Presenting and solving a bi-objective integer programming model to simultaneously optimize energy consumption and building construction costs by optimally selecting the type of materials and equipment required for building construction

Document Type : Research Article

Authors

1 Department of Mathematics and Computer Sciences, Faculty of Sciences, University of Qom, Qom, IRAN.

2 Department if Mathematics, Faculty of Sciences, University of Qom, QoIRAN.

10.22091/jaem.2025.14494.1033

Abstract

Abstract
Construction materials and equipment significantly influence both the initial building cost and its long-term energy performance. This study develops a bi-objective integer programming model aimed at simultaneously minimizing construction costs and operational energy consumption. The model selects the optimal combination of materials and equipment subject to structural and budgetary constraints. A linear programming formulation is proposed and solved using QSB++. The results demonstrate that integrating cost and energy considerations into a unified optimization framework can reduce total expenses while improving the building’s energy efficiency. The proposed model provides a simple yet practical decision-support tool for designers and engineers.
In this study, the problems of minimizing construction costs and maximizing the energy efficiency of buildings were addressed through a dual-objective integer programming model. The bi-objective formulation was converted into a single-objective problem and solved using the simplex method. Cutting-plane techniques were then applied to restrict the feasible region so that the optimal integer solutions would lie at the corner points of the reduced polyhedron. The numerical results demonstrate that the proposed method successfully balances two conflicting objectives: reducing total construction costs while improving the building’s energy performance. Although more energy-efficient materials might be available in practice, their higher prices may move the solution away from optimality, showing the importance of evaluating cost–benefit trade-offs carefully. Overall, the method proves effective from both operational and empirical perspectives, enabling building designers and contractors to input their specific project data and use the optimized outputs as a quantitative decision-making tool.

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Main Subjects

Advances in Energy and Materials Research

Articles in Press, Accepted Manuscript
Available Online from 13 December 2025

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