Abstract
Enterprises such as hospitals and worker owned cooperative enterprises such as the Mondragon Corporation are institutions for which the profit motive takes second place to employee satisfaction. These enterprises must make sure that they have the required number of personnel on duty 24 hours a day, seven days a week. For our purposes this scheduling problem requires filling all the time slots with employees in a fair way taking into account the wishes and desires of the employees themselves. A utilitarian approach assumes that the employees will provide their inputs in terms of their preferred schedules as well as their preferences regarding compensation. The solution would maximize employees' satisfaction in the sense of maximizing their collective utility for their jobs. Computational complexity has been hitherto so demanding that solutions have been difficult to attain although AI has made possible brute force algorithmic solutions.

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