In this article, we discuss an alternative method for deriving conservative approximation models for two-stage robust optimization problems. The method extends in a natural way a linearization scheme that was recently proposed to construct tractable reformulations for robust static problems involving profit functions that decompose as a sum of piecewise linear concave expressions. Given that th...

In this article, we discuss an alternative method for deriving conservative approximation models for two-stage robust optimization problems. The method extends in a natural way a linearization scheme that was recently proposed to construct tractable reformulations for robust static problems that involve profit functions that decompose as a sum of piecewise linear concave expressions. Given that...

optimization of maintenance resources to maximize the system availability is a major concern in different manufacturing systems. therefore, a lot of effort is put to construct optimization models to reach the maximum availability level and to reduce the costs of lack of availability. however, despite these efforts, data uncertainty in the real world problems was neglected in proposed models whi...

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 problem are subject to uncertainty, we pro...

Robust counterpart optimization techniques are studied in this paper. Different uncertainty sets, including those studied in literature (i.e., interval set; combined interval and ellipsoidal set; combined interval and polyhedral set) and new ones (i.e., adjustable box; pure ellipsoidal; pure polyhedral; combined interval, ellipsoidal, and polyhedral set) are studied in this work and their geome...

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 conic optimization problems that (a) prese...

In this paper, we introduce the extended affinely adjustable robust counterpart to modeling and solving multistage uncertain linear programs with fixed recourse. Our approach first reparameterizes the primitive uncertainties and then applies the affinely adjustable robust counterpart proposed in the literature, in which recourse decisions are restricted to be linear in terms of the primitive un...

This article explores the development of previous models to determine hubs in a competitive environment. In this paper, by comparing parameters of the ticket price, travel time and the service quality of hub airports, airline hubs are divided into six categories. The degree of importance of travel time and travel cost are determined by a multivariate Lagrange interpolation method, which can pla...

In this paper, we introduced a novel method for asymmetric uncertainty set construction based on the distributional information of sampling data. Deterministic robust counterpart optimization formulation is derived for D-norm induced uncertainty set with the proposed method. Furthermore, the asymmetric set induced robust optimization model is compared with the classical symmetric set induced ro...