This paper considers the efficient design of routing path and wavelength assignment in the single-hop WDM optical transport networks. The connection demands between node-pairs are given and a connection between a pair of nodes must be made by only one lightpath. It is assumed that no wavelength conversion is allowed and the physical topology of the network and the number of available wavelengths of a physical link are also given. This paper proposes the method to route a path and assign a wavelength to the path, which guarantees fairness to every node pair. In order to guarantee fairness and maximize connections, an optimization model is established, which successively maximizes minimum connection ratio to the demand of each node pair. A heuristic algorithm with polynomial iterations is developed for the problem since the problem is NP-hard. The heuristic algorithm is implemented and applied to the networks with real problem sizes. The results of the application are compared with GAMS/OSL.