Sharif University of TechnologyScientia Iranica1026-309822620151201Notes on mathematical formulation and complexity considerations for blocks relocation problemNotes on mathematical formulation and complexity considerations for blocks relocation problem272227283815ENH.EskandariDepartment of Industrial Engineering, Tarbiat Modares University, Tehran, IranE.AzariDepartment of Industrial Engineering, Tarbiat Modares University, Tehran, IranJournal Article20160104In a recent paper, Caserta et al. [M. Caserta, S. Schwarze, and S. Vo. A mathematical formulation and complexity considerations for the blocks relocation problem", European Journal of Operational Research, 219, pp. 96-104 (2012)] proposed two mathematical models for the blocks relocation problem. Because of the complexity of their rst model, called BRP-I, they employed a simplifying assumption and introduced a relatively fast model, called BRP-II, to solve medium-sized instances. In this paper, it is rst proven that the BRP-II model is incorrect. Then, the corrected and improved formulation of BRP-II, called BRP2c and BRP2ci, respectively, are presented. By correcting a constraint in BRP-II, the reported optimal solution is either corrected or improved in many instances. Also, it is proven that some results of BRP-II reported by Caserta et al. are incorrect. Incorporating some new cut constraints into BRP2ci, the computational time of solving instances is decreased 25 times, on average.http://scientiairanica.sharif.edu/article_3815_316808799e185d34e57564a8342dd57d.pdf