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- Dimitris Bertsimas, Melvyn Sim
- Operations Research
- 2004

A robust approach to solving linear optimization problems with uncertain data has been proposed in the early 1970s, and has recently been extensively studied and extended. Under this approach, we are willing to accept a suboptimal solution for the nominal values of the data, in order to ensure that the solution remains feasible and near optimal when the… (More)

- Dimitris Bertsimas, Melvyn Sim
- Math. Program.
- 2003

We propose an approach to address data uncertainty for discrete optimization and network flow problems that allows controlling the degree of conservatism of the solution, and is computationally tractable both practically and theoretically. In particular, when both the cost coefficients and the data in the constraints of an integer programming problem are… (More)

- Joel Goh, Melvyn Sim
- Operations Research
- 2010

In this paper, we focus on a linear optimization problem with uncertainties, having expectations in the objective and in the set of constraints. We present a modular framework to obtain an approximate solution to the problem that is distributionally robust, and more flexible than the standard technique of using linear rules. Our framework begins by firstly… (More)

- Xin Chen, Melvyn Sim, Peng Sun, Jiawei Zhang
- Operations Research
- 2008

Stochastic optimization, especially multistage models, is well known to be computationally excruciating. Moreover, such models require exact specifications of the probability distributions of the underlying uncertainties, which are often unavailable. In this paper, we propose tractable methods of addressing a general class of multistage stochastic… (More)

- Wolfram Wiesemann, Daniel Kuhn, Melvyn Sim
- Operations Research
- 2014

Distributionally robust optimization is a paradigm for decision-making under uncertainty where the uncertain problem data is governed by a probability distribution that is itself subject to uncertainty. The distribution is then assumed to belong to an ambiguity set comprising all distributions that are compatible with the decision maker's prior information.… (More)

- Dimitris Bertsimas, Melvyn Sim
- Math. Program.
- 2006

In earlier proposals, the robust counterpart of conic optimization problems exhibits a lateral increase in complexity, i.e., robust linear programming problems (LPs) become second order cone problems (SOCPs), robust SOCPs become semidefinite programming problems (SDPs), and robust SDPs become NP-hard. We propose a relaxed robust counterpart for general… (More)

- Xin Chen, Melvyn Sim, Peng Sun
- Operations Research
- 2007

In this paper, we introduce an approach for constructing uncertainty sets for robust optimization using new deviation measures for random variables termed the forward and backward deviations. These deviation measures capture distributional asymmetry and lead to better approximations of chance constraints. Using a linear decision rule, we also propose a… (More)

- Xin Chen, Melvyn Sim, David Simchi-Levi, Peng Sun
- Operations Research
- 2007

– Traditional inventory models focus on risk-neutral decision makers, i.e., characterizing replenishment strategies that maximize expected total profit, or equivalently, minimize expected total cost over a planning horizon. In this paper, we propose a framework for incorporating risk aversion in multi-period inventory models as well as multi-period models… (More)

- Karthik Natarajan, Dessislava Pachamanova, Melvyn Sim
- Operations Research
- 2009

We illustrate the correspondence between uncertainty sets in robust optimization and some popular risk measures in finance, and show how robust optimization can be used to generalize the concepts of these risk measures. We also show that by using properly defined uncertainty sets in robust optimization models, one can construct coherent risk measures. Our… (More)

Expected utility models in portfolio optimization is based on the assumption of complete knowledge of the distribution of random returns. In this paper, we relax this assumption to the knowledge of only the mean, covariance and support information. No additional assumption on the type of distribution such as normality is made. The investor's utility is… (More)