Multiple conflicting objectives such as costs versus quality are part of many optimization processes in the area of production and logistics management. Exactly such a case is also examined in this work. For an already existing resource-constrained project scheduling problem, a second objective function, inspired by the steel industry, is taken into account. Together with the presentation of the related mixed integer programming (MIP) and constraint programming (CP) models, the recently developed balanced box method (Boland, Charkhgard, and Savelsbergh 2015) is used to solve this bi-objective optimization problem. Both approaches (MIP and CP) are compared in terms of runtime and solution quality, showing the advantages of using CP.