Characterization of robust solutions of multi-objetive optimization models with uncertain weights: applications in a sawmill

Abstract

The use of weights in multi-objective problems is one of the simplest ways to include multiple criteria in optimization models, in what is known as a weighted-sum approach. However, the solution to these models is highly dependent on the value of the weights, which is difficult to determine accurately. In this paper, we consider that the weights are defined as intervals of possible values rather than point estimates, and formulate a robust version of the traditional multi-objective optimization model. We explore, through a computational experiment, the effect that the uncertainty in the weights has on the optimal decisions and the levels obtained of the different objectives. Robust solutions favor decisions that produce similar levels of the different objectives and produce more of those objectives for which the weights are more certain. We apply this model to a lumber production problem where, in practice, more than a single performance indicator is pursued, but there is no clear preference relationship among them