A Robust Branch-Cut-and-Price Algorithm for the Heterogeneous Fleet Vehicle Routing Problem

  • Artur Alves Pessoa
  • Marcus Poggi de Aragão
  • Eduardo Uchoa
    • Categories Combinatorial Optimization, Linear, Cone and Semidefinite Programming, Transportation Tags , ,

    This paper presents a robust branch-cut-and-price algorithm for the Heterogeneous Fleet Vehicle Routing Problem (HFVRP), vehicles may have various capacities and fixed costs. The columns in the formulation are associated to $q$-routes, a relaxation of capacitated elementary routes that makes the pricing problem solvable in pseudo-polynomial time. Powerful new families of cuts are also proposed, … Read more

    Nonlinear programming without a penalty function or a filter

  • Nicholas I. M. Gould
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization, Nonlinear Systems and Least-Squares, Systems governed by Differential Equations Optimization Tags , , ,

    A new method is introduced for solving equality constrained nonlinear optimization problems. This method does not use a penalty function, nor a barrier or a filter, and yet can be proved to be globally convergent to first-order stationary points. It uses different trust-regions to cope with the nonlinearities of the objective function and the constraints, … Read more

    Exploiting group symmetry in truss topology optimization

  • Yanqin Bai
  • Etienne de Klerk
  • Renata Sotirov
  • Dmitrii V. Pasechnik
    • Categories Applications - Science and Engineering, Semi-definite Programming Tags , ,

    We consider semidefinite programming (SDP) formulations of certain truss topology optimization problems, where a lower bound is imposed on the fundamental frequency of vibration of the truss structure. These SDP formulations were introduced in: [M. Ohsaki, K. Fujisawa, N. Katoh and Y. Kanno, Semi-definite programming for topology optimization of trusses under multiple eigenvalue constraints, Comp. … Read more

    Robust Inventory Management Using Tractable Replenishment Policies

  • Chuen-Teck See
  • Melvyn Sim
    • Categories Robust Optimization, Stochastic Programming, Supply Chain Management Tags ,

    We propose tractable replenishment policies for a multi-period, single product inventory control problem under ambiguous demands, that is, only limited information of the demand distributions such as mean, support and deviation measures are available. We obtain the parameters of the tractable replenishment policies by solving a deterministic optimization problem in the form of second order … Read more

    A Geometric Analysis of Renegar’s Condition Number, and its interplay with Conic Curvature

  • Alexandre Belloni
  • Robert M. Freund
    • Categories Linear, Cone and Semidefinite Programming

    For a conic linear system of the form Ax \in K, K a convex cone, several condition measures have been extensively studied in the last dozen years. Herein we show that Renegar’s condition number is bounded from above and below by certain purely geometric quantities associated with A and K, and highlights the role of … Read more

    Maximum Utility Product Pricing Models and Algorithms Based on Reservation Prices

  • Tor G.J. Myklebust
  • Romy Shioda
  • Levent Tunçel
    • Categories Applications - OR and Management Sciences Tags , ,

    We consider a revenue management model for pricing a product line with several customer segments under the assumption that customers’ product choices are determined entirely by their reservation prices. We highlight key mathematical properties of the maximum utility model and formulate it as a mixed-integer programming problem, design heuristics and valid cuts. We further present … Read more

    Monotonicity of L”{o}wner Operators and Its Applications to Symmetric Cone Complementarity Problems

  • Lingchen Kong
  • Levent Tunçel
  • Naihua Xiu
    • Categories Complementarity and Variational Inequalities, Generalized Convexity/Monoticity, Semi-definite Programming Tags , , , ,

    This paper focuses on monotone L\”{o}wner operators in Euclidean Jordan algebras and their applications to the symmetric cone complementarity problem (SCCP). We prove necessary and sufficient conditions for locally Lipschitz L\”{o}wner operators to be monotone, strictly monotone and strongly monotone. We also study the relationship between monotonicity and operator-monotonicity of L\”{o}wner operators. As a by-product … Read more

    On the solution of stochastic multiobjective integer linear programming problems with a parametric study

  • Osama E. Imam
  • Omar M. Saad
    • Categories Integer Programming, Multi-Criteria Optimization, Stochastic Programming

    In this study we consider a multiobjective integer linear stochastic programming problem with individual chance constraints. We assume that there is randomness in the right-hand sides of the constraints only and that the random variables are normally distributed. Some stability notions for such problem are characterized. An auxiliary problem is discussed and an algorithm as … Read more

    Modeling and Simulation of Metabolic Networks for Estimation of Biomass Accumulation Parameters

  • Lorenz T. Biegler
  • Bulent Karasozen
  • Metin Turkay
  • Ugur Kaplan
    • Categories Biomedical Applications, Systems governed by Differential Equations Optimization Tags , ,

    Metabolic networks are defined as the collection of biochemical reactions within a cell that define the functions of that cell. Due to the growing need to understand the functions of biological organisms for industrial and medical purposes, modeling and simulation of metabolic networks has attracted a lot of attention recently. Traditionally, metabolic networks are modeled … Read more

    Objective space for multiple objectives linear fractional programming

  • Ragabia Sallam
  • Said Tantawy
    • Categories Multi-Criteria Optimization Tags , , , ,

    In this paper we give the construction of the objective space of multiple objectives linear fractional programming (MOLFP) with equal denominators under the linear fractional mapping .In this case the decision space maps to an objective space of less dimension. The important of this study is that the decision-Maker may depend on extreme points of … Read more