(761d) Two-Stage Stochastic Programming with Chance Constraints for Refinery Optimization

Maximizing profit while meeting product quality specifications is always the primary goal of refining industry in a highly competitive market with increasingly stringent environmental regulations. Noting that the properties of feedstocks and operating conditions in fact are subject to uncertainties, any decisions based on the nominal parameters can be infeasible in reality and result in a substantial loss. Hence, a robust decision-making system is highly necessary for refining industry. To this end, the entire operations of refinery is usually modeled by two-stage stochastic programming (SP) with a number of sampled scenarios [1]. By solving this formulation to global optimum, we may find a robust strategy to direct real operations.

However, in practice, some constraints at Stage-II in SP can be softened since recovery operations can be employed if an infeasible scenario occurs at Stage-II. This motivates us consider a SP with probabilistic constraints. For this new SP, at Stage-I, the decision of upstream operations is made to ensure that final products meet quality specification with high probability. At Stage-II, the uncertainty is realized and the optimal blending recipe is decided accordingly. If the real scenario is infeasible to the normal operations, a special operation will be triggered to recover the quality of products. To make this formulation more tractable, we consider a linear model of refinery operations and assume that uncertain parameters satisfy normal distribution. This novel two-stage decision process will lead to a mixed-integer linear programming (MILP) with sampled scenarios. Here we allow the recovery operations in 5% scenarios at most, if they are infeasible under the decision made at Stage-I. In other scenarios, we have to use normal operations. There are two difficulties for applying this model. First, the number of binary variables in MILP is proportional to the number of scenarios. On the one hand, more scenarios implies more accurate solution to the real process; on the other hand, the resulting formulation becomes more computationally demanding. Second, the feasibility of unsampled scenarios are not guaranteed.

To overcome these two limitations, we first improve the existing Benders decomposition method [2] to obtain the global optimal solution of scenario-based chance-constrained programming much more rapidly. Second, given the optimal solution of Stage-I based on sampled scenarios, we integrate second-order cone programming and linear decision-rule to evaluate its feasibility. We can show that if there exists a linear decision-rule such that the proposed second-order cone programming is feasible, then the Stage-I solution satisfies the probabilistic constraints no matter how many scenarios are considered in proposed MILP.

The presented scheme is able to handle a large number of uncertain parameters in the model and provide a global optimal solution promptly. The performance and effectiveness of this approach are demonstrated by optimizing a simplified refining process model under uncertainties.

Reference

[1] Yang Y, Barton PI. Integrated crude selection and refinery optimization under uncertainty. AIChE Journal. 2016;62:1038-1053.

[2] Liu X, Kucukyavuz S, Luedtke J. Decomposition algorithms for two-stage chance constrained programs. Mathematical Programming. 2016;157:219-243.