SSRN Author: Dick den HertogDick den Hertog SSRN Content
http://www.ssrn.com/author=252707
http://www.ssrn.com/rss/en-usFri, 23 Dec 2016 01:26:48 GMTeditor@ssrn.com (Editor)Fri, 23 Dec 2016 01:26:48 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: Centered Solutions for Uncertain Linear EquationsOur contribution is twofold. Firstly, for a system of uncertain linear equations where the uncertainties are column-wise and reside in general convex sets, we show that the intersection of the set of possible solutions and any orthant is convex.We derive a convex representation of this intersection. Secondly, to obtain centered solutions for systems of uncertain linear equations, we compute the maximum size inscribed convex body (MCB) of the set of all possible solutions. The obtained MCB is an inner approximation of the solution set, and its center is a potential solution to the system. We compare our method both theoretically and numerically with an existing method that minimizes the worst-case violation. Applications to the input-output model, Colley's Matrix Rankings and Article Influence Scores demonstrate the advantages of the new method.
http://www.ssrn.com/abstract=2651004
http://www.ssrn.com/1553288.htmlThu, 22 Dec 2016 15:51:27 GMTREVISION: Computing the Maximum Volume Inscribed Ellipsoid of a Polytopic ProjectionWe introduce a novel scheme based on a blending of Fourier-Motzkin elimination (FME) and adjustable robust optimization techniques to compute the maximum volume inscribed ellipsoid (MVE) in a polytopic projection. It is well-known that deriving an explicit description of a projected polytope is NP-hard. Our approach does not require an explicit description of the projection, and can easily be generalized to find a maximally sized convex body of a polytopic projection. Our obtained MVE is an inner approximation of the projected polytope, and its center is a centralized relative interior point of the projection. Since FME may produce many redundant constraints, we apply an LP-based procedure to keep the description of the projected polytopes at its minimal size. Furthermore, we propose an upper bounding scheme to evaluate the quality of the inner approximations. We test our approach on a simple polytope and a color tube design
problem, and observe that as more auxiliary variables are ...
http://www.ssrn.com/abstract=2553293
http://www.ssrn.com/1551205.htmlWed, 14 Dec 2016 17:37:56 GMTNew: The Nutritious Supply Chain: Optimizing Humanitarian Food AidThe UN World Food Programme (WFP) is the largest humanitarian agency fighting hunger worldwide, reaching around 80 million people with food assistance in 75 countries each year. To deal with the operational complexities inherent to its mandate, WFP has been developing tools to assist their decision makers with integrating the supply chain decisions across departments and functional areas. This paper describes a mixed integer linear programming model that simultaneously optimizes the food basket to be delivered, the sourcing plan, the routing plan, and the transfer modality of a long-term recovery operation for each month in a pre-defined time horizon. By connecting traditional supply chain elements to nutritional objectives, we made significant breakthroughs in the operational excellence of WFP's most complex operations, such as Iraq and Yemen. We show how we used optimization to reduce the operational costs in Iraq by 17%, while still supplying 98% of the nutritional targets. ...
http://www.ssrn.com/abstract=2880438
http://www.ssrn.com/1549240.htmlTue, 06 Dec 2016 23:37:57 GMTREVISION: Computing the Maximum Volume Inscribed Ellipsoid of a Polytopic ProjectionThis paper introduces a method for computing the maximum volume inscribed ellipsoid and k-ball of a projected polytope. It is known that deriving an explicit description of a projected polytope is NP-hard. By using adjustable robust optimization techniques, we construct a computationally tractable method that does not require an explicit description of the projection. The obtained centers of the projected polytope are considered as the robust solutions, e.g., for design centering problems. We perform numerical experiments on a simple polytope and a color tube design problem. The color tube design problem demonstrates that the obtained solutions are much more robust than the nominal approach with a slight compromise on the objective value. Some other potential applications include ellipsoidal approximations to polytopic sets, nominal scenario recovery, and cutting-plane method.
http://www.ssrn.com/abstract=2553293
http://www.ssrn.com/1548630.htmlMon, 05 Dec 2016 08:04:27 GMTREVISION: Adjustable Robust Strategies for Flood ProtectionFlood protection is of major importance to many flood-prone regions and involves substantial investment and maintenance costs. Modern flood risk management requires often to determine a cost-efficient protection strategy, i.e., one with lowest possible long run cost and satisfying flood protection standards imposed by the regulator throughout the entire planning horizon. There are two challenges that complicate the modeling: (i) uncertainty - many of the important parameters on which the strategies are based (e.g. the sea level rise) are uncertain, and will be known only in the future, and (ii) adjustability - decisions implemented at later time stages need to adapt to the realized uncertainty values. We develop a new mathematical model addressing both, based on recent advances in integer robust optimization and we implement it on the example of the Rhine Estuary - Drechtsteden area in the Netherlands. Our approach shows, among others, that (i) considering 40% uncertainty about the ...
http://www.ssrn.com/abstract=2842275
http://www.ssrn.com/1531855.htmlFri, 30 Sep 2016 04:34:49 GMTNew: Efficient Methods for Several Classes of Ambiguous Stochastic Programming Problems Under Mean-MAD InformationWe consider decision making problems under uncertainty, assuming that only partial distributional information is available - as is often the case in practice. In such problems, the goal is to determine here-and-now decisions, which optimally balance deterministic immediate costs and worst-case expected future costs. These problems are challenging, since the worst-case distribution needs to be determined while the underlying problem is already a difficult multistage recourse problem. Moreover, as found in many applications, the model may contain integer variables in some or all stages. Applying a well-known result by Ben-Tal and Hochman (1972), we are able to efficiently solve such problems without integer variables, assuming only readily available distributional information on means and mean-absolute deviations. Moreover, we extend the result to the non-convex integer setting by means of convex approximations (see Romeijnders et al. (2016a)), proving corresponding performance bounds. ...
http://www.ssrn.com/abstract=2845229
http://www.ssrn.com/1531799.htmlThu, 29 Sep 2016 18:21:57 GMTREVISION: Adjustable Robust Strategies for Flood ProtectionFlood protection is of major importance to many flood-prone regions and involves substantial investment and maintenance costs. Modern flood risk management requires often to determine a cost-efficient protection strategy, i.e., one with lowest possible long run cost and satisfying flood protection standards imposed by the regulator throughout the entire planning horizon. There are two challenges that complicate the modeling: (i) uncertainty - many of the important parameters on which the strategies are based (e.g. the sea level rise) are uncertain, and will be known only in the future, and (ii) adjustability - decisions implemented at later time stages need to adapt to the realized uncertainty values. We develop a new mathematical model addressing both, based on recent advances in integer robust optimization and we implement it on the example of the Rhine Estuary - Drechtsteden area in the Netherlands. Our approach shows, among others, that (i) considering 40% uncertainty about the ...
http://www.ssrn.com/abstract=2842275
http://www.ssrn.com/1530876.htmlMon, 26 Sep 2016 14:39:30 GMTREVISION: Multi-Stage Adjustable Robust Mixed-Integer Optimization via Iterative Splitting of the Uncertainty SetIn this paper we propose a methodology for constructing decision rules for integer and continuous decision variables in multiperiod robust linear optimization problems. This type of problems finds application in, for example, inventory management, lot sizing, and manpower management. We show that by iteratively splitting the uncertainty set into subsets one can differentiate the later-period decisions based on the revealed uncertain parameters. At the same time, the problem’s computational complexity stays at the same level as for the static robust problem. This holds also in the non-fixed recourse situation. In the fixed recourse situation our approach can be combined with linear decision rules for the continuous decision variables. We provide theoretical results how to split the uncertainty set by identifying sets of uncertain parameter scenarios to be divided for an improvement in the worst-case objective value. Based on this theory, we propose several splitting heuristics. ...
http://www.ssrn.com/abstract=2502825
http://www.ssrn.com/1466155.htmlMon, 01 Feb 2016 15:29:27 GMT