Robust supplier selection problem, in a scenario-based approach has been proposed, when the demand and exchange rates are subject to uncertainties. First, a deterministic multi-objective mixed integer linear programming is developed; then, the robust counterpart of the proposed mixed integer linear programming is presented using the recent extension in robust optimization theory. We discuss dec...

In this paper, we considered a Stochastic Interval-Valued Linear Fractional Programming problem(SIVLFP). In this problem, the coefficients and scalars in the objective function are fractional-interval, and technological coefficients and the quantities on the right side of the constraints were random variables with the specific distribution. Here we changed a Stochastic Interval-Valued Fractiona...

The notion of a Markov chain is ubiquitous in linear algebra and probability books. In linear algebra a Markov chain is a sequence {xk} of vectors defined recursively by a specified vector x0, a square matrix P and the recursion xk = Pxk−1 for k = 1, 2, . . .. That is, xk = P x0. Natural probabilistic restrictions are imposed on x0 and P . It is assumed that x0 is a probability vector; that is,...