Solution of the Compromise Optimization Problem of Network Graphics on the Criteria of Uniform Personnel Loading and Distribution of Funds

Abstract

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.