### Mathematical model of optimal project portfolio forming based on random factors

#### Abstract

**Purpose**. To identify the ways of perspective development for railway transport one should solve the problem of forming the investment project portfolio. Thus, it is necessary to deal with uncertainty in the input data (prices of services, materials, energy products). To take into account this uncertainty it is proposed to use the developed model of stochastic programming. **Methodology**. For accounting of uncertain data the probabilistic limits on the quantities of resources, which are used in the project portfolio are imposed. As the objective function it is proposed to maximize the threshold, which with a given probability may exceed the planning interval of the net income. **Findings.** Stochastic programming model with line-by-line probabilistic constraints was obtained. Coefficients of this model are normally distributed random variables. Ratios, which allow calculating mathematical expectations and covariance matrices of these coefficients, were concluded. **Originality**. Known methods of forming the optimal project portfolio are based on the fact that all inputs are known exactly. On the basis of this consideration, the authors of works on the creating an optimal project portfolio have come to a scheme of deterministic mathematical programming. In this article we propose to take into account the uncertainty in the input data, which will increase the reliability of the portfolio effectiveness estimation through the use of stochastic mathematical programming scheme. **Practical value**. The developed model can be used in order to solve the planning problems of railway transport development.

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DOI: https://doi.org/10.15802/stp2014/23787

### Cited-by:

1. **ANALYSIS ON THE USAGE OF DECISION-MAKING METHODS IN PROJECT MANAGEMENT**

I. V. Trifonov, I. A. Korkhina*Science and Transport Progress. Bulletin of Dnipropetrovsk National University of Railway Transport* Issue: 1(67) First page: 63 Year: 2017

doi: 10.15802/stp2017/93171

This work is licensed under a Creative Commons Attribution 4.0 International License.

**ISSN** 2307–3489 (Print)**І****SSN** 2307–6666 (Online)** **