Design of mechanisms for ensuring the execution of tasks in project planning

TL;DR

This paper develops mathematical models and iterative methods for optimizing task hierarchies in project planning, considering constraints like cost and duration, to improve decision-making in various fields.

Contribution

It introduces new verbal and mathematical models for task hierarchy construction and iterative methods for minimizing project duration and cost.

Findings

Effective models for task hierarchy construction.

Iterative methods for minimum project duration.

Boolean programming approach for cost estimation.

Abstract

This paper reports an analysis of aspects of the project planning stage. The object of research is the decision-making processes that take place at this stage. This work considers the problem of building a hierarchy of tasks, their distribution among performers, taking into account restrictions on financial costs and duration of project implementation. Verbal and mathematical models of the task of constructing a hierarchy of tasks and other tasks that take place at the stage of project planning were constructed. Such indicators of the project implementation process efficiency were introduced as the time, cost, and cost-time efficiency. In order to be able to apply these criteria, the tasks of estimating the minimum value of the duration of the project and its minimum required cost were considered. Appropriate methods have been developed to solve them. The developed iterative method for assessing the minimum duration of project implementation is based on taking into account the possibility of simultaneous execution of various tasks. The method of estimating the minimum cost of the project is to build and solve the problem of Boolean programming. The values obtained as a result of solving these problems form an {\guillemotleft}ideal point{\guillemotright}, approaching which is enabled by the developed iterative method of constructing a hierarchy of tasks based on the method of sequential concessions. This method makes it possible to devise options for management decisions to obtain valid solutions to the problem. According to them, the decision maker can introduce a concession on the value of one or both components of the {\guillemotleft}ideal point{\guillemotright} or change the input data to the task. The models and methods built can be used when planning projects in education, science, production, etc.