SSRN Author: Krzysztof PostekKrzysztof Postek SSRN Content
http://www.ssrn.com/author=2244639
http://www.ssrn.com/rss/en-usMon, 05 Dec 2016 00:06:26 GMTeditor@ssrn.com (Editor)Mon, 05 Dec 2016 00:06:26 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: 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