The information age that we are living in is characterized by exponentially increasing needs and corresponding means to access, transmit and use data in a variety of business settings. Fast growing demand, which is translated to market opportunities, has led to the emergence of many new and well-established firms entering into the telecommunications market, resulting in a crowded, highly competitive business environment with numerous providers and carriers offering a wide range of data services. Today's firms use telecommunication networks in a variety of ways to carry out their daily communications such as video conferencing, voice over IP and other data-intensive transmissions. In this paper, we report on a study in which we investigate a cost optimization problem that a firm encounters when acquiring network bandwidth from a telecommunication market that consists of many backbone providers offering different combinations of pricing policies and quality of service (QoS) levels. After the acquisition of network resources (bandwidth), firms allocate these resources to their daily data transmissions (tasks) according to the QoS requirement of the tasks. In an optimal allocation scheme, it is generally presumed that each task has to be assigned to a network resource which is capable of providing an equal or higher level of QoS than required by the task. However, it is shown with the proposed heuristic approach (presented herein) that QoS degradations during the allocation of tasks can lead to more favorable outcomes, especially when certain cost penalty policies are applied to the reduction of QoS requirements.