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Mathematical Modeling for the Break-Even Point Problem in a Non-homogeneous System

Abstract— This paper presents a mathematical formulation for the break-even problem in a nonhomogeneous system. The optimization problem aims to obtain the composition of the best product mix in a non-homogeneous industrial plant, with the lowest cost until the Break-Even Point is reached. The constraints of the problem represent real constraints of a generic inhomogeneous industrial plant for n distinct products. The proposed model can solve the break-even problem simultaneously for all products, unlike existing approaches that propose a sequential solution, considering each product in isolation and providing a suboptimal solution to the problem. The results indicate that the product mix found through the proposed model has economic advantages over the traditional approach used.

Index Terms— branch and bound, break-even point, non-homogeneous production system, integer linear programming, management accounting.

Filipe Oliveira
Industrial Engineering, Polytechnic Institute, Federal University of Bahia, Salvador, Brazil
Lino Silva
Electrical Engineering Collegiate – CENEL, Federal University of the São Francisco Valley, Brazil
Ademar Nascimento
Polytechnic Institute, Federal University of Bahia, Salvador, Brazil
Cristiano Fontes
Industrial Engineering, Polytechnic Institute, Federal University of Bahia, Salvador, Brazil

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Cite: Filipe Oliveira, Lino Silva, Ademar Nascimento, Cristiano Fontes, " Mathematical Modeling for the Break-Even Point Problem in a Non-homogeneous System, " WCSE 2022 Spring Event: 2022 9th International Conference on Industrial Engineering and Applications, pp. 405-411, Sanya, China, April 15-18, 2022.