A new method for robustness in rolling horizon planning

In this paper we describe a new method to solve Linear Programming (LP) problems with uncertain parameters. We apply this to planning problems where a rolling planning horizon is used. The method is based on a decomposition scheme where we iteratively solve an upper level problem for the first time period where the parameters are assumed to be known. The lower level problem use the upper level solution and computes a worst case scenario for an anticipation period with uncertain parameters. Information in 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 satisfy the last generated valid inequality. We test the proposed method on a integrated production, transportation and inventory planning problem. We compare our approach with a deterministic approach with and without safety stocks. The result shows that the method works well and perform better than the deterministic approach with safety stock.