The airline crew rostering problem consists of assignment of crews to planned round trips resulting in the construction of personalized monthly crew schedules called rosters. Airline companies have a monthly task of building these rosters for crews available with them. A mixed integer linear programming MIP formulation is presented to find an optimal solution. The objective of this formulation is to minimize the crew cost associated with the round trips and the cost of reserve crews, who remain idle throughout the scheduling horizon. Computational experiments were also carried to test the effectiveness of the heuristic for small size problems on randomly generated test data.