Quantum key distribution (QKD) has potential of providing long-term security as it is based on the fundamental principles of quantum mechanics. Security of information transmitted through optical networks has attracted attention recently due to its vulnerability to attacks post quantum computers. Hence, the integration of QKD into optical networks can significantly improve the security of existing and future optical networks. In QKD-secured optical networks, the quantum channel and the classical channel are integrated into a single optical fiber to reduce the deployment cost of the network infrastructure. However, due to limited network resources in a single optical fiber, the efficient provisioning of network resources (wavelengths and time slots) and blocking are two major issues in such networks. In this work, a resource assignment strategy with scheduling, namely, resource assignment with scheduling (RA-WS) has been proposed for utilization of network resources efficiently. In the RA-WS strategy, the QKD lightpath requests (QLPRs) have been served according to the proposed scheduling criterion. Moreover, the proposed scheduling criterion for routing, wavelength and time-slot assignment (RWTA) can reduce the effect of QLPRs blocking because of the limited network resources. The performance of the proposed RA-WS strategy has been analyzed in terms of blocking probability (BP), success probability of update secret key (SPUSK), and time-slot utilization ratio (TSAR) with different reserved wavelengths for quantum signal channel (QSCh), i.e., W-Q and different time slots (n(tr)). Simulations performed on NSFNET network topology indicate that the RA-WS strategy performs better than the baseline strategy, i.e., resource assignment without scheduling (RA-WOS) in terms of all the considered metrics.