This paper addresses a scheduling problem aimed at minimizing makespan in a permutation flow shop with two machines and an inspection process that must be conducted at least once every certain number of outcomes from the first machine. A mathematical programming approach and a genetic algorithm, incorporating Johnson's rule and a specific mutation process, were developed to solve this problem. Johnson's rule was used to generate an initial population, while the mutation process ensured compliance with the inspection constraints. The results showed that within a computation time limit of 300 seconds, the mathematical programming approach often failed to provide optimal or feasible solutions, especially for larger job sets. For instance, when the process times of both machines were similar and the inspection time was longer, the mathematical programming approach failed to solve all 10 experiments with just 15 jobs and only had a 50% success rate for 100 jobs. In contrast, the proposed genetic algorithm solved all instances and delivered equal or superior results compared to the mathematical programming approach.

1. 서 론
2. 선행연구
3. 문제상황 및 수리계획법
4. 유전 알고리즘
    4.1 염색체 구성 및 적합도
    4.2 초기 모집단 생성
    4.3 선택(Selection)
    4.4 교차(Crossover)
    4.5 변이(Mutation)
5. 실험 결과
    5.1 주요 파리미터 설정
    5.2 실험 결과
6. 결 론
Acknowledgement
References

• Ye Jin Kim(Department of Business Administration, Pusan National University) | 김예진 (부산대학교 경영학과)
• Ye Jin Seo(Department of Business Administration, Pusan National University) | 서예진 (부산대학교 경영학과)
• Kyungsu Park(Department of Business Administration, Pusan National University) | 박경수 (부산대학교 경영학과) Corresponding author
• Jun-Hee Han(Department of Industrial Engineering, Pusan National University) | 한준희 (부산대학교 산업공학과) Corresponding author