%0 Journal Article
%T Notes on mathematical formulation and complexity considerations for blocks relocation problem
%J Scientia Iranica
%I Sharif University of Technology
%Z 1026-3098
%A Eskandari, H.
%A Azari, E.
%D 2015
%\ 12/01/2015
%V 22
%N 6
%P 2722-2728
%! Notes on mathematical formulation and complexity considerations for blocks relocation problem
%K Logistics
%K Blocks relocation problem
%K Integer programming
%K Cut constraints
%K optimization
%R
%X In 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.
%U http://scientiairanica.sharif.edu/article_3815_316808799e185d34e57564a8342dd57d.pdf