We present the case study of a complex, mixed-initiative scheduling system to illustrate Work-Centered Design (WCD), a new approach for the design of information systems. WCD is based on theory of distributed cognition and extends established user-centered methods with abstract task modeling, using innovative techniques for work ontology and top-level algorithms to capture the logic of a human-computer interaction paradigm. WCD addresses a long-standing need for more effective methods of function allocation. The illustrating case study succeeded on a large, difficult problem for aircraft scheduling where prior expensive attempts failed. The new system, called Solver, reduces scheduling labor from 9 person-days a week to about 1 person-hour. These results were obtained from the first user test, demonstrating notable effectiveness of WCD. Further, the value of Solver's higher quality schedules is far-reaching. WCD extends HCI methods to fill an important need for technical problem-solving systems.