Two-stage stochastic programming with fixed recourse via scenario planning with economic and operational risk management for petroleum refinery planning under uncertainty

This work proposes a hybrid of stochastic programming (SP) approaches for an optimal midterm refinery planning that addresses three sources of uncertainties: prices of crude oil and saleable products, demands, and yields. An SP technique that utilizes compensating slack variables is employed to explicitly account for constraints’ violations to increase model tractability. Four approaches are considered to ensure solution and model robustness: (1) the Markowitzʹs mean-variance (MV) model to handle randomness in the objective function coefficients by minimizing the variance (economic risk) of the expected value of the random coefficients; (2): the two-stage SP with fixed recourse approach to deal with randomness in the RHS and LHS coefficients of the constraints by minimizing the expected recourse costs due to constraints’ violations; (3) incorporation of the MV model within the framework developed in (2) to formulate a mean–risk model that minimizes both the expectation and the operational risk measure of variance of the recourse costs; and (4) reformulation of the model in (3) by adopting mean-absolute deviation (MAD) as the measure of operational risk imposed by the recourse costs for a novel refinery planning application. A representative numerical example is illustrated.