In this paper, a dynamic scheduling scheme is proposed for delivery of on-demand multimedia contents (e.g. movies) for internet service providers (ISP) that receive requests for different available contents from the customers for near future delivery. Each ISP is interested in assigning the available resources to the requests in such a way that the delivery time remains lower than a threshold, and also the profit is maximized. Regarding the diversity of customers in terms of their willingness to pay, there exists a group of budget-constrained receivers who are ready to wait longer. Therefore, since the ISP dynamically receives the requests for future delivery, postponing transmission of videos to some customers can provide the opportunity to increase the profit by reducing cost of distribution paths via multicast cost sharing. So, it can be profitable to postpone transmitting the content for some receivers (who cannot be clustered into cost saving multicast groups in the current transmission period) in hope for receiving more requests until the next transmission period, and consequently sharing the cost with a larger number of receivers. We propose a heuristic algorithm for topology-based multicast scheduling problem to find cost efficient multicast groups in each transmission period. Performance of the proposed algorithm is evaluated and compared with a popularity-based scheduling algorithm for a wide range of parameters via extensive simulation experiments.