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In this research, we consider a flight scheduling problem for oligopolistic competition with direct flights and a point to point network. In this type of market situation, passengers are sensitive to the departure time of a flight rather than the transfer time. The airline needs to carefully consider the departure times of their competitors when determining their own. Therefore, unlike past approaches which have only considered one departure time for a competitor's flight, a flight scheduling framework is developed which takes into consideration possible competitor departure times. The framework includes two dependent stages which are repeatedly solved during the solution process. In addition, an upper bound model is also designed to evaluate the solution quality. Numerical tests are performed using data for Taiwan's outlying island route which is characterized by the above market situation. Satisfactory results are obtained, showing the good performance of the framework. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]