/desautels/taxonomy/term/2972/all en /desautels/channels/news/primal-dual-lifting-scheme-two-stage-robust-optimization-295769 <p><strong>Authors</strong>: <strong>Angelos Georghiou</strong>, Angelos Tsoukalas, Wolfram Wiesemann</p> <p><strong>Publication</strong>: <em>Operations Research</em>, Forthcoming</p> <p><strong>Abstract: </strong></p> <p>Two-stage robust optimization problems, in which decisions are taken both in anticipation of and in response to the observation of an unknown parameter vector from within an uncertainty set, are notoriously challenging. In this paper, we develop convergent hierarchies of primal (conservative) and dual (progressive) bounds for these problems that trade off the competing goals of tractability and optimality: While the coarsest bounds recover a tractable but suboptimal affine decision rule approximation of the two-stage robust optimization problem, the refined bounds lift extreme points of the uncertainty set until an exact but intractable extreme point reformulation of the problem is obtained. Based on these bounds, we propose a primal-dual lifting scheme for the solution of two-stage robust optimization problems that accommodates for generic polyhedral uncertainty sets, infeasible problem instances as well as the absence of a relatively complete recourse. The incumbent solutions in each step of our algorithm afford rigorous error bounds, and they can be interpreted as piecewise affine decision rules. We illustrate the performance of our algorithm on illustrative examples and on an inventory management problem.</p> <p> Thu, 28 Mar 2019 14:22:03 +0000 angela.l.williams@mcgill.ca 74137 at /desautels /desautels/channels/news/fluid-model-one-sided-bipartite-matching-queues-match-dependent-rewards-329992 <p><strong>Authors: <a href="/desautels/yichuan-daniel-ding">Yichuan Ding</a></strong>, S.T. McCormick and M. Nagarajan<br /> <br /> <strong>Publication: </strong><em>Operations Research</em>, Forthcoming<br /> <br /> <strong>Abstract: </strong></p> Wed, 24 Mar 2021 17:48:19 +0000 julie.lapalme@affiliate.mcgill.ca 80635 at /desautels /desautels/channels/news/robust-dual-dynamic-programming-291746 <p><strong>Authors</strong>: <a href="/desautels/angelos-georghiou"><strong>Angelos Georghiou,</strong></a> Angelos Tsoukalas, Wolfram Wiesemann</p> <p><strong>Publication</strong>: <em>Operations Research</em>, Forthcoming</p> <p><strong>Abstract: </strong></p> <p>Multi-stage robust optimization problems, where the decision maker can dynamically react to consecutively observed realizations of the uncertain problem parameters, pose formidable theoretical and computational challenges. As a result, the existing solution approaches for this problem class typically determine suboptimal solutions under restrictive assumptions. In this paper, we propose a robust dual dynamic programming (RDDP) scheme for multi-stage robust optimization problems. The RDDP scheme takes advantage of the decomposable nature of these problems by bounding the costs arising in the future stages through lower and upper cost to-go functions. For problems with uncertain technology matrices and/or constraint right-hand sides, our RDDP scheme determines an optimal solution in finite time. If also the objective function and/or the recourse matrices are uncertain, our method converges asymptotically (but deterministically) to an optimal solution. Our RDDP scheme does not require a relatively complete recourse, and it offers deterministic upper and lower bounds throughout the execution of the algorithm. We demonstrate the promising performance of our algorithm in a stylized inventory management problem.</p> <p> Thu, 15 Nov 2018 15:52:25 +0000 angela.l.williams@mcgill.ca 73693 at /desautels /desautels/channels/news/optimizing-foreclosed-housing-acquisitions-societal-response-foreclosures-290601 <p><strong>Authors: </strong>Senay Solak, Armagan Bayram, <strong><a href="/desautels/mehmet-gumus">Mehmet Gumus</a></strong>,<strong> </strong>Yueran Zhuo</p> <p><strong>Publication: </strong><em>Operations Research</em>, <span>Forthcoming</span></p> <p><strong>Abstract:</strong></p> <p>A dramatic increase in U.S. mortgage foreclosures during and after the great economic recession of 2007-2009 had devastating impacts on the society and the economy. In response to such negative impacts, non-profit community development corporations (CDCs) throughout the U.S. utilize various resources, such as grants and lines of credit, in acquiring and redeveloping foreclosed housing units to support neighborhood stabilization and revitalization. Given that the cost of all such acquisitions far exceeds the resources accessible by these non-profit organizations, we identify socially optimal policies for CDCs in dynamically selecting foreclosed properties to target for potential acquisition as they become available over time. We evaluate our analytical results in a numerical study involving a CDC serving a major city in the U.S, and specify social return based thresholds defining selection decisions at different funding levels. We also find that for most foreclosed properties CDCs should not offer more than the asking price, and should typically consider overbidding only when the total available budget is low. Overall, comparisons of optimal policies with historical acquisition data suggest a potential improvement of around 20% in expected total impacts of the acquisitions on nearby property values. Considering a CDC with annual fund availability of $4 million for investment, this corresponds to an estimated additional value of around $280,000 for the society.</p> <p> Mon, 15 Oct 2018 14:59:47 +0000 angela.l.williams@mcgill.ca 73568 at /desautels /desautels/research/desautels-top-tier-publications/operations-research <p><big><a href="http://pubsonline.informs.org/journal/opre" target="_blank"><em>Operations Research</em></a> aims to publish high-quality papers that represent the true breadth of the methodologies and applications that define our field. It serves the entire Operations Research community including practitioners, researchers, educators, and students. In that respect, the papers that appear in the journal must satisfy three essential requirements: operations-focused, scientific, and broad.</big></p> Fri, 21 Jul 2017 16:28:10 +0000 julie.lapalme@mcgill.ca 67671 at /desautels