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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

Abstract. 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… (More)

- Dimitris Bertsimas, Dessislava Pachamanova, Melvyn Sim
- Oper. Res. Lett.
- 2004

We propose a framework for robust modeling of linear programming problems using uncertainty sets described by an arbitrary norm. We explicitly characterize the robust counterpart as a convex optimization problem that involves the dual norm of the given norm. Under a Euclidean norm we recover the second order cone formulation in BenTal and Nemirovski [1, 2],… (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)

- Joel Goh, Melvyn Sim
- Operations Research
- 2010

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

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

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

- 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)

- Hoong Chuin Lau, Melvyn Sim, Kwong Meng Teo
- European Journal of Operational Research
- 2003

This paper introduces a variant of the vehicle routing problem with time windows where a limited number of vehicles is given (m-VRPTW). Under this scenario, a feasible solution is one that may contain either unserved customers and/or relaxed time windows. We provide a computable upper bound to the problem. To solve the problem, we propose a tabu search… (More)