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Real sports scheduling problems are difficult to solve due to the variety of different constraints that might be imposed. Over the last decade, through the work of a number of researchers, it has become easier to solve round-robin tournament problems. These tournaments can then become building blocks for more complicated schedules. For example, we have worked extensively with Major League Baseball on creating “what-if” schedules for various league formats. Success in providing those schedules has depended on breaking the schedule into easily solvable pieces. Integer programming and constraint programming methods each have their places in this approach, depending on the constraints and objective function.