This tutorial is by Erick Delage, HEC Canada and Dan Iancu, Stanford in Room 108A today Sunday at 4:30pm.
The key underlying philosophy behind the robust optimization modeling paradigm is that, in many practical situations, a complete stochastic description of the uncertainty may not be available. Instead, one may only have information with less detailed structure, such as bounds on the magnitude of the uncertain quantities or rough relations linking multiple unknown parameters. In such cases, one may be able to describe the unknowns by specifying a set in which all realizations should lie, the so-called «uncertainty set». The decision maker then seeks to ensure that the constraints in the problem remain feasible for any possible realization, while optimizing an objective that corresponds to the worst possible outcome. Initially, the key emphases of development of the robust optimization methodology were typically on tractability (i.e. characterizing the complexity of solving the resulting « robust counterpart ») and degree of conservatism (namely how a given model might offer some probabilistic guarantees). More recently, there has been a growing number of successful applications of the methodology to decision problems in which one can adjust some of the available actions to information that becomes progressively available.
As a testimony to more than 10 years of academic and practical developments revolving around the robust multi-stage decision making framework, this tutorial attempts to provide a succinct and unified view of the methodology, while highlighting potential pitfalls and indicating several open questions. In particular, our objectives with the tutorial are to:
- Provide tools for identifying a static versus a fully or partially adjustable decision variable,
- Highlight some tractability issues related to the dynamic formulation,
- Clarify the connection to robust dynamic programming,
- Provide motivations for using simple policies instead of more complex ones, and finally
- Illustrate how time consistency issues might arise.
The target audience for our tutorial are primarily academics interested in learning more about robust multi-stage decision making, as well as practitioners seeking a gentle introduction to the framework. The tutorial assumes basic knowledge of the robust optimization paradigm for static problems, as well as basic familiarity with concepts in dynamic optimization (dynamic programming, Bellman principle, etc.).
Erick Delage is an associate professor at HEC Montréal in the department of Decision Sciences. He entertains an interest for quantitative methodologies for managing risks related to market, environmental or physical uncertainty present in industrial and financial decision problems. His research spans the areas of optimization, decision analysis, artificial intelligence and applied statistics.
Dan Iancu is an Associate Professor of Operations, Information and Technology at the Stanford Graduate School of Business. His research interests include dynamic optimization under uncertainty and risk, with applications in supply chain management, revenue management, and problems at the interface of finance and operations.