Abstract
We study two-stage robust optimization problems with mixed discrete-continuous decisions in both stages. Despite their broad range of applications, these problems pose two fundamental challenges: (i) they constitute infinite-dimensional problems that require a finite-dimensional approximation, and (ii) the presence of discrete recourse decisions typically prohibits duality-based solution schemes. We address the first challenge by studying a K-adaptability formulation that selects K candidate recourse policies before observing the realization of the uncertain parameters and that implements the best of these policies after the realization is known. We address the second challenge through a branch-and-bound scheme that enjoys asymptotic convergence in general and finite convergence under specific conditions. We illustrate the performance of our algorithm in numerical experiments involving benchmark data from several application domains.
Highlights
Dynamic decision-making under uncertainty, where actions need to be taken both in anticipation of and in response to the realization of a priori uncertain problem parameters, arguably forms one of the most challenging domains of operations research and optimization theory
We study two-stage robust optimization problems with mixed discrete-continuous decisions in both stages
We investigate when the approximation offered by the K -adaptability problem is tight, and under which conditions the two-stage robust optimization and K -adaptability problems reduce to single-stage problems
Summary
Dynamic decision-making under uncertainty, where actions need to be taken both in anticipation of and in response to the realization of a priori uncertain problem parameters, arguably forms one of the most challenging domains of operations research and optimization theory. It is shown in [12,13] that for polynomial time solvable deterministic combinatorial optimization problems, the associated instances of problem (2) without first-stage decisions x can be solved in polynomial time if all of the following conditions hold: (i) Ξ is convex, (ii) only the objective coefficients d are uncertain, and (iii) K > N2 policies are sought This result has been extended to discrete uncertainty sets in [14], in which case pseudo-polynomial solution algorithms can be developed. For a logical expression E, we define I[E] as the indicator function which takes a value of 1 is E is true and 0 otherwise
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