Stochastic Programming with Economic and Operational Risk Management in Petroleum Refinery Planning under Uncertainty

Rising crude oil price and global energy concerns have revived great interests in the oil
and gas industry, including the optimization of oil refinery operations. However, the
economic environment of the refining industry is typically one of low margins with
intense competition. This state of the industry calls for a continuous improvement in
operating efficiency by reducing costs through business-driven engineering strategies.
These strategies are derived based on an acute understanding of the world energy
market and business processes, with the incorporation of advanced financial modeling
and computational tools. With regards to this present situation, this work proposes the
application of the two-stage stochastic programming approach with fixed recourse to
effectively account for both economic and operational risk management in the planning
of oil refineries under uncertainty. The scenario analysis approach is adopted to
consider uncertainty in three parameters: prices of crude oil and commercial products,
market demand for products, and production yields. However, a large number of
scenarios are required to capture the probabilistic nature of the problem. Therefore, to
circumvent the problem posed by the resulting large-scale model, a Monte Carlo
simulation approach is implemented based on the sample average approximation (SAA)
technique. The SAA technique enables the determination of the minimum number of
scenarios required yet still able to compute the true optimal solution of the problem for
a desired level of accuracy within the specified confidence intervals. We consider
Conditional Value-at-Risk (CVaR) as the risk metric to hedge against the three
parameters of uncertainty, which affords a framework that also involves the use of the
Value-at-Risk (VaR) measure. We adopt two approaches in formulating appropriate
two-stage stochastic programs with mean–CVaR objective function. The first approach
is by using the conventional definition of CVaR that leads to a linear optimization
model approximation coupled with a graphical-based solution strategy to determine the
value of VaR using SAA in order to arrive at the optimal solution. The second approach
is to utilize auxiliary variables to formulate a suite of stochastic linear programs with
CVaR-based constraints. We conduct computational studies on a representative refinery
planning problem to investigate the various model formulations using GAMS/CPLEX
and offer some remarks about the merits of these formulations.