Robust Discrete Optimization and Its Applications

This book deals with decision making in environments of significant data un certainty, with particular emphasis on operations and production management applications. For such environments, we suggest the use of the robustness ap proach to decision making, which assumes inadequate knowledge of the decision maker about the random state of nature and develops a decision that hedges against the worst contingency that may arise. The main motivating factors for a decision maker to use the robustness approach are: - It does not ignore uncertainty and takes a proactive step in response to the fact that forecasted values of uncertain parameters will not occur in most environments; - It applies to decisions of unique, non-repetitive nature, which are common in many fast and dynamically changing environments; - It accounts for the risk averse nature of decision makers; and - It recognizes that even though decision environments are fraught with data uncertainties, decisions are evaluated ex post with the realized data. For all of the above reasons, robust decisions are dear to the heart of opera tional decision makers. This book takes a giant first step in presenting decision support tools and solution methods for generating robust decisions in a variety of interesting application environments. Robust Discrete Optimization is a comprehensive mathematical programming framework for robust decision making.

1 Approaches for Handling Uncertainty in Decision Making.- 2 A Robust Discrete Optimization Framework.- 3 Computational Complexity Results of Robust Discrete Optimization Problems.- 4 Easily Solvable Cases of Robust Discrete Optimization Problems.- 5 Algorithmic Developments for Difficult Robust Discrete Optimization Problems.- 6 Robust 1-Median Location Problems: Dynamic Aspects and Uncertainty.- 7 Robust Scheduling Problems.- 8 Robust Uncapacitated Network Design and International Sourcing Problems.- 9 Robust Discrete Optimization: Past Successes and Future Challenges.