STOCHASTIC MODEL OF CAPACITY TYPE RESOURCE ALLOCATION

Abstract

Purpose of the study. The problem of forming a project team to complete tasks of a given complexity within a specified timeframe and with minimal costs is considered. The productivity of each specialist is modeled as a random variable obeying a normal distribution, which leads to the formulation of a stochastic programming problem with a probabilistic constraint. Materials and Methods. The main attention is paid to methods of reducing a stochastic problem to a deterministic equivalent by transforming a probabilistic constraint using the properties of the normal distribution law. This operation allows us to reduce the original problem to a nonlinear form. This circumstance excludes the use of well-tested algorithms. The main complexity of the solution lies in the nonlinearity and integer nature of the variables. Constraint linearization methods, including Taylor series expansion and piecewise linear approximation, are studied, and simple heuristic selection criteria are analyzed. The proposed main solution method is to linearize the nonlinear constraint obtained by transitioning from a probabilistic constraint in linear form to a deterministic version, but in nonlinear form. The paper describes approaches to nonlinear constraint linearization, including Taylor series expansion and piecewise linear approximation. Results. Heuristic criteria for selecting specialists are proposed, taking into account their productivity, cost and labor stability. Four criteria are introduced: an efficiency criterion using two characteristic parameters: productivity and cost; a stability criterion taking into account the standard deviation and productivity; a complex criterion, which is the product of the first two; and a combined criterion taking into account all three factors. The advantages and disadvantages of these approaches to solving the original problem are shown. Conclusion. It is shown that taking into account the stochastic nature of individual initial parameters of the problem leads to the need to solve optimization problems of stochastic programming, which presents certain difficulties. In this case, the focus is no longer on obtaining analytical solutions. A practical example demonstrates that accounting for stochasticity leads to increased team size and costs compared to a deterministic case. A conclusion is drawn regarding the need to use combined criteria and iterative algorithms to obtain solutions close to optimal.