In the paper we address an important problem in minimum cost design of Elastic Optical Networks (EON), namely the problem of optimizing the configurations of Sliceable-Bandwidth Variable Transceivers (S-BVT) at the EON nodes. We first show how this optimization problem can be viewed and modeled as a combination of three bin-packing subproblems, with additional constraints ensuring feasibility of the solution. Then, we propose various valid inequalities and symmetry breaking constraints to strengthen the introduced model. Finally, we show, through computational results, that the strengthening techniques very effectively enable achieving near-optimal solutions.