Groupe d’études et de recherche en analyse des décisions

The decision rule approach to optimization under uncertainty: Theory and applications

Angelos Georghiou Université McGill, Canada

Decision making under uncertainty has a long and distinguished history in operations research. However, most of the existing solution techniques suffer from the curse of dimensionality, which restricts their applicability to small and medium-sized problems, or they rely on simplifying modeling assumptions (e.g. absence of recourse actions). Recently, a new solution technique has been proposed, which is referred to as the decision rule approach. By approximating the feasible region of the decision problem, the decision rule approach aims to achieve tractability without changing the fundamental structure of the problem. Despite their success, existing decision rules (a) are typically constrained by their a priori design and (b) do not incorporate in their modeling binary recourse decisions. In this talk, we present a methodology for the near optimal design of continuous and binary decision rules using mixed-integer optimization, and demonstrate its potential in operations management and control applications.