The New York City public school system needed a new tool that would generate schedules for a set of experimental schools. These schools focus on individualized instruction, making the scheduling problem challenging and novel. In particular, the educators in these schools wanted to create master schedules that could accommodate each student's specific needs while satisfying teacher and other resource constraints. We took a graphtheoretic approach to this problem by developing an algorithm that breaks it into a series of subproblems and applies randomized direct heuristics. Educators have multiple competing objectives with trade-offs that they cannot quantify precisely; therefore, our solution generates a diverse set of schedules that they can compare, combine, and change, before ultimately choosing one schedule to use. Prior to our engagement, school administrators spent approximately eight weeks each year manually generating schedules, a time commitment that was likely to grow as school enrollment increased. Our tool, iSchedule, generated a far richer set of feasible schedules, allowing administrators to focus on satisfying individual student needs. It also reduced the time required to generate a complete schedule to about two weeks. [ABSTRACT FROM AUTHOR]