Karthik Natarajan Worst-case bounds on the expected shortfall risk given only limited information on the distribution of the random variables has been studied extensively in the literature. In this paper, we develop a new worst-case bound on the expected shortfall when the univariate marginals are known exactly and additional expert information is available in terms of bivariate … Read more
Crashing is a method for optimally shortening the project makespan by reducing the time of one or more activities in a project network by allocating resources to it. Activity durations are however uncertain and techniques in stochastic optimization, robust optimization and distributionally robust optimization have been developed to tackle this problem. In this paper, we … Read more
We show that the worst case moment bound on the expected optimal value of a mixed integer linear program with a random objective c is closely related to the complexity of characterizing the convex hull of the points CH{(1 x) (1 x)’: x \in X} where X is the feasible region. In fact, we can … Read more
A popular discrete choice model that incorporates correlation information is the Multinomial Probit (MNP) model where the random utilities of the alternatives are chosen from a multivariate normal distribution. Computing the choice probabilities is challenging in the MNP model when the number of alternatives is large and simulation is used to approximate the choice probabilities. … Read more
The Quadratic Convex Reformulation (QCR) method is used to solve quadratic unconstrained binary optimization problems. In this method, the semidefinite relaxation is used to reformulate it to a convex binary quadratic program which is solved using mixed integer quadratic programming solvers. We extend this method to random quadratic unconstrained binary optimization problems. We develop a … Read more
In this paper, we develop a distributionally robust portfolio optimization model where the robustness is to different dependency structures among the random losses. For a Frechet class of distributions with overlapping marginals, we show that the distributionally robust portfolio optimization problem is efficiently solvable with linear programming. To guarantee the existence of a joint multivariate … Read more
In this paper, we propose a probabilistic model for minimizing the anticipated regret in combinatorial optimization problems with distributional uncertainty in the objective coefficients. The interval uncertainty representation of data is supplemented with information on the marginal distributions. As a decision criterion, we minimize the worst-case conditional value-at-risk of regret. The proposed model includes the … Read more
Given a combinatorial optimization problem with an arbitrary partition of the set of random objective coefficients, we evaluate the tightest possible bound on the expected optimal value for joint distributions consistent with the given multivariate marginals of the subsets in the partition. For univariate marginals, this bound was first proposed by Meilijson and Nadas (Journal … Read more
In this paper, we analyze mixed 0-1 linear programs under objective uncertainty. The mean vector and the second moment matrix of the nonnegative objective coefficients is assumed to be known, but the exact form of the distribution is unknown. Our main result shows that computing a tight upper bound on the expected value of a … Read more
The traditional decision-making framework for newsvendor models is to assume a distribution of the underlying demand. However, the resulting optimal policy is typically sensitive to the choice of the distribution. A more conservative approach is to assume that the distribution belongs to a set parameterized by a few known moments. An ambiguity-averse newsvendor would choose … Read more