Adjustable Robust Optimizations with Decision Rules Based on Inexact Revealed Data

Abstract: Adjustable robust optimization (ARO) is a technique to solve dynamic (multistage) optimization problems. In ARO, the decision in each stage is a function of the information accumulated from the previous periods on the values of the uncertain parameters. This information, however, is often inaccurate; there is much evidence in the information management literature that evenin our Big Data era the data quality is often poor. Reliance on the data \as is" may then lead to poor performance of ARO, or in fact to any \data-driven" method. In this paper, we remedy this weakness of ARO by introducing a methodology that treats past data itself as an uncertain parameter. We show that algorithmic tractability of the robust counterparts associated with this extension of ARO is still maintained. The bene t of the new approach is demonstrated by a production-inventory application.