Recently, there is has been significant interest in the allocation systems of rail track capacities with considerations of the multiple train operating companies. The system indicates both a well-defined procedure and an algorithmic method to allocate the rail track capacities. Among them, this study considers the algorithmic method to derive the optimal timetable for the trains, which the companies propose together with their arrival and departure times at each station. However, most studies have focused on the adjustment of the departure and arrival times without conflicts, which could result in incompatible allocations with the line plan, which would result in an insufficient number of trains on each line to satisfy the demands. Our study presents a new optimization model and algorithm for the allocation problem in order to reflect the predetermined line plan. Furthermore, we provide the experimental results that were applied to the Korean high-speed railway network including the Suseo lines.