The Concept of Competition in Optimal Resource Allocation and Methods for Its Assessment

Aim. The presented study aims to define the concept of competition in optimal resource allocation and to determine indicators of competition in practical tasks directly in the mathematical formulation of the problem.Tasks. The authors determine mathematical indicators that characterize the level of competition in resource allocation optimization tasks and show examples of the adequacy and sensitivity of the selected competition indicators in various economic situations.Methods. The selected competition indicators for these tasks are based on the concept of “rigorous selection” of competitors applying for resources. The indicators are calculated in full accordance with the known optimization methods and optimality conditions for problems of this class, making it possible to interpret the results of optimization as a measure of competition for resources.Results. Two types of competition indicators for linear and non-linear cases of optimal resource allocation problems are defined and formalized. Examples of the dependence of efficiency on different compositions of the competitive environment are shown. Dependencies of the “rigorous selection” of competitors in the context of resource depletion are described.Conclusions. The competition indicators considered in the study can be included in the standard analysis for solving the problems of optimal resource allocation, which involves finding an extremum, searching for an optimal plan, analyzing stability, limits, the effect of restrictions on the target function, dual estimates, a measure of resource scarcity, etc. Adding the competition indicator to this analysis provides another factor for analysis, which can be significant under otherwise equal conditions. The competition indicator can be used both in a multi-step procedure for finding the extremum of a function (for example, as an additional criterion for choosing a free variable) and in the analysis of the results of problem-solving.