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A variant of examination timetabling problem

The examination timetabling problem is a typical combinatorial optimization problem. In literature, heuristic methods are usually chosen to solve these problems, and mathematical programming approaches have not been well developed. This paper raises a variant of exam timetabling, with multiple exam paper versions, which comes from real-world applications. The mathematical formulation is presented, and further refined under assumptions to make it solvable for large-scale problems. Then, a preprocessing procedure, called ldquogroup-and-dividerdquo, is introduced to improve the solution quality by reducing the size of the input data. In addition, the symmetry of the model is studied, and a set of constraints are added to break the strong symmetry existing in the model. Real data are tested using CPLEX solver, and the results show that our approach is effective and applicable for real-world problems.