(Mixed) Integer Linear Programming

Relating Single-Scenario Facets to the Convex Hull of the Extensive Form of a Stochastic Single-Node Flow Polytope

  • Victor A. Gonzalez
  • Andrew J. Schaefer
  • Mehdi Hemmati
  • David T. Mildebrath
    • Categories (Mixed) Integer Linear Programming, Polyhedra, Stochastic Programming Tags , ,

    Stochastic mixed-integer programs (SMIPs) are a widely-used modeling paradigm for sequential decision making under uncertainty. One popular solution approach to solving SMIPs is to solve the so-called “extensive form” directly as a large-scale (deterministic) mixed-integer program. In this work, we consider the question of when a facet-defining inequality for the convex hull of a deterministic, … Read more

    Feeder Routing for Air-to-Air Refueling Operations

  • Christoph Hansknecht
  • Imke Joormann
  • Bernd Korn
  • Fabian Morscheck
  • Sebastian Stiller
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences Tags , , , ,

    We consider the problem of routing a fleet of feeders for civil air-to-air refueling operations. In the air-to-air refueling problem, a fixed set of cruisers requires refueling by a fleet of feeders at fixed locations and fixed points in time. A typical objective function is to minimize the fuel consumption or the total number of … Read more

    Arc routing with electric vehicles: dynamic charging and speed-dependent energy consumption

  • Elena Fernandez
  • Markus Leitner
  • Ivana Ljubić
  • Mario Ruthmair
    • Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms, Production and Logistics Tags , , , , , ,

    Concerns about greenhouse gas emissions and government regulations foster the use of electric vehicles. Several recently published articles study the use of electric vehicles (EVs) in node-routing problems. In contrast, this article considers EVs in the context of arc routing while also addressing practically relevant aspects that have not been addressed sufficiently so far. These … Read more

    Globalized Robust Optimization with Gamma-Uncertainties

  • Andreas Bärmann
  • Christina Büsing
  • Frauke Liers
    • Categories (Mixed) Integer Linear Programming, Combinatorial Optimization, Robust Optimization Tags , , ,

    Globalized robust optimization has been proposed as a generalization of the standard robust optimization framework in order to allow for a controlled decrease in protection depending on the distance of the realized scenario from the predefined uncertainty set. In this work, we specialize the notion of globalized robustness to Gamma-uncertainty in order to extend its … Read more

    Portfolio Optimization with Irreversible Long-Term Investments in Renewable Energy under Policy Risk: A Mixed-Integer Multistage Stochastic Model and a Moving-Horizon Approach

  • Nadine Gatzert
  • Martin Schmidt
  • Alexander Martin
  • Benjamin Seith
  • Nikolai Vogl
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Stochastic Programming Tags , , , ,

    Portfolio optimization is an ongoing hot topic of mathematical optimization and management science. Due to the current financial market environment with low interest rates and volatile stock markets, it is getting more and more important to extend portfolio optimization models by other types of investments than classical assets. In this paper, we present a mixed-integer … Read more

    Generalized Chvatal-Gomory closures for integer programs with bounds on variables

  • Sanjeeb Dash
  • Oktay Gunluk
  • Dabeen Lee
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches Tags , , ,

    Integer programming problems that arise in practice often involve decision variables with one or two sided bounds. In this paper, we consider a generalization of Chvatal-Gomory inequalities obtained by strengthening Chvatal-Gomory inequalities using the bounds on the variables. We prove that the closure of a rational polyhedron obtained after applying the generalized Chvatal-Gomory inequalities is … Read more

    A Generic Exact Solver for Vehicle Routing and Related Problems

  • Artur Alves Pessoa
  • Ruslan Sadykov
  • Eduardo Uchoa
  • François Vanderbeck
    • Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms, Modeling Languages and Systems Tags , ,

    Major advances were recently obtained in the exact solution of Vehicle Routing Problems (VRPs). Sophisticated Branch-Cut-and-Price (BCP) algorithms for some of the most classical VRP variants now solve many instances with up to a few hundreds of customers. However, adapting and reimplementing those successful algorithms for other variants can be a very demanding task. This … Read more

    Risk-Averse Bi-Level Stochastic Network Interdiction Model for Cyber-Security Risk Management

  • Tanveer Hossain Bhuiyan
  • Mahantesh Halappanavar
  • Hugh R. Medal
  • Apurba Nandi
    • Categories (Mixed) Integer Linear Programming, Network Optimization, Stochastic Programming Tags , , , ,

    Security of cyber networks is crucial; recent severe cyber-attacks have had a devastating effect on many large organizations. The attack graph, which maps the potential attack paths of a cyber network, is a popular tool for analyzing cyber system vulnerability. In this study, we propose a bi-level stochastic network interdiction model on an attack graph … Read more

    Decomposing the Train Scheduling Problem into Integer Optimal Polytopes

  • Masoud Barah
  • James Ostrowski
  • Abbas Seifi
    • Categories (Mixed) Integer Linear Programming, Polyhedra, Transportation Tags , ,

    This paper presents conditions for which the linear relaxation for the train scheduling problem is integer-optimal. These conditions are then used to identify how to partition a general problem’s feasible region into integer-optimal polytopes. Such an approach yields an extended formulation that contains far fewer binary variables. Our computational experiments show that this approach results … Read more

    Radius of Robust Feasibility for Mixed-Integer Problems

  • Frauke Liers
  • Lars Schewe
  • Johannes Thürauf
    • Categories (Mixed) Integer Linear Programming, Robust Optimization Tags , , ,

    For a mixed-integer linear problem (MIP) with uncertain constraints, the radius of robust feasibility (RRF) determines a value for the maximal “size” of the uncertainty set such that robust feasibility of the MIP can be guaranteed. To the best of our knowledge, the approaches for the RRF presented in the literature are restricted to continuous … Read more