lack of a unified procedure that allows finding a solution to the problem of compromise optimization, for which the optimization criteria can have a different nature of the influence of input variables on them. In this study, such criteria are the criteria for the uniformity of the workload of personnel and the distribution of funds. Two alternative cases are considered: with monthly planning and with quarterly planning of allocation of funds and staff load. The methods of mathematical planning of the experiment and the ridge analysis of the response surface are used. The peculiarities of the proposed procedure for solving the problem of compromise optimization are its versatility and the possibility of visualization in one-dimensional form – the dependence of each of the alternative criteria on one parameter describing the constraints. The solution itself is found as the point of intersection of equally labeled ridge lines, which are curves that describe the locally optimal values of the output variables. The proposed procedure, despite the fact that it is performed only on a model network diagram, can be used to solve the trade-off optimization problem on arbitrary network graphs. This is due to the fact that the combination of locally optimal solutions in a parametric form on one graph allows visualizing all solutions to the problem. The results obtained at the same time make it possible to select early dates for the start of operations in such a way that, as much as possible, take into account possible difficulties due to the formation of bottlenecks at certain stages of the project. The latter may be due to the fact that for the timely execution of some operation, it may be necessary to combine two criteria, despite the fact that the possible costs may turn out to be more calculated and estimated as optimal.
The object of research is a test network diagram, in relation to which the task of minimizing the objective function qmax/qmin→min is posed, which requires maximizing the uniformity of the workload of personnel when implementing an arbitrary project using network planning. The formulation of the optimization problem, therefore, assumed finding such times of the beginning of the execution of operations, taken as input variables, in order to ensure the minimum value of the ratio of the peak workload of personnel to the minimum workload. The procedure for studying the response surface proposed in the framework of RSM is described in relation to the problem of optimizing network diagrams. A feature of this procedure is the study of the response surface by a combination of two methods – canonical transformation and ridge analysis. This combination of methods for studying the response surface allows to see the difference between optimal solutions in the sense of "extreme" and in the sense of "best". For the considered test network diagram, the results of the canonical transformation showed the position on the response surface of the extrema in the form of maxima, which is unacceptable for the chosen criterion for minimizing the objective function qmax/qmin→min. It is shown that the direction of movement towards the best solutions with respect to minimizing the value of the objective function is determined on the basis of a parametric description of the objective function and the restrictions imposed by the experiment planning area. A procedure for constructing nomograms of optimal solutions is proposed, which allows, after its implementation, to purposefully choose the best solutions based on the real network diagrams of your project
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