In this paper, we consider wavelength assignment problem (WAP) in Wavelength division multiplexed (WDM) unidirectional optical telecommunication ring networks. We show that, even though WAP on unidirectional ring belongs to NP-hard, WAP can be exactly solvable in real-sized WDM rings for near future demand. To accomplish this, we convert WAP to the vertex coloring problem of the related graph and choose a special integer programming formulation for the vertex coloring problem. We use a column generation technique in a branch-and-price framework for the suggested formulation. We also propose some generic heuristics and do the performance comparison with the suggested optimization algorithm.