Researcher:
Rudolf, Gabor

Profile Picture
ORCID

Job Title

Faculty Member

First Name

Gabor

Last Name

Rudolf

Name

Name Variants

Rudolf, Gabor

Email Address

Birth Date

Filters

2014 - 201942020 - 20221

Advanced Search

Filter by

Settings

Researcher Of Publications: search.filters.isAuthorOfPublication.7f920f78-c596-4b7c-bcf5-d096a01033fb

Search Results

Now showing 1 - 5 of 5
  • Placeholder
    PublicationMetadata only
    Optimization with stochastic preferences based on a general class of scalarization functions
    (The Institute for Operations Research and the Management Sciences (INFORMS), 2018) Noyan, Nilay; Department of Industrial Engineering; Rudolf, Gabor; Faculty Member; Department of Industrial Engineering; College of Engineering; 125501
    It is of crucial importance to develop risk-averse models for multicriteria decision making under uncertainty. A major stream of the related literature studies optimization problems that feature multivariate stochastic benchmarking constraints. These problems typically involve a univariate stochastic preference relation, often based on stochastic dominance or a coherent risk measure such as conditional value-at-risk, which is then extended to allow the comparison of random vectors by the use of a family of scalarization functions: All scalarized versions of the vector of the uncertain outcomes of a decision are required to be preferable to the corresponding scalarizations of the benchmark outcomes. While this line of research has been dedicated almost entirely to linear scalarizations, the corresponding deterministic literature uses a wide variety of scalarization functions that, among other advantages, offer a high degree of modeling flexibility. In this paper we aim to incorporate these scalarizations into a stochastic context by introducing the general class of min-biaffine functions. We study optimization problems in finite probability spaces with multivariate stochastic benchmarking constraints based on min-biaffine scalarizations. We develop duality results, optimality conditions, and a cut generation method to solve these problems. We also introduce a new characterization of the risk envelope of a coherent risk measure in terms of its Kusuoka representation as a tool toward proving the finite convergence of our solution method. The main computational challenge lies in solving cut generation subproblems; we develop several mixed-integer programming formulations by exploiting the min-affine structure and leveraging recent advances for solving similar problems with linear scalarizations. We conduct a computational study on a well-known homeland security budget allocation problem to examine the impact of the proposed scalarizations on optimal solutions, and illustrate the computational performance of our solution methods.
  • Placeholder
    PublicationMetadata only
    Kusuoka representations of coherent risk measures in general probability spaces
    (Springer, 2015) Noyan, Nilay; Department of Industrial Engineering; Rudolf, Gabor; Faculty Member; Department of Industrial Engineering; College of Engineering; 125501
    Kusuoka representations provide an important and useful characterization of law invariant coherent risk measures in atomless probability spaces. However, the applicability of these results is limited by the fact that such representations do not always exist in probability spaces with atoms, such as finite probability spaces. We introduce the class of functionally coherent risk measures, which allow us to use Kusuoka representations in any probability space. We show that this class contains every law invariant risk measure that can be coherently extended to a family containing all finite discrete distributions. Thus, it is possible to preserve the desirable properties of law invariant coherent risk measures on atomless spaces without sacrificing generality. We also specialize our results to risk measures on finite probability spaces, and prove a denseness result about the family of risk measures with finite Kusuoka representations.
  • Placeholder
    PublicationMetadata only
    Modeling sequence scrambling and related phenomena in mixed-model production lines
    (Elsevier, 2014) Noyan, Nilay; Giard, Vincent; Department of Industrial Engineering; Rudolf, Gabor; Faculty Member; Department of Industrial Engineering; College of Engineering; 125501
    In this paper we examine the various effects that workstations and rework loops with identical parallel processors and stochastic processing times have on the performance of a mixed-model production line. of particular interest are issues related to sequence scrambling. In many production systems (especially those operating on just-in-time or in-line vehicle sequencing principles), the sequence of orders is selected carefully to optimize line efficiency while taking into account various line balancing and product spacing constraints. However, this sequence is often altered due to stochastic factors during production. This leads to significant economic consequences, due to either the degraded performance of the production line, or the added cost of restoring the sequence (via the use of systems such as mix banks or automated storage and retrieval systems). We develop analytical formulas to quantify both the extent of sequence scrambling caused by a station of the production line, and the effects of this scrambling on downstream performance. We also develop a detailed Markov chain model to analyze related issues regarding line stoppages and throughput. We demonstrate the usefulness of our methods on a range of illustrative numerical examples, and discuss the implications from a managerial point of view. (C) 2014 Elsevier B.V. All rights reserved.
  • Thumbnail Image
    PublicationOpen Access
    On the complexity and approximation of the maximum expected value all-or-nothing subset
    (2018) Goldberg, Noam; Department of Industrial Engineering; Rudolf, Gabor; Faculty Member; Department of Industrial Engineering; College of Engineering
    An unconstrained nonlinear binary optimization problem of selecting a maximum expected value subset of items is considered. Each item is associated with a profit and probability. Each of the items succeeds or fails independently with the given probabilities, and the profit is obtained in the event that all selected items succeed. The objective is to select a subset that maximizes the total value times the product of probabilities of the chosen items. The problem is proven NP-hard by a nontrivial reduction from subset sum. Then we develop a fully polynomial time approximation scheme (FPTAS) for this problem.
  • Thumbnail Image
    PublicationOpen Access
    Distributionally robust optimization under a decision-dependent ambiguity set with applications to machine scheduling and humanitarian logistics
    (The Institute for Operations Research and the Management Sciences (INFORMS), 2022) Noyan, Nilay; Lejeune, Miguel; Department of Industrial Engineering; Rudolf, Gabor; Faculty Member; Department of Industrial Engineering; College of Engineering
    We introduce a new class of distributionally robust optimization problems under decision-dependent ambiguity sets. In particular, as our ambiguity sets, we consider balls centered on a decision-dependent probability distribution. The balls are based on a class of earth mover's distances that includes both the total variation distance and the Wasserstein metrics. We discuss the main computational challenges in solving the problems of interest and provide an overview of various settings leading to tractable formulations. Some of the arising side results, such as the mathematical programming expressions for robustified risk measures in a discrete space, are also of independent interest. Finally, we rely on state-of-the-art modeling techniques from machine scheduling and humanitarian logistics to arrive at potentially practical applications, and present a numerical study for a novel risk-averse scheduling problem with controllable processing times. Summary of Contribution: In this study, we introduce a new class of optimization problems that simultaneously address distributional and decision-dependent uncertainty. We present a unified modeling framework along with a discussion on possible ways to specify the key model components, and discuss the main computational challenges in solving the complex problems of interest. Special care has been devoted to identifying the settings and problem classes where these challenges can be mitigated. In particular, we provide model reformulation results, including mathematical programming expressions for robustified risk measures, and describe how these results can be utilized to obtain tractable formulations for specific applied problems from the fields of humanitarian logistics and machine scheduling. Toward demonstrating the value of the modeling approach and investigating the performance of the proposed mixed-integer linear programming formulations, we conduct a computational study on a novel risk-averse machine scheduling problem with controllable processing times. We derive insights regarding the decision-making impact of our modeling approach and key parameter choices.