Refinery planning under correlated and truncated price and demand uncertainties

Abstract

Because of the difficulty in computing the bivariate integral originated from the correlated demand and price, most research work on uncertainty assumes that the demand and price are independent. This can cause significant discrepancies in revenue calculation and hence yield sub-optimal planning strategies. This paper presents a novel approach to handle correlated and truncated demand and price uncertainties. A bivariate normal distribution is used to describe demand and price. The double integral for unintegrable standard normal cumulative distribution function in the single integrals is approximated by polynomial functions. Case studies show that, assuming independent price and demand may underestimate the revenue by up to 20%. Since the real world demands or prices vary in limited ranges, integrating over the whole range of a normal distribution, which some research has done, may give incorrect results. This paper uses a bivariate double-truncated normal distribution to describe demand and price. The influence of different degrees of truncation on plant revenue is studied. © 2006 Elsevier B.V. All rights reserved.