benders decomposition

Solving Multi-Follower Mixed-Integer Bilevel Problems with Binary Linking Variables

  • Vladimir Stadnichuk
  • Arie M.C.A. Koster
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches, Network Optimization Tags , , , ,

    We study multi-follower bilevel optimization problems with binary linking variables where the second level consists of many independent integer-constrained subproblems. This problem class not only generalizes many classical interdiction problems but also arises naturally in many network design problems where the second-level subproblems involve complex routing decisions of the actors involved. We propose a novel … Read more

    Energy-efficient Timetables for Railway Traffic: Incorporating DC Power Models

  • Robert Burlacu
  • Patrick Gemander
  • Tobias Kuen
  • Jorge Weston
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Transportation Tags , , ,

    Efficient operation of underground railway systems is critical not only for maintaining punctual service but also for minimizing energy consumption, a key factor in reducing operational costs and environmental impact. To evaluate the energy consumption of the timetables, this paper delves into the development of mathematical models to accurately represent energy dynamics within the underground … Read more

    Benders decomposition with scaled cuts for multistage stochastic mixed-integer programs

  • Ward Romeijnders
  • Niels van der Laan
    • Categories Stochastic Programming Tags , ,

    We consider Benders decomposition algorithms for multistage stochastic mixed-integer programs (SMIPs) with general mixed-integer decision variables at every node in the scenario tree. We derive a hierarchy of convex polyhedral lower bounds for the value functions and expected cost to-go functions in multistage SMIPs using affine parametric cutting planes in extended spaces for the feasible … Read more

    A novel Pareto-optimal cut selection strategy for Benders Decomposition

  • Lukas Glomb
  • Frauke Liers
  • Florian Rösel
    • Categories (Mixed) Integer Linear Programming Tags ,

    Decomposition methods can be used to create efficient solution algorithms for a wide range of optimization problems. For example, Benders Decomposition can be used to solve scenario-expanded two-stage stochastic optimization problems effectively. Benders Decomposition iteratively generates Benders cuts by solving a simplified version of an optimization problem, the so-called subproblem. The choice of the generated … Read more

    Resilient Relay Logistics Network Design: A k-Shortest Path Approach

  • Onkar Anand Kulkarni
  • Mathieu Dahan
    • Categories (Mixed) Integer Linear Programming, Facility Planning and Design, Production and Logistics Tags , , , ,

    Problem definition: We study the problem of designing large-scale resilient relay logistics hub networks. We propose a model of k-Shortest Path Network Design, which aims to improve a network’s efficiency and resilience through its topological configuration, by locating relay logistics hubs to connect each origin-destination pair with k paths of minimum lengths, weighted by their … Read more

    Leveraging Decision Diagrams to Solve Two-stage Stochastic Programs with Binary Recourse and Logical Linking Constraints

  • Moira MacNeil
  • Merve Bodur
    • Categories Stochastic Programming Tags , , ,

    Two-stage stochastic programs with binary recourse are challenging to solve and efficient solution methods for such problems have been limited. In this work, we generalize an existing binary decision diagram-based (BDD-based) approach of Lozano and Smith (Math. Program., 2018) to solve a special class of two-stage stochastic programs with binary recourse. In this setting, the … Read more

    Planning of Container Crossdocking for an Express Shipment Service Network

  • Anton J. Kleywegt
  • Haotian Wu
    • Categories Applications - OR and Management Sciences, Stochastic Programming, Transportation Tags , , , ,

    In air transportation, container crossdocking refers to a loaded container that is transferred at an airport from an incoming flight to an outgoing flight without handling the freight on the container. It reduces handling time and handling cost relative to unloading the container and sorting the freight, and is an economical alternative if a sufficient … Read more

    Exact Solutions to a Carsharing Pricing and Relocation Problem under Uncertainty

  • Giovanni Pantuso
    • Categories Stochastic Programming, Transportation Tags , ,

    In this article we study the problem of jointly deciding carsharing prices and vehicle relocations. We consider carsharing services operating in the context of multi-modal urban transportation systems. Pricing decisions take into account the availability of alternative transport modes, and customer preferences with respect to these. In order to account for the inherent uncertainty in … Read more

    Hub Network Design Problem with Capacity, Congestion and Stochastic Demand Considerations

  • Vedat Bayram
  • Barış Yıldız
  • M. Saleh Farham
    • Categories Second-Order Cone Programming, Stochastic Programming, Transportation Tags , , , , , , ,

    We introduce the hub network design problem with congestion, capacity, and stochastic demand considerations (HNDC), which generalizes the classical hub location problem in several directions. In particular, we extend state-of-the-art by integrating capacity acquisition decision and congestion cost effect into the problem and allowing dynamic routing for origin-destination pairs. Connecting strategic and operational level decisions, … Read more

    Adjustable robust optimization with discrete uncertainty

  • Henri Lefebvre
  • Enrico Malaguti
  • Michele Monaci
    • Categories Robust Optimization Tags , , ,

    In this paper, we study Adjustable Robust Optimization (ARO) problems with discrete uncertainty. Under a very general modeling framework, we show that such two-stage robust problems can be exactly reformulated as ARO problems with objective uncertainty only. This reformulation is valid with and without the fixed recourse assumption and is not limited to continuous wait-and-see … Read more