Network Optimization

Optimizing Expeditionary Logistics: Dynamic Discretization for Fleet Management

  • Haden Boone
  • Mathieu Dahan
    • Categories (Mixed) Integer Linear Programming, Network Optimization, Production and Logistics Tags , , ,

    We introduce the Expeditionary Logistics Network Design Problem (ELNDP), a new formulation for operational-level planning in expeditionary environments where multi-modal vehicle coordination is critical and penalties for unmet demand dominate transportation costs. ELNDP extends the classical Scheduled Service Network Design Problem by incorporating flexible commodity sourcing and heterogeneous vehicle capabilities, both essential in military logistics. … Read more

    Investment and Operational Planning for an electric market with massive entry of renewable energy

  • Matías Vera
  • Alejandro Jofré
  • Nicolas Hernández-Santibáñez
    • Categories Dynamic Programming, Network Optimization, Stochastic Programming Tags

    In this paper, we study a joint problem in which the Independent System Operator (ISO) intends to minimize the joint cost of operation and investment in a network structure. The problem is formulated through operational and investment control variables; we discuss the hierarchy between them and use the so-called Day Ahead Problem to find an … Read more

    Arc-Based Dynamic Discretization Discovery for Continuous-Time Service Network Design

  • Alexander Helber
    • Categories Combinatorial Optimization, Network Optimization, Transportation Tags , , ,

    In the continuous time service network design problem, a freight carrier decides the path of shipments in their network as well as the dispatch times of the vehicles transporting the shipments. State-of-the-art algorithms to solve this problem are based on the dynamic discretization discovery framework. These algorithms solve a relaxation of the problem using a … Read more

    The Undirected Team Orienteering Arc Routing Problem: Formulations, Valid Inequalities, and Exact Algorithms

  • Wenjin Yan
  • Elena Fernandez
  • Ivana Ljubić
    • Categories Branch and Cut Algorithms, Combinatorial Optimization, Network Optimization Tags , , ,

    We address the Undirected Team Orienteering Arc Routing Problem (UTOARP). In this problem, demand is placed at some edges of a given undirected graph and served demand edges produce a profit. Feasible routes must start and end at a given depot and there is a time limit constraint on the maximum duration of each route. … Read more

    Direct-search methods for decentralized blackbox optimization

  • Elhoucine Bergou
  • Youssef Diouane
  • Vyacheslav Kungurtsev
  • Clément W. Royer
    • Categories Network Optimization, Nonlinear Optimization, Unconstrained Optimization

    Derivative-free optimization algorithms are particularly useful for tackling blackbox optimization problems where the objective function arises from complex and expensive procedures that preclude the use of classical gradient-based methods. In contemporary decentralized environments, such functions are defined locally on different computational nodes due to technical or privacy constraints, introducing additional challenges within the optimization process. … Read more

    Optimal Control of Semilinear Graphon Systems

  • Martin T. Köhler
  • Artemi Makarow
  • Christian Kirches
    • Categories Infinite Dimensional Optimization, Network Optimization, Systems governed by Differential Equations Optimization Tags , , ,

    Controlling the dynamics of large-scale networks is essential for a macroscopic reduction of overall consumption and losses in the context of energy supply, finance, logistics, and mobility. We investigate the optimal control of semilinear dynamical systems on asymptotically infinite networks, using the notion of graphons. Graphons represent a limit object of a converging graph sequence … Read more

    Strengthening Dual Bounds for Multicommodity Capacitated Network Design with Unsplittable Flow Constraints

  • Lacy M. Greening
  • Santanu S. Dey
  • Alan L. Erera
    • Categories Integer Programming, Network Optimization, Production and Logistics Tags , , ,

    Multicommodity capacitated network design (MCND) models can be used to optimize the consolidation of shipments within e-commerce fulfillment networks. In practice, fulfillment networks require that shipments with the same origin and destination follow the same transfer path. This unsplittable flow requirement complicates the MCND problem, requiring integer programming (IP) formulations with binary variables replacing continuous … Read more

    New Dynamic Discretization Discovery Strategies for Continuous-Time Service Network Design

  • Shengnan Shu
  • Zhou Xu
  • Roberto Baldacci
    • Categories Applications - OR and Management Sciences, Integer Programming, Network Optimization Tags , , ,

    Service Network Design Problems (SNDPs) are prevalent in the freight industry. While the classic SNDP is defined on a discretized planning horizon with integral time units, the Continuous-Time SNDP (CTSNDP) uses a continuous-time horizon to avoid discretization errors. Existing CTSNDP algorithms primarily rely on the Dynamic Discretization Discovery (DDD) framework, which iteratively refines discretization and … Read more

    Bi-Parameterized Two-Stage Stochastic Min-Max and Min-Min Mixed Integer Programs

  • Sumin Kang
  • Manish Bansal
    • Categories Integer Programming, Network Optimization, Stochastic Programming Tags , , , ,

    We introduce two-stage stochastic min-max and min-min integer programs with bi-parameterized recourse (BTSPs), where the first-stage decisions affect both the objective function and the feasible region of the second-stage problem. To solve these programs efficiently, we introduce Lagrangian-integrated \(L\)-shaped (\(L^2\)) methods, which guarantee exact solutions when the first-stage decisions are pure binary. For mixed-binary first-stage … Read more

    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