Simge Küçükyavuz

Joint chance-constrained programs and the intersection of mixing sets through a submodularity lens

  • Fatma Kılınç-Karzan
  • Simge Küçükyavuz
  • Dabeen Lee
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , ,

    A particularly important substructure in modeling joint linear chance-constrained programs with random right-hand sides and finite sample space is the intersection of mixing sets with common binary variables (and possibly a knapsack constraint). In this paper, we first revisit basic mixing sets by establishing a strong and previously unrecognized connection to submodularity. In particular, we … Read more

    Integer Programming for Learning Directed Acyclic Graphs from Continuous Data

  • Simge Küçükyavuz
  • Hasan Manzour
  • Ali Shojaie
  • Hao-Hsiang Wu
    • Categories (Mixed) Integer Linear Programming, Statistics Tags , , ,

    Learning directed acyclic graphs (DAGs) from data is a challenging task both in theory and in practice, because the number of possible DAGs scales superexponentially with the number of nodes. In this paper, we study the problem of learning an optimal DAG from continuous observational data. We cast this problem in the form of a … Read more

    An Exact Method for Constrained Maximization of the Conditional Value-at-Risk of a Class of Stochastic Submodular Functions

  • Simge Küçükyavuz
  • Hao-Hsiang Wu
    • Categories Integer Programming, Stochastic Programming

    We consider a class of risk-averse submodular maximization problems (RASM) where the objective is the conditional value-at-risk (CVaR) of a random nondecreasing submodular function at a given risk level. We propose valid inequalities and an exact general method for solving RASM under the assumption that we have an efficient oracle that computes the CVaR of … Read more

    Risk Aversion to Parameter Uncertainty in Markov Decision Processes with an Application to Slow-Onset Disaster Relief

  • Simge Küçükyavuz
  • Merve Merakli
    • Categories Integer Programming, Stochastic Programming, Supply Chain Management Tags , , , , ,

    In classical Markov Decision Processes (MDPs), action costs and transition probabilities are assumed to be known, although an accurate estimation of these parameters is often not possible in practice. This study addresses MDPs under cost and transition probability uncertainty and aims to provide a mathematical framework to obtain policies minimizing the risk of high long-term … Read more

    On Intersection of Two Mixing Sets with Applications to Joint Chance-Constrained Programs

  • Fatma Kılınç-Karzan
  • Simge Küçükyavuz
  • Xiao Liu
    • Categories Integer Programming, Stochastic Programming

    We study the polyhedral structure of a generalization of a mixing set described by the intersection of two mixing sets with two shared continuous variables, where one continuous variable has a positive coefficient in one mixing set, and a negative coefficient in the other. Our developments are motivated from a key substructure of linear joint … Read more

    Two-stage Stochastic Programming under Multivariate Risk Constraints with an Application to Humanitarian Relief Network Design

  • Simge Küçükyavuz
  • Merve Merakli
  • Nilay Noyan
    • Categories Stochastic Programming

    In this study, we consider two classes of multicriteria two-stage stochastic programs in finite probability spaces with multivariate risk constraints. The first-stage problem features a multivariate stochastic benchmarking constraint based on a vector-valued random variable representing multiple and possibly conflicting stochastic performance measures associated with the second-stage decisions. In particular, the aim is to ensure … Read more

    Path Cover and Path Pack Inequalities for the Capacitated Fixed-Charge Network Flow Problem

  • Alper Atamturk
  • Simge Küçükyavuz
  • Birce Tezel
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches Tags , , ,

    Capacitated fixed-charge network flows are used to model a variety of problems in telecommunication, facility location, production planning and supply chain management. In this paper, we investigate capacitated path substructures and derive strong and easy-to-compute path cover and path pack inequalities. These inequalities are based on an explicit characterization of the submodular inequalities through a … Read more

    A Polyhedral Study of the Static Probabilistic Lot-Sizing Problem

  • Simge Küçükyavuz
  • Xiao Liu
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Cutting Plane Approaches

    We study the polyhedral structure of the static probabilistic lot-sizing (SPLS) problem and propose facets that subsume existing inequalities for this problem. In addition, the proposed inequalities give the convex hull description of a related stochastic lot-sizing problem. We propose a new compact formulation that exploits the simple recourse structure, which can be applied to … Read more

    Robust Multicriteria Risk-Averse Stochastic Programming Models

  • Simge Küçükyavuz
  • Nilay Noyan
  • Xiao Liu
    • Categories Stochastic Programming

    In this paper, we study risk-averse models for multicriteria optimization problems under uncertainty. We use a weighted sum-based scalarization and take a robust approach by considering a set of scalarization vectors to address the ambiguity and inconsistency in the relative weights of each criterion. We model the risk aversion of the decision makers via the … Read more

    Cut Generation for Optimization Problems with Multivariate Risk Constraints

  • Simge Küçükyavuz
  • Nilay Noyan
    • Categories Integer Programming, Multi-Criteria Optimization, Stochastic Programming

    We consider a class of multicriteria stochastic optimization problems that features benchmarking constraints based on conditional value-at-risk and second-order stochastic dominance. We develop alternative mixed-integer programming formulations and solution methods for cut generation problems arising in optimization under such multivariate risk constraints. We give the complete linear description of two non-convex substructures appearing in these … Read more