Applications – OR and Management Sciences

ALGORITHM & DOCUMENTATION: MINRES-QLP for Singular Symmetric and Hermitian Linear Equations and Least-Squares Problems

  • Sou-Cheng Choi
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering, Optimization Software and Modeling Systems Tags , , , , , , , , ,

    We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite … Read more

    Reliable p-median facility location problem: two-stage robust models and algorithms

  • Yu An
  • Bo Zeng
  • Yu Zhang
  • Long Zhao
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , , ,

    In this paper, we propose a set of two-stage robust optimization models to design reliable p-median facility location networks subject to disruptions. A customized column-and- constraint generation approach is implemented and shown to be more effective than Benders cutting plane method. Numerical experiments are performed on real data and management insights on system design are … Read more

    Solving the integrated airline recovery problem using column-and-row generation

  • Stephen J. Maher
    • Categories (Mixed) Integer Linear Programming, Airline Optimization Tags , ,

    Airline recovery presents very large and difficult problems requiring high quality solutions within very short time limits. To improve computational performance, the complete airline recovery problem is generally formulated as a series of sequential stages. While the sequential approach greatly simplifies the complete recovery problem, there is no guarantee of global optimality or solution quality. … Read more

    Efficient Heuristic Algorithms for Maximum Utility Product Pricing Problems

  • Tor G.J. Myklebust
  • M. A. Sharpe
  • Levent Tunçel
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Combinatorial Optimization Tags , , ,

    We propose improvements to some of the best heuristic algorithms for optimal product pricing problem originally designed by Dobson and Kalish in the late 1980’s and in the early 1990’s. Our improvements are based on a detailed study of a fundamental decoupling structure of the underlying mixed integer programming (MIP) problem and on incorporating more … Read more

    Two methods of pruning Benders’ cuts and their application to the management of a gas portfolio

  • Romain Apparigliato
  • Laurent Pfeiffer
  • Sophie Auchapt
    • Categories Finance and Economics, Stochastic Programming Tags , , , ,

    In this article, we describe a gas portfolio management problem, which is solved with the SDDP (Stochastic Dual Dynamic Programming) algorithm. We present some improvements of this algorithm and focus on methods of pruning Benders’ cuts, that is to say, methods of picking out the most relevant cuts among those which have been computed. Our … Read more

    Solving mixed integer nonlinear programming problems for mine production planning with stockpiling

  • Andreas Bley
  • Natashia Boland
  • Gary Froyland
  • Mark Zuckerberg
    • Categories (Mixed) Integer Nonlinear Programming, Production and Logistics Tags

    The open-pit mine production scheduling problem has received a great deal of attention in recent years, both in the academic literature, and in the mining industry. Optimization approaches to strategic planning for mine exploitation have become the industry standard. However most of these approaches focus on extraction sequencing, and don’t consider the material flow after … Read more

    Worst-case-expectation approach to optimization under uncertainty

  • Joari Paulo da Costa
  • Alexander Shapiro
  • Murilo Pereira Soares
  • Wajdi Tekaya
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , , , , , , , ,

    In this paper we discuss multistage programming with the data process subject to uncertainty. We consider a situation were the data process can be naturally separated into two components, one can be modeled as a random process, with a specified probability distribution, and the other one can be treated from a robust (worst case) point … Read more

    Minimal Representation of Insurance Prices

  • Alois Pichler
  • Alexander Shapiro
    • Categories Convex Optimization, Finance and Economics, Statistics Tags , , ,

    This paper addresses law invariant coherent risk measures and their Kusuoka representations. By elaborating the existence of a minimal representation we show that every Kusuoka representation can be reduced to its minimal representation. Uniqueness — in a sense specified in the paper — of the risk measure’s Kusuoka representation is derived from this initial result. … Read more

    Simulation Optimization for the Stochastic Economic Lot Scheduling Problem with Sequence-Dependent Setup Times

  • Nils Löhndorf
  • Stefan Minner
  • Manuel Riel
    • Categories Optimization of Simulated Systems, Scheduling, Stochastic Approaches Tags , , , , ,

    We consider the stochastic economic lot scheduling problem (SELSP) with lost sales and random demand, where switching between products is subject to sequence-dependent setup times. We propose a solution based on simulation optimization using an iterative two-step procedure which combines global policy search with local search heuristics for the traveling salesman sequencing subproblem. To optimize … Read more