A new method for robustness in rolling horizon planning

In this paper, we describe a new method to solve Linear Programming (LP) problems which have uncertain right-hand-sides. We apply this to planning problems where a rolling planning horizon is used and where robustness is important. In particular, we are interested in applications where the uncertainty has an underlying structure and can be described with practical constraints. The method proposed is based on a decomposition scheme where we iteratively solve an upper level problem for the first time period in which the parameters are assumed to be known. The lower level problem uses the upper level solution and computes a worst case scenario for an anticipation period that has uncertain parameters. Information about how the worst case scenario is affected by the upper level decisions is given back as a valid inequality. This process is repeated until the upper level solution satisfies the last generated valid inequality. The models used in the solution process can be kept as small as the corresponding deterministic model which has no uncertainties. We test the proposed method on an integrated production, transportation and inventory planning problem. We make use of simulations to compare our approach with a traditional deterministic approach with safety stocks. The result shows that the proposed method works well and performs better than the deterministic approach.