An interior point method implementation for solving large planning problems in the oil refinery industry

Abstract

AbstractMulti‐period planning problems in the oil and refinery industry are typically large, sparse, staircase/band diagonal structured and nonlinear optimization problems. Successive linear programming (SLP) type methods have been widely used for solving these planning problems. But, it has long been recognized that the simplex method used in solving linear programs requires a large number of iterations for staircase/band diagonal structured problems. In this paper, we report results of an application of a recently developed interior point method that promises to be many times faster than the simplex method for multi‐period planning problems. However, to facilitate the use of interior point method in the current SLP algorithms a hybrid method combining the interior point method and the simplex method is developed. Therefore, the results determined with this hybrid method are qualitatively equivalent to that obtained with the simplex method alone. The CPU times corresponding to the hybrid method are compared with the CPU times of simplex and dual affine methods. The new hybrid method generates a basic feasible solution of the linear programming problem and is approximately 7 times faster than the simplex method on the tested planning problems. Moreover, the interior point and hybrid methods become faster as the problem size increases.