A multi-stage stochastic integer programming approach for a multi-echelon lot-sizing problem with returns and lost sales

  • Quan Dong
  • Safia Kedad-Sidhoum
  • Céline Gicquel
  • Franco Quezada
    • Categories Applications - OR and Management Sciences, Branch and Cut Algorithms, Production and Logistics Tags , , , , , ,

    We consider an uncapacitated multi-item multi-echelon lot-sizing problem within a remanufacturing system involving three production echelons: disassembly, refurbishing and reassembly. We seek to plan the production activities on this system over a multi-period horizon. We consider a stochastic environment, in which the input data of the optimization problem are subject to uncertainty. We propose a … Read more

    Conditional Extragradient Algorithms for Solving Constrained Variational Inequalities

  • Yunier Bello-Cruz
  • R. Diaz Millan
  • Hung M. Phan
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Global Optimization Tags , ,

    In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing non-null normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different linesearches. We then establish convergence results for these algorithms under mild assumptions. Our study suggests that non-null normal vectors may significantly improve convergence … Read more

    On robust fractional 0-1 programming

  • Colin Gillen
  • Andrés Gómez
  • Oleg A. Prokopyev
  • Erfan Mehmanchi
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Robust Optimization Tags , ,

    We study single- and multiple-ratio robust fractional 0-1 programming problems (RFPs). In particular, this work considers RFPs under a wide-range of disjoint and joint uncertainty sets, where the former implies separate uncertainty sets for each numerator and denominator, and the latter accounts for different forms of inter-relatedness between them. First, we demonstrate that, unlike the … Read more

    On Subadditive Duality for Conic Mixed-Integer Programs

  • Burak Kocuk
  • Diego Moran
    • Categories (Mixed) Integer Nonlinear Programming

    In this paper, we show that the subadditive dual of a feasible conic mixed-integer program (MIP) is a strong dual whenever it is feasible. Moreover, we show that this dual feasibility condition is equivalent to feasibility of the conic dual of the continuous relaxation of the conic MIP. In addition, we prove that all known … Read more

    Decomposition Branching for Mixed Integer Programming

  • Natashia Boland
  • Martin Savelsbergh
  • Barış Yıldız
    • Categories (Mixed) Integer Linear Programming

    We introduce a novel and powerful approach for solving certain classes of mixed integer programs (MIPs): decomposition branching. Two seminal and widely used techniques for solving MIPs, branch-and-bound and decomposition, form its foundation. Computational experiments with instances of a weighted set covering problem and a regionalized p-median facility location problem with assignment range constraints demonstrate … Read more

    Asymptotic results of Stochastic Decomposition for Two-stage Stochastic Quadratic Programming

  • Junyi Liu
  • Suvrajeet Sen
    • Categories Convex and Nonsmooth Optimization, Stochastic Programming Tags , ,

    This paper presents stochastic decomposition (SD) algorithms for two classes of stochastic programming problems: 1) two-stage stochastic quadratic-linear programming (SQLP) in which a quadratic program defines the objective function in the first stage and a linear program defines the value function in the second stage; 2) two-stage stochastic quadratic-quadratic programming (SQQP) which has quadratic programming … Read more

    A Partial PPA block-wise ADMM for Multi-Block Constrained Separable Convex Optimization

  • Yuan Shen
    • Categories Applications - OR and Management Sciences, Unconstrained Optimization Tags , , ,

    The alternating direction method of multipliers(ADMM) has been proved to be effective for solving two-block separable convex optimization subject to linear constraints. However, it is not necessarily convergent when it is extended to multiple-block case directly. One remedy could be regrouping multiple-block variables into two groups firstly and then adopting the classic ADMM to the … Read more

    A proximal ADMM with the Broyden family for Convex Optimization Problems

  • Yan Gu
  • Nobuo Yamashita
    • Categories Convex Optimization Tags , , ,

    Alternating direction methods of multipliers (ADMM) have been well studied and effectively used in various application fields. The classical ADMM must solve two subproblems exactly at each iteration. To overcome the difficulty of computing the exact solution of the subproblems, some proximal terms are added to the subproblems. Recently, Gu and Yamashita studied a special … Read more

    An Iterative Re-optimization Framework for the Dynamic Vehicle Routing Problem with Roaming Delivery Locations

  • Gizem Ozbaygin
  • Martin Savelsbergh
    • Categories Network Optimization, Transportation Tags , , ,

    Branch-and-price has established itself as an effective solution methodology for a wide variety of planning problems. We investigate its potential as a solution method- ology for solving operational problems. Specifically, we explore its potential in the context of a dynamic variant of the vehicle routing problem with roaming delivery locations, in which customer itineraries may … Read more

    Efficient global unconstrained black box optimization

  • Morteza Kimiaei
  • Arnold Neumaier
    • Categories Stochastic Approaches, Unconstrained Optimization Tags , , , ,

    For the unconstrained optimization of black box functions, this paper introduces a new randomized algorithm called VRBBO. In practice, VRBBO matches the quality of other state-of-the-art algorithms for finding, in small and large dimensions, a local minimizer with reasonable accuracy. Although our theory guarantees only local minimizers our heuristic techniques turn VRBBO into an efficient … Read more