Due to rapid urbanization and population growth, the use of the rail transportation system is gradually increasing. However, the widespread use of rail transportation systems in urban transport causes large-scale and difficult-to-solve problems. In particular, many problems arise, such as imbalances in the planning of train trips, inability to adjust shift scheduling and working-rest periods of the machinists. For this reason, it has become obligatory to generate fast and appropriate solutions to the problems in order to plan, operate and maintain these systems. In this study, it is aimed to create a fair task schedule by equalizing the total working time and the number of shifts of all the machinists of a company serving in the light rail transportation system. In the current situation, it is very time-consuming to manually perform the task schedule of the machinist. In addition, the lack of equal work distribution in the schedule created leads to employee dissatisfaction. Therefore, in this study, the goal programming model for the machinist scheduling problem has been developed and solved by using GAMS/CPLEX program. With the proposed mathematical model, fair task assignment has been achieved and it is expected that the quality of service will increase with the increased motivation and satisfaction of the employees.