A Multiobjective Model for the Cutting Pattern Problem with Unclear Preferences

The cutting pattern problem has been traditionally approached using single objective optimization models, although the sawmill performance is usually measured using more than a single indicator. One of the shortcoming of using multiobjective approaches is that they need a preference relationship among the objectives, which is difficult to determine in practice, and solutions are very sensitive to these preferences. In this article, we consider different criteria in a sawmill decisionmaking context using a multiobjective linear optimization model and handle the unclear definition of the objective preferences by formulating a robust version of the model. Although the deterministic formulation assumes perfect information of the objective preferences, in the robust formulation we consider that preferences may be different from their estimate. We show that deterministic decisions are more balanced in terms of the different criteria than the traditional single objective models, although their quality is very sensitive to the objective preferences. We also show that robust decisions are also balanced but less sensitive to the preferences. We explore how the level of the different indicators and the cutting decisions are affected when the preferences are unclear.