Characterization of petroleum refinery LP results under conditions of degeneracy

Scope and Method of Study. The phenomenon of degeneracy inevitably occurs in most large LP models. An LP could be primal degenerate, dual degenerate, or both primal and dual degenerate. Primal degeneracy of LP and its solution interpretation is well established in literature, but the notion of dual degeneracy (alternative optima) has received less attention. The condition of dual degeneracy or alternative optima leads to multiple optimal bases with multiple activity values or multiple primal solutions. Current refinery optimization practitioners are not fully aware of the consequences of degeneracy and business decisions are made using a single LP run.;The purpose of this study is to investigate the effects of dual degeneracy in the context of petroleum refinery optimization and simultaneously to develop strategies to select a specific set of activity values for implementation based on business logic. When an LP has alternate optimal solutions or is dual degenerate, it will be primal degenerate in the dual space. This property of the dual degenerate problem is exploited in this research to derive business logic on the interpretation of LP solutions produced by a dual degenerate LP.;This study developed a novel dual incremental analysis approach to choose a desired set of activity values based on small changes in the market price of activities when the LP is dual degenerate. Furthermore, a perturbation technique implementing parametric programming is developed to generate multiple optimal bases when the LP is dual degenerate. Results are presented, along with a simplified refinery model containing 33 decision variables and 37 constraints.;Findings and Conclusion' Findings of this study indicated that for the dual degenerate refinery LP the magnitude of the difference among activity values obtained for each of the alternate optimal solutions is significant. Although the optimality criteria (primal and dual feasible) for the LP is satisfied for each of the alternate optimal solutions in the base case, the optimality criteria may not be satisfied even for an infinitesimal change in the market price of activities. The dual incremental analysis approach and the underlying business logic developed in this research serves two purposes for a dual degenerate LP: 1) characterize each of the activity values obtained for a single LP run, and 2) choose a desired set of activity values for implementation among multiple optimal solutions generated.