Development of the Markovian model for the life cycle of a project's benefits

Abstract

This study has improved the standard P5 (Personnel, planet, profit, process, product), which has already been widely applied globally in the practice of project management. However, the standard P5 provides a scheme of the life cycle of projects' benefits, which makes it possible to represent the lifecycle processes only at the qualitative level. In order to pass to the quantitative estimates, it has been proposed to apply the Markovian chain that maps a phenomenological representation of complex systems without considering their physical character. We have constructed a cognitive Markovian model of the life cycle of a project's benefits using the communications between the states of the project system. The cognitive structure of the life cycle is similar to a directed graph where vertices indicate the state of the system, and links are the communications between them. We have proposed an approach to determining transitional probabilities based on the evaluation of communications, taking into consideration the time costs to perform operations in the form of rules. The character of communications between states s→j in the Markovian chain defines the magnitude of transition probabilities nsj. The time costs required for each state are divided into five intervals nsj: 0 - no costs; 0.01-0.1 - insignificant time costs; 0.1-0.3 - the lowest level of time costs; 0.3-0.7 - average time costs; 0.7-1.0 - the largest time costs. The logic of choosing values for conditional transition probabilities in the Markovian chain makes it possible to determine data for the simulation of the trajectory of the life cycle of projects' benefits in the coordinates of the probabilities of states of the system and steps. It has been shown that the application of the Markovian chains is rational in order to represent the life cycle of projects' benefits. An analysis was performed to determine a certain level of technological maturity of the project environment (organization), which corresponds to the totality of values for transition probabilities. We have studied the influence of the level of technological maturity of the project environment (organization) on the projects' efficiency. Another example of the implementation of the project aimed at forming the positive image of an educational establishment by applying the frontal information communication via television, the press, by taking part in mass political activities, has also revealed positive estimation. The probability distribution at the beginning of the project (V1) and upon its completion (V2) differs significantly. The implementation of the project increased the magnitudes of probabilities of states p7 (Benefit) and p8 (Additional benefit). At the beginning of the project: p7(V1)+p8(V2)=0.14+0.05=0.19. Upon implementation of the project: p7(V1)+p8(V2)=0.22+0.08=0.30. The evaluation of this project aimed at positive image formation of an educational establishment showed that the results obtained do not contradict the hypothesis about the possibility of applying the Markovian chains to determine the characteristics of the life cycle of a project's benefits.