This paper presents a mathematical approach to solve railway rescheduling problems. The approach assumes that the trains are able to resume their journey after a given time frame of disruption whereby The train that experiences disruption and trains affected by the incident are rescheduled. The approach employed mathematical model to prioritise certain types of train according the railway operator's requirement. A pre-emptive goal programming model was adapted to find an optimal solution that satisfies the operational constraints and the company's stated goals. Initially, the model minimises the total service delay of all trains while adhering to the minimum headway requirement and track capacity. Subsequently, it maximises the train service reliability by only considering the trains with delay time window of five minutes or less. The model uses MATLAB R2014a software which automatically generates the optimal solution of the problem based on the input matrix of constraints. An experiment with three incident scenarios on a double-track railway of local network was conducted to evaluate the performance of the proposed model. The new provisional timetable was produced in short computing time and the model was able to prioritise desired train schedule.