In this paper, we consider a unidirectional ring network with limited reconfigurability and take up the problem of supporting all-to-all traffic - while minimizing the worst-case wavelength range of the reconfigurable optical add drop multiplexers (ROADMs). ROADMs can be limited in range (L-ROADMs) or have full range (F-ROADMs). The cost of such a network is dominated by the number of wavelengths to be added or dropped by ROADMs. Limiting the range of wavelengths that can be accessed at a node reduces costs. Here, we develop an integer linear programming (ILP) formulation for this problem, and also propose a new wavelength assignment heuristic where we evalute it using the ILP formulation. We conclude that the performance of our proposed heuristic is very close to optimal and the worst-case range is only about 65% of the full range for moderately large number of network nodes.