Because optical WDM networks will be realized as network backbone in the near future, multicasting in WDM networks needs to be supported for various network applications. In this paper, we propose a new dynamic multicast routing problem under delay constraints (DMR-DC) for finding an optimal light-forest with the minimum multicast cost from these links with available wavelengths for routing a multicast request that arrives in random with a given delay bound in a WDM network with heterogeneous light splitting capabilities, where a light-forest is a set of light-trees used to set up switches to route the request. Multicast cost is defined by communication cost ratio and wavelength consumption ratio. The problem is to determine a light-forest with less wavelength consumption and less communication cost. This problem is NP-hard because it can be reduced from the minimum Steiner tree problem. In this paper, we propose an efficient three-phase (generation, refinement, and conversion) solution model to find approximate solutions in a reasonable time.