Mathematical methods of supporting network analysis of the project and assessment of planning risk in case of fuzzy information on work duration

Abstract

The article is devoted to the actual problem of planning modern projects under conditions of uncertainty and risk, in which information about the duration of work can be represented by fuzzy LR-intervals. At the same time, it is important for the project manager not only to determine the parameters of the work and events of the project at the stage of network analysis, but also to assess the risk of project planning associated with the possible exceedance of the deadlines due to uncertainty at the planning stage. To calculate the project parameters and planning risk, an approach based on the construction of a-level cuts of the membership functions of the duration of work and the subsequent transition to interval calculations of the parameters of events, works and the critical path was reasonably chosen. The article presents formulas for calculating a-level cuts of fuzzy time parameters: early and late times for the completion of project events, early and late dates for the start and end of work, the length of the critical path. Approximation of the obtained a-level cuts allows, if necessary, to build membership functions of the calculated parameters. The paper introduces an important indicator for planning under conditions of uncertainty — risk assessment of project planning with fuzzy information about the duration of work. This indicator is a quantitative assessment of risk as a threat of exceeding the deadlines for project implementation due to the uncertainty of information in planning and network analysis. The article presents the properties of the planning risk assessment, proposes an iterative algorithm for its calculation, based on the construction of a-level cuts of the fuzzy critical path and the calculation of private estimates of the planning risk. For the practical implementation of the algorithm, a software product has been developed that makes it possible to reduce the time for making decisions on planning and evaluating the feasibility of project implementation. The article presents and analyzes the results of calculations on the example of an IT-project. The analysis of the results made it possible to draw conclusions about the practical possibility of applying the described approach and outline further ways to improve it.