The Value of Adaptability

We consider linear optimization problems with deterministic parameter uncertainty. We consider a departure from the robust optimization paradigm, allowing the decision-maker some limited, finite adaptability. Equivalently, we can view this as though the decision-maker can obtain some additional information about the uncertainty before committing to a decision. The central problem we address is optimally structuring finite adaptability, and understanding the marginal value of adaptability. We propose a hierarchy of increasing adaptability that bridges the gap between the robust formulation, and the re-optimization (or fully adjustable) formulation. We show some negative complexity results; then we provide an efficient (heuristic) algorithm for adaptability, and provide some computational evidence of its efficacy. The framework we propose is also appropriate for problems with discrete variables. To the best of our knowledge, this is the first proposal for adaptability that can accommodate discrete variables. We also compare our proposal to the model of affine adaptability proposed in [2].