The tasks and methods of the organization's maturity level increasing in the field of project management

The article considers the task of the organization's maturity level increasing on the convergence mechanisms basis. The essence of these mechanisms in the transfer of effective elements of various methodologies of project, programs and project portfolios management (best practices) to the methodology of project, programs and project portfolios management of the organization to improve its maturity level in the field of project management. The article presents the formulation and methods for solving the problem of the methodological elements optimal to increase the level of organizations maturity with minimum expenditure of funds and (or) time. The first task is to select m elements of the methodology with a minimal cost of increase their value to the required level. The second task is also to choose the m elements of the methodology in the presence of two criteria: the time of adaptation of new elements and the cost of their adaptation. The problem is reduced to the previous one based on a linear convolution of the criteria. Finally, the third task is to minimize one of the criteria (for example - time) while another criterium is limited. The Lagrange multipliers method is proposed to solve this problem. This method either gives an approximate solution, or - an estimate for the initial problem, which can be used in the method of branches and boundaries. A different algorithm of estimates obtaining based on the network programming method (I.V. Burkova) is also proposed. The essence of the method consists in splitting the costs of adapting each element into two parts. We obtain two evaluation problems. The sum of optimal values of these problems gives us an upper bound for the original problem. The problem of finding the optimal partition is called a generalized dual problem, which is the problem of convex programming. Optimality conditions for solutions of the direct and generalized dual problems are obtained. Using computer experiments, the advantage of the network programming method is shown.