Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 657608, 12 pages
http://dx.doi.org/10.1155/2011/657608
Research Article

Stochastic Fractional Programming Approach to a Mean and Variance Model of a Transportation Problem

V. Charles,1 V. S. S. Yadavalli,2 M. C. L. Rao,3 and P. R. S. Reddy3

1CENTRUM Católica, Escuela de Graduados de Negocios, Pontificia Universidad Católica del Perú, Lima 33, Peru
2Department of Industrial and Systems Engineering, University of Pretoria, Pretoria 0002, South Africa
3Department of Statistics, Sri Venkateswara University, Tirupati, A.P. 517502, India

Received 2 March 2010; Revised 3 November 2010; Accepted 23 February 2011

Academic Editor: J. J. Judice

Copyright © 2011 V. Charles et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, we propose a stochastic programming model, which considers a ratio of two nonlinear functions and probabilistic constraints. In the former, only expected model has been proposed without caring variability in the model. On the other hand, in the variance model, the variability played a vital role without concerning its counterpart, namely, the expected model. Further, the expected model optimizes the ratio of two linear cost functions where as variance model optimize the ratio of two non-linear functions, that is, the stochastic nature in the denominator and numerator and considering expectation and variability as well leads to a non-linear fractional program. In this paper, a transportation model with stochastic fractional programming (SFP) problem approach is proposed, which strikes the balance between previous models available in the literature.