Long-range process planning under uncertainty via parametric programming

Scenario analysis within a multi-stage stochastic programming formulation offers an attractive framework for modelling uncertainties in long-range planning models. However, whether the expected outcome is implicitly / explicitly evaluated, such formulations lead to computationally intensive optimization problems. Focussing here on the scenario planning / multi-period approach for mixed integer linear programming (MILP) problems under uncertainty, this paper presents a novel decomposition strategy for its solution. The proposed algorithm circumvents the direct solution of the large-scale deterministic equivalent MILP problem by exploiting its block-angular structure. Through the use of parametric programming, separable subproblems are formulated and solved in parallel at a relatively low computational cost. Computational studies show that the algorithm is ideally suited for problems where a large number of scenarios inhibits the direct solution of the deterministic equivalent problem.