Many extreme-scale scientific applications are distributed in nature and oftentimes need to move vast amounts of data between multiple locations for various remote operations. Such applications require fast and reliable data transfer services with guaranteed finish time, which can be realized by making bandwidth reservation for dedicated channel provisioning in high-performance networks. From an individual perspective, a user always wishes to achieve the earliest finish time for a given data transfer request that typically specifies the maximum Local Area Network (LAN) bandwidth constraint, the data size, data available time, and the deadline. From a global perspective, the network service provider would attempt to serve as many users' bandwidth reservation requests (BRRs) as possible to maximize the overall network resource utilization and throughput. As for the high-performance network consuming vast amounts energy and network resources, the network service provider would also want to process BRRs efficiently to save energy, network resource and the network maintenance cost. These goals are potentially conflictive and require a careful design of the bandwidth reservation and scheduling algorithm. In this paper, we focus on one particular type of scheduling problem under the constraint of fixed path and varying bandwidth (FPVB), which has been proven to be NP-complete in the literature. We develop two heuristic algorithms, namely Least Available Bandwidth of Edge (LABE) and Largest Available Bandwidth of Path (LABP), to solve this problem and conduct simulation-based performance evaluation. The extensive simulation results illustrate the superiority of these proposed algorithms in terms of execution time, success ratio, and average data transfer completion time of BRRs in comparison with two existing scheduling algorithms.