Dantzig-Wolfe and block coordinate-descent decomposition in large-scale integrated refinery-planning

The integrated refinery-planning (IRP), an instrumental problem in the petroleum industry, is made of several subsystems, each of them involving a large number of decisions. Despite the complexity of the overall planning problem, this work presents a mathematical model of the refinery operations characterized by complete horizontal integration of subsystems from crude oil purchase through to product distribution. This is the main contribution from a modelling point of view. The IRP, with a planning horizon ranging from 2 to 300 days, results in a large-scale linear programming (LP) problem of up to one million constraints, 2.5 million variables and 59 millions of nonzeroes in the constraint matrix. Large instances become computationally challenging for generic state-of-the-art LP solvers, such as CPLEX. To avoid this drawback, after the identification of the nonzero structure of the constraints matrix, structureexploiting techniques such as Dantzig-Wolfe and block coordinate-descent decomposition were applied to IRP. It was also observed that interior-point methods are far more efficient than simplex ones in large IRP instances. These were the main contributions from the optimization viewpoint. A set of realistic instances were dealt with generic algorithms and these two decomposition methods. In particular the block coordinate-descent heuristic, with a reverse order of the subsystems, appeared as a promising approach for very large integrated refinery problems, obtaining either the optimal or an approximate feasible solution in all the instances tested.