Optimizing an objective function under a bivariate probability model

The motivation of this paper is to obtain an analytical closed form of a quadratic objective function arising from a stochastic decision process with bivariate exponential probability distribution functions that may be dependent. This method is applicable when results need to be offered in an analytical closed form without double integrals. However, the study only applies to cases where the correlation coefficient between the two variables is positive or null. A stochastic, stationary objective function, involving a single decision variable in a quadratic form is studied. We use a primitive of a bivariate exponential distribution as first expressed by Downton (1970) and revisited in Iliopoulos (2003). With this primitive, optimization of objective functions in Operations Research, supply chain management or any other setting involving two random variables, or calculations which involve evaluating conditional expectations of two joint random variables are direct. We believe the resul...

• Type: Journal
• Year: 2007
• Where: EOR
• Authors: Xavier Brusset, Nico M. Temme
• Keywords: Analytical Closed Form, Bivariate Exponential Probability, EOR 2007, Objective Function