Scheduling workers in a restaurant is a difficult and time consuming task that involves matching the needs of the restaurant with respect to filling various shifts for different positions, the varying availabilities of the workers, along with their seniority levels and qualifications, among other factors. The restaurant manager/scheduler must adhere to these individual workers' restrictions, while at the same time satisfy the restaurant's needs. Another issue that a manager tries to accommodate is to equitably assign shifts to workers, attempting to balance their expressed wishes with their relative merits and qualifications; although in practice, this goal is rarely achieved. In this thesis, a mathematical model is developed to solve the scheduling problem, with attention focused on maximizing worker satisfaction levels, considering their seniority levels and their qualifications, while meeting with the restaurant's needs of filling various required shifts for various positions with capable workers. We show that this model possesses a hidden network structure that can be revealed via some simple variable substitutions. Consequently, an efficient network-flow approach can be used to solve the model and derive an optimal (integer) solution. We illustrate the model and the proposed algorithmic approach by generating a schedule using real data obtained via specially designed surveys from the Cheddar's restaurant in Newport News, Virginia. Further results on a variety of test problems are used to evaluate the performance of the algorithm, and suitable pre- and post-processor considerations are addressed to permit the use of this technology in a productive environment. / Master of Science