In this paper, we investigate the problem of transmission grant scheduling in multichannel optical access networks using a scheduling theoretic approach. A novel cost-effective multichannel Ethernet passive optical network (EPON) is considered for our study. We show that the problem can be modeled as an open shop (OS) and we formulate the joint scheduling and wavelength assignment problem as a mixed integer linear program (MILP). Since the problem is shown to be NP-hard, we introduce a tabu-search-based heuristic for solving the joint problem. Different other heuristics are also considered and their performances are compared with those of tabu and MILP. Results indicate that by appropriately scheduling transmission grants and assigning wavelengths, substantial and consistent improvements may be obtained in the network performance. For example, tabu shows a reduction of up to 29% in the schedule length with substantial reduction in channel idle gaps yielding to both higher channel utilization and lower queueing delays. Additionally, when the number of channels in the network is not small, the benefits of performing appropriate wavelength assignment, together with transmission scheduling, are observed and discussed. We further perform a packet-level simulation on the considered network to study the benefits of efficient grant scheduling.