In the paper we present integer programming (IP) optimization models for flexgrid elastic optical networks (EON). We consider several different basic assumptions regarding flexibility of EON that lead to a variety of IP formulations differing in precision and complexity. As usual, detailed models aiming at precisely describing technological aspects of EON suffer from tractability issues resulting from their greater complexity and have to be reasonably simplified. To achieve this, we consider cases where the bandwidth is divided into predefined slots, cases where the bandwidth is continuous and can be divided between demands with no restrictions, cases where a list of predefined paths is available, and finally cases where all the paths are indirectly taken into account. We present both compact and non-compact formulations. The non-compact formulations are accompanied with brief description of the dedicated column generation algorithms

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