(494j) Identification of Physically Realizable Solutions for a Refinery LP

Opportunities to increase profit margins in a refinery are determined from the refinery LP (linear program). The refinery LP model used to perform optimization is often characterized by degeneracy, which produces multiple optimal solutions. Furthermore, a LP model can be (a) primal degenerate if some of the activities are zero, (b) dual degenerate if some of the shadow prices are zero, or (c) both. Primal degeneracy results in multiple shadow prices (marginal value) and dual degeneracy results in multiple values for activities and input-output coefficients. Since shadow price, activities, and input-output coefficients obtained from the refinery LP guide the refinery planning decisions, degeneracy in the refinery LP has significant business implications.

In order to choose the right strategy, the refinery manager or the decision maker should not only identify the presence of multiple solutions but also the physically realizable solutions among them. This is particularly difficult because the software package that runs the LP can converge on any of the possible multiple solutions and the presence of degeneracy is ignored.

This poster demonstrates the need for determining true LP solutions among multiple optimal solutions. We define true LP solutions as the values of activities, shadow price and input-output coefficients that can be physically realizable in the real process. Determination of physically realizable shadow price under conditions of primal degeneracy is well established in literature. However, the study on the identification of physically realizable activities and input-output coefficients under conditions of dual degeneracy in literature is lacking. The primary focus of this poster is to emphasis the effects of dual degeneracy in a refinery LP and its business implications.

The poster will present a pictorial explanation on why a particular solution is physically realizable with the aid of graphical solution obtained for a 2-D LP. In addition to this solutions obtained for a 33 variable refinery LP will be presented to demonstrate how to identify whether a LP is primal degenerate, dual degenerate. Furthermore, the multiple optimal solutions obtained for the refinery LP will be presented to distinguish between physically realizable and non-physically realizable solutions.