We consider an uncertain variant of the knapsack problem that arises when the exact weight of each item is not exactly known in advance but belongs to a given interval, and the number of items whose weight differs from the nominal value is bounded by a constant. We analyze the worsening of the optimal solution … Read more
We study the loss in objective value when an inaccurate objective is optimized instead of the true one, and show that “on average” this loss is very small, for an arbitrary compact feasible region. CitationTechnical Report 1479, School of Operations Research and Information Engineering, Cornell University, Ithaca, NY 14853, April 2011ArticleDownload View PDF
Following a polynomial approach, many robust fixed-order controller design problems can be formulated as optimization problems whose set of feasible solutions is modelled by parametrized polynomial matrix inequalities (PMI). These feasibility sets are typically nonconvex. Given a parametrized PMI set, we provide a hierarchy of linear matrix inequality (LMI) problems whose optimal solutions generate inner … Read more
In this paper, we propose a chance-constrained mathematical program for fixed broadband wireless networks under unreliable channel conditions. The model is reformulated as integer linear program and valid inequalities are derived for the corresponding polytope. Computational results show that by an exact separation approach the optimality gap is closed by 42 % on average. ArticleDownload … Read more
An optimal planning of future wireless networks is fundamental to satisfy rising traffic demands jointly with the utilization of sophisticated techniques, such as OFDMA. Current methods for this task require a static model of the problem. However, uncertainty of data arises frequently in wireless networks, e. g., fluctuat- ing bit rate requirements. In this paper, … Read more
In this paper, we investigate the recoverable robust knapsack problem, where the uncertainty of the item weights follows the approach of Bertsimas and Sim (2003,2004). In contrast to the robust approach, a limited recovery action is allowed, i.e., upto k items may be removed when the actual weights are known. This problem is motivated by … Read more
Admission control problems have been studied extensively in the past. In a typical setting, resources like bandwidth have to be distributed to the different customers according to their demands maximizing the profit of the company. Yet, in real-world applications those demands are deviating and in order to satisfy their service requirements often a robust approach … Read more
The problem of production management can often be cast in the form of a linear program with uncertain parameters and risk constraints. Typically, such problems are treated in the framework of multi-stage Stochastic Programming. Recently, a Robust Counterpart (RC) approach has been proposed, in which the decisions are optimized for the worst realizations of problem … Read more
We consider robust formulations of the mid-term optimal power management problem. For this type of problems, classical approaches minimize the expected generation cost over a horizon of one year, and model the uncertain future by means of scenario trees. In this setting, extreme scenarios -with low probability in the scenario tree- may fail to be … Read more
A methodology, based on the concept of Affinely Adjustable Robust Optimization, for optimizing daily operation of pumping stations is proposed, which takes into account the fact that a water distribution system in reality is unavoidably affected by uncertainties. For operation control, the main source of uncertainty is the uncertainty in the demand. Traditional methods for … Read more