Integer Programming Solution Approach for Inventory-Production-Distribution Problems with Direct Shipments

  • Miguel A. Lejeune
  • François Margot
    • Categories Branch and Cut Algorithms, Cutting Plane Approaches, Supply Chain Management Tags , , ,

    We construct an integrated multi-period inventory-production-distribution replenishment plan for three-stage supply chains. The supply chain maintains close-relationships with a small group of suppliers, and the nature of the products (bulk, chemical, etc.) makes it more economical to rely upon a direct shipment, full-truck load distribution policy between supply chain nodes. In this paper, we formulate … Read more

    New class of limited-memory variationally-derived variable metric methods

  • Ladislav Lukšan
  • Jan Vlček
    • Categories Nonlinear Optimization Tags , ,

    A new family of limited-memory variationally-derived variable metric or quasi-Newton methods for unconstrained minimization is given. The methods have quadratic termination property and use updates, invariant under linear transformations. Some encouraging numerical experience is reported. CitationTechnical Report V-973. Prague, ICS AS CR 2006.ArticleDownload View PDF

    From CVaR to Uncertainty Set: Implications in Joint Chance Constrained Optimization

  • Wenqing Chen
  • Jie Sun
  • Chung-Piaw Teo
  • Melvyn Sim
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    In this paper we review the different tractable approximations of individual chance constraint problems using robust optimization on a varieties of uncertainty set, and show their interesting connections with bounds on the condition-value-at-risk CVaR measure popularized by Rockafellar and Uryasev. We also propose a new formulation for approximating joint chance constrained problems that improves upon … Read more

    Inverse Stochastic Linear Programming

  • Lewis Ntaimo
  • Andrew J. Schaefer
  • Gorkem Saka
    • Categories Stochastic Programming Tags , ,

    Inverse optimization perturbs objective function to make an initial feasible solution optimal with respect to perturbed objective function while minimizing cost of perturbation. We extend inverse optimization to two-stage stochastic linear programs. Since the resulting model grows with number of scenarios, we present two decomposition approaches for solving these problems. CitationUnpublished: 07-1, University of Pittsburgh, … Read more

    Sensitivity analysis in linear semi-infinite programming via partitions

  • Miguel A. Goberna
  • Tamás Terlaky
  • Maxim I. Todorov
    • Categories Other Topics, Semi-infinite Programming Tags , , ,

    This paper provides sufficient conditions for the optimal value function of a given linear semi-infinite programming problem to depend linearly on the size of the perturbations, when these perturbations are directional, involve either the cost coefficients or the right-hand-side function or both, and they are sufficiently small. Two kinds of partitions are considered. The first … Read more

    On the Closedness of the Linear Image of a Closed Convex Cone

  • Gabor Pataki
    • Categories Convex Optimization, Second-Order Cone Programming, Semi-definite Programming

    When is the linear image of a closed convex cone closed? We present very simple, and intuitive necessary conditions, which 1) unify, and generalize seemingly disparate, classical sufficient conditions: polyhedrality of the cone, and “Slater” type conditions; 2) are necessary and sufficient, when the dual cone belongs to a class, that we call nice cones. … Read more

    Extending Algebraic Modelling Languages for Stochastic Programming

  • Robert Fourer
  • Gautam Mitra
  • Mustapha Sadki
  • Christian Valente
    • Categories Modeling Languages and Systems, Optimization Software Design Principles, Stochastic Programming Tags

    Algebraic modelling languages have gained wide acceptance and use in Mathematical Programming by researchers and practitioners. At a basic level, stochastic programming models can be defined using these languages by constructing their deterministic equivalent. Unfortunately, this leads to very large model data instances. We propose a direct approach in which the random values of the … Read more

    Norm-induced densities and testing the boundedness of a convex set

  • Alexandre Belloni
    • Categories Convex Optimization

    In this paper we explore properties of a family of probability density functions, called norm-induced densities, defined as $$f_t(x) = \left\{ \begin{array}{ll} \displaystyle \frac{ e^{-t\|x\|^p}dx}{\int_K e^{-t\|y\|^p}dy}, & x \in K \\ 0, & x \notin K,\\ \end{array}\right. $$ where $K$ is a $n$-dimensional convex set that contains the origin, parameters $t > 0$ and $p … Read more

    Finding a point in the relative interior of a polyhedron

  • Coralia Cartis
  • Nicholas I. M. Gould
    • Categories Constrained Nonlinear Optimization, Linear Programming Tags ,

    A new initialization or `Phase I’ strategy for feasible interior point methods for linear programming is proposed that computes a point on the primal-dual central path associated with the linear program. Provided there exist primal-dual strictly feasible points — an all-pervasive assumption in interior point method theory that implies the existence of the central path … Read more

    StAMPL: A Filtration-Oriented Modeling Tool for Stochastic Programming

  • Robert Fourer
  • Leonardo B. Lopes
    • Categories Modeling Languages and Systems, Optimization Software Design Principles, Stochastic Programming Tags , ,

    Every multistage stochastic programming problem with recourse (MSPR) contains a filtration process. In this research, we created a notation that makes the filtration process the central syntactic construction of the MSPR. As a result, we achieve lower redundancy and higher modularity than is possible with the mathematical notation commonly associated with stochastic programming. To experiment … Read more