Theme of master`s work
The modelling of optimum control processes under uncertainty Introduction
Scientific adviser: Dmitrieva Olga

Introduction

 

This work is devoted to modeling optimal control processes in conditions of uncertainty.

Research of complicated economical systems and developing mathematical optimal control models in conditions of uncertainty require executing system analysis of problem being considered, usage of optimal control methods, correction of completion terms; games theory methods; simulation modeling according to Monte Carlo method.

Actuality of research subject  
Actuality of subject selected is stipulated by improving projects’ control in conditions of uncertainty.

Problem of effective control is very critical of Ukrainian enterprises today. Success of each organization depends on its capability to adapt to external environment changes.

 

Figure 1.1 – Designing tendencies on different level 

 

It is necessary to pay significant attention to projects’ control and development, as percentage of their realization will decrease year by year.

Review of subject-devoted researches and elaborations

Many scientists achieved significant scientific results, and namely: A. Volkov, V.V. Akimenko, I.M. Sobol, A.O. Nedosekin etc., have paid their attention to optimal control processes in conditions of uncertainty,

Targets and tasks of the research
Target of this work is developing a model that allows decreasing the project completion terms.

Research tasks are:

• to define the subject field;
• to analyze existing approaches on eliminating the uncertainty in projects;
• to receive clear analytical decisions.

Main work content during its creation

Modern control processes of IT projects

Universal projects’ control methods allow solving following tasks: definition of project targets; preparation of project justification; its structuring; definition of financial needs and financing sources.   

There are 5 process control groups which are represented on figure 1.2.

Figure 1.2 – Diagram on project control process

Feature of IT projects is that, almost each enterprise meets in its activities this or that IT project, because targets, results and conditions of these projects’ realization are different; that is why we can speak about their variety and complexity.

Problems of projects’ optimal control

One of reasons to demark the projects’ control into separate knowledge field is uncertainty. The fact how the uncertainty is controlled within the project (including risks as well), directly impacts on project duration, on its success.

Researches of Standish Group 1 for traditional projects’ control methods are represented on figure 1.3.

 

Figure 1.3 – Traditional projects control methods

Having a traditional approach to projects’ control, problems related to uncertainty, Parkinson law and simultaneous employees’ work on several tasks, are resolved by including the risk and uncertainty into task estimation.

Putting a task

Combination ‘n’ of production enterprises organized on the basis of fan hierarchy and manufacturing single-type products, are considered in the work:

 

 Where:

C₀ –  coordinator managing the combination, is located at the 1st hierarchy level;
C_i – enterprise, located at the 2nd hierarchy level and manufacturing the products in P_i volume accordingly; P_i – scalar values;
u_i –  resource provided by center (C₀), which should be spent to create main enterprise funds (C_i);

(1)
L_i – manpower number at he enterprise C_i;
w_i, m_i – parameters specifying the activity of enterprise C_i, this information arrives the center (C₀) on feedback channels.

Hypothesis 1. Volume P_i produced by manufacturing enterprise C_i, is defined by means of Cobb-Douglas production function:

 

         (2)

Where:
x_i  –  amount of main funds of the enterprise
k_i  –  setting the enterprise constant 

Hypothesis 2. Under strategic behaviour, enterprise C_i tries to maximize own profit I_i:

  (3) 

Where:
C_i – unit price of products manufactured P_i;
w_i – average wage within the enterprise C_i;

In terms of fixed x_i, u_i,  w_i, solution of this task is explicit.

 

Conclusion

Researches of projects’ control problems are always under development stage. It is stipulated by the fact that control over projects of any activity field impacts on quality of performed work, and, accordingly, on life activity level. Projects’ control in conditions of uncertainty is natural at most enterprises. It specifies a great role of projects’ control in enterprises’ activity system.

 

References:

 

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