Abstract
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
Highlights
Optimizing network diagrams is a logical continuation of their construction
The procedure for studying the response surface proposed in the framework of response surface methodology (RSM) in relation to the problem of optimizing network diagrams allows to see solutions that meet the specified criteria
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 a given objective function»
Summary
Optimizing network diagrams is a logical continuation of their construction. different end goals of projects give reason to use different approaches to optimization. Separation of methods according to this principle is substantiated in this work using a typical triad: «defined variables – objective function – constraints» It is quite rightly noted at the same time that any specific practical task has a set of its limitations. It is emphasized that one can’t ignore the following circumstances: the model of minimizing the duration of a project with a fixed budget can’t always be technically implemented, and a specific problem under consideration may not have solutions under existing constraints. This conclusion, obviously, should be understood in the context of the search for the optimal solutions. The variant of such a control action should lead, according to the author, to an increase in the efficiency of project implementation
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