This study develops a mixed-integer linear programming (MILP) formulation to minimize the global warming potential (GWP) of timber-steel hybrid truss structures. Based on Hull Reformulation, it addresses the weak LP relaxation commonly observed in conventional Big-M models. Although the Big-M formulation gives correct integer solutions, its relaxed problem may allow members with zero cross-sectional area to carry internal forces, resulting in an unrealistically low best bound. To avoid this issue, each member's internal force is divided into timber and steel components, and corresponding stress constraints are imposed in proportion to the effective cross-sectional area of each material. The bilinear product between the cross-sectional area and the binary material variable is linearized using the McCormick envelope. Numerical examples show that the proposed formulation provides much tighter bounds than the Big-M model. In the two-dimensional cantilever example, both formulations obtained the same optimum of 25.72 kgCO2e, but the Big-M model retained a 72.38% optimality gap, while the Hull formulation reached a 0% gap in about 0.3 s. In the three-dimensional cantilever example, the Big-M gap increased to 99.99%, whereas the Hull formulation again converged to a 0% gap. Across all examples (cantilever and simply supported), the hybrid designs achieved approximately 9–12% GWP reductions compared with all-steel designs.

Abstract
1. 서론
2. MILP 기반 최적화 방법론
    2.1 문제 정의
    2.2 Big-M 정식화
    2.3 Hull Reformulation
3. 수치 예제
    3.1 2차원 예제
    3.2 3차원 예제
4. 결론
감사의 글
References

• 이돈우(한국기술교육대학교 건축공학과 박사 후 연구원, 공학박사) | Lee Don-Woo (Dept. of Architectural Engineering, Korea University of Technology and Education) Corresponding author
• 성종혁(한국기술교육대학교 일반대학원 건축공학과, 석사과정) | Seong Jong-Hyeok (Dept. of Architectural Engineering, Korea University of Technology and Education)
• 이승재(한국기술교육대학교 건축공학과 교수, 공학박사) | Lee Seung-Jae (Dept. of Architectural Engineering, Korea University of Technology and Education)