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This paper formulates the price-based unit commitment (PBUC) problem based on the mixed integer programming (MIP) method. The proposed PBUC solution is for a generating company (GENCO) with thermal, combined-cycle, cascaded-hydro, and pumped-storage units. The PBUC solution by utilizing MIP is compared with that of Lagrangian relaxation (LR) method. Test results on the modified IEEE 118-bus system show the efficiency of our MIP formulation and advantages of the MIP method for solving PBUC. It is also shown that MIP could be applied to solve hydro-subproblems including cascaded-hydro and pumped-storage units in the LR-based framework of hydro-thermal coordination. Numerical experiments on large systems show that the MIP-based computation time and memory requirement would represent the major obstacles for applying MIP to large UC problems. It is noted that the solution of large UC problems could be accomplished by improving the MIP formulation, the utilization of specific structure of UC problems, and the use of parallel processing.