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This research discusses the sequence of inbound and outbound aircrafts on a mixed operation single runway at an airport. Influenced by the climate, the target airport cannot meet landing conditions. As a result, aircrafts have to land at other nearby airports. Since the sequence for considering both normal and alternate aircrafts arriving in a fixed time window becomes difficult, few studies have considered this situation. Therefore, in this article, we propose a mixed integer programming model for formulating and possibly solving this problem to minimize total delay time. Since the problem is NP-hard, we propose an Improved Immunoglobulin-based Artificial Immune System (IIAIS) to find an optimal or near optimal solution to the considered aircraft scheduling problem. Using the problem instances from the OR library and a real-life practical case, we empirically evaluate the performance of the proposed algorithm. The results show that the proposed algorithm performs better than other existing algorithms.