Applications – OR and Management Sciences

Bi-Perspective Functions for Mixed-Integer Fractional Programs with Indicator Variables

  • Adam N. Letchford
  • Qiang Ni
  • Zhaoyu Zhong
    • Categories (Mixed) Integer Nonlinear Programming, Telecommunications Tags , ,

    Perspective functions have long been used to convert fractional programs into convex programs. More recently, they have been used to form tight relaxations of mixed-integer nonlinear programs with so-called indicator variables. Motivated by a practical application (maximising energy efficiency in an OFDMA system), we consider problems that have a fractional objective and indicator variables simultaneously. … Read more

    Constraints reduction programming by subset selection: a study from numerical aspect

  • Yuan Shen
    • Categories 0-1 Programming, Applications - OR and Management Sciences, Convex Optimization Tags , , , , , ,

    We consider a novel method entitled constraints reduction programming which aims to reduce the constraints in an optimization model. This method is derived from various applications of management or decision making, and has potential ability to handle a wider range of applications. Due to the high combinatorial complexity of underlying model, it is difficult to … Read more

    Resilient Course and Instructor Scheduling in the Mathematics Department at the United States Naval Academy

  • Joseph Foraker
  • Nelson A. Uhan
  • Stephen J. Ward
    • Categories Scheduling, Stochastic Programming Tags , ,

    In this work, we study the problem of scheduling courses and instructors in the Mathematics Department at the United States Naval Academy (USNA) in a resilient manner. Every semester, the department needs to schedule around 70 instructors and 150-180 course sections into 30 class periods and 30 rooms. We formulate a stochastic integer linear program … Read more

    A Criterion Space Search Algorithm for Biobjective Mixed Integer Programming: the Boxed Line Method

  • Natashia Boland
  • Diego Pecin
  • Martin Savelsbergh
  • Tyler Perini
    • Categories Applications - OR and Management Sciences Tags , ,

    Despite recent interest in multiobjective integer programming, few algorithms exist for solving biobjective mixed integer programs. We present such an algorithm: the Boxed Line Method. For one of its variants, we prove that the number of single-objective integer programs solved is bounded by a linear function of the number of nondominated line segments in the … Read more

    Partially-Ranked Choice Models for Data-Driven Assortment Optimization

  • Sanjay Dominik Jena
  • Andrea Lodi
  • Hugo Palmer
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Marketing

    The assortment of products carried by a store has a crucial impact on its success. However, finding the right mix of products to attract a large portion of the customers is a challenging task. Several mathematical models have been proposed to optimize assortments. In particular, rank-based choice models have been acknowledged for representing well high-dimensional … Read more

    Computation of exact bootstrap confidence intervals: complexity and deterministic algorithms

  • Dimitris Bertsimas
  • Bradley Sturt
    • Categories Applications - OR and Management Sciences, Approximation Algorithms, Statistics Tags , , , ,

    The bootstrap is a nonparametric approach for calculating quantities, such as confidence intervals, directly from data. Since calculating exact bootstrap quantities is believed to be intractable, randomized resampling algorithms are traditionally used. Motivated by the fact that the variability from randomization can lead to inaccurate outputs, we propose a deterministic approach. First, we establish several … Read more

    Same-Day Delivery with Drone Resupply

  • John-Paul Clarke
  • Iman Dayarian
  • Martin Savelsbergh
    • Categories Applications - OR and Management Sciences, Transportation

    Unmanned Aerial Vehicles (UAVs), commonly referred to as drones, have recently seen an increased level of interest as their potential use in same-day home delivery has been promoted and advocated by large retailers and courier delivery companies. We introduce a novel way to exploit drones in same-day home delivery settings: drone resupply. We consider a … Read more

    Comparative Analysis of Capacitated Arc Routing Formulations for Branch-Cut-and-Price Algorithms

  • Diego Pecin
  • Eduardo Uchoa
    • Categories Combinatorial Optimization, Integer Programming, Transportation

    The current best exact algorithms for the Capacitated Arc Routing Problem are based on the combination of cut and column generation. This work presents a deep theoretical investigation of the formulations behind those algorithms, classifying them and pointing similarities and differences, advantages and disadvantages. In particular, we discuss which families of cuts and branching strategies … Read more

    Planar Maximum Coverage Location Problem with Partial Coverage and General Spatial Representation of Demand and Service Zones

  • Manish Bansal
    • Categories Approximation Algorithms, Nonlinear Optimization, Production and Logistics

    We introduce a new generalization of the classical planar maximum coverage location problem (PMCLP) in which demand zones and service zone of each facility are represented by spatial objects such as circles, polygons, etc., and are allowed to be located anywhere in a continuous plane. In addition, we allow partial coverage in its true sense, … Read more

    The Adaptive Robust Multi-Period Alternating Current Optimal Power Flow Problem

  • Alvaro Lorca
  • Xu Andy Sun
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , ,

    This paper jointly addresses two major challenges in power system operations: i) dealing with non-convexity in the power flow equations, and ii) systematically capturing uncertainty in renewable power availability and in active and reactive power consumption at load buses. To overcome these challenges, this paper proposes a two-stage adaptive robust optimization model for the multi-period … Read more