APPLICATION OF THE GENERAL ALGORITHM OF LINEARIZATION IN LINEAR FRACTIONAL OPTIMIZATION PROBLEMS IN PROJECT MANAGEMENT

Abstract

Effective planning of resources and optimization of the work schedule allows you to minimize costs and adhere to project deadlines, which ensures the quality of results. Many real projects include complex interdependencies and constraints that can be described by nonlinear models, complicating the process of their optimization. The use of a general linearization algorithm for nonlinear optimization problems offers an innovative approach to simplifying and solving complex planning problems. Linearization makes it possible to transform non-linear models into linear forms that are more convenient for calculation, which facilitates the application of linear programming methods. This is especially important in conditions of limited resources and strict constraints on the time and budget of the project. If the project has a complex schedule with many interdependent tasks, as well as limited resources, we believe that the original model contains nonlinear constraints, for example, dependencies between different tasks that affect the duration and use of resources. Using linearization techniques, such as replacing nonlinear constraints with linear approximations or using partial derivatives for local linearization, the problem can be simplified to a linear form. After linearization, linear optimization methods, such as linear programming, are used to determine the optimal resource allocation and task execution schedule.One of the most common examples of using the linear fractional optimization in project management is given by a problem of minimizing the expense per a unit of time or resource while maximizing the tasks completion quality. For example, in planning of a construction project, managers can use linear fractional models for optimizing the expense for construction materials and manpower with ensuring a high quality of works and good meeting of the schedule milestones at the same time.