In this paper, a two-staged method of determining the order of medical examinations is presented to reduce sojourn times for patients visiting a department of cardiology. The first stage works as the batch process in the nighttime, and determines the order of medical examinations for patients with appointments. The second stage is designed for patients without appointments, and searches free time slots into which the examinations for such patients can be inserted in the list of examinations that the first stage generated during the night. When determining orders, the proposed method uses values randomly generated from surveillance results as examination times. Experimental results show that the proposed method achieves short sojourn times both for patients without appointments and for those with appointments, compared with the determination manually made by a nurse.