Planning under Correlated and Truncated Price and Demand Uncertainties

This paper presents a novel approach to handle refinery planning under correlated and truncated random demand and price uncertainties. To compute the expectation of plant revenue, which is the main difficulty for a planning problem under uncertainty, a bivariate normal distribution is used to describe demand and price. Formulae for revenue calculation under correlated and truncated price and demand are derived. It is found that the correlation and truncation of price and demand have major influences on plant net profit. A plan that ignores these factors can be far from optimal. The Type 2 service level or fill rate undercorrelated and truncated random price and demand is derived and efficiently calculated in this paper. Maximum plant net profit that satisfies certain fill rate target can thus be obtained. The proposed approach can be generally applied for modeling other chemical plants under uncertainty.