In this paper, we analyze a variety of approaches to obtain lower bounds for multi-level production planning problems with big bucket capacities, i.e., problems in which multiple items compete for the same resources. We give an extensive survey of both known and new methods, and also establish relationships between some of these methods that, to our knowledge, have not been presented before. As will be highlighted, understanding the substructures of difficult problems provide valuable insights on why these problems are hard to solve. We conclude with computational results from widely used test sets and discussion of future research.
In Press, Computational Optimization and Applications, DOI: 10.1007/s10589-012-9465-z. The final publication is available at springerlink.com, http://dx.doi.org/10.1007/s10589-012-9465-z