Applications – OR and Management Sciences

Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service System Staffing and Scheduling with Arrival Rate Uncertainty

  • Merve Bodur
  • James R. Luedtke
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Stochastic Programming Tags , , , ,

    We study server scheduling in multiclass service systems under stochastic uncertainty in the customer arrival volumes. Common practice in such systems is to first identify staffing levels, and then determine schedules for the servers that cover these targets. We propose a new stochastic integer programming model that integrates these two decisions, which can yield lower … Read more

    Minimizing Value-at-Risk in Single-Machine Scheduling

  • Semih Atakan
  • Kerem Bülbül
  • Nilay Noyan
    • Categories Scheduling

    The vast majority of the machine scheduling literature focuses on deterministic problems in which all data is known with certainty a priori. In practice, this assumption implies that the random parameters in the problem are represented by their point estimates in the scheduling model. The resulting schedules may perform well if the variability in the … Read more

    Dynamic Linear Programming Games with Risk-Averse Players

  • Alejandro Toriello
  • Nelson A. Uhan
    • Categories Applications - OR and Management Sciences, Game Theory, Stochastic Programming Tags , ,

    Motivated by situations in which independent agents, or players, wish to cooperate in some uncertain endeavor over time, we study dynamic linear programming games, which generalize classical linear production games to multi-period settings under uncertainty. We specifically consider that players may have risk-averse attitudes towards uncertainty, and model this risk aversion using coherent conditional risk … Read more

    Optimization Methods for Disease Prevention and Epidemic Control

  • Yan Deng
  • Siqian Shen
  • Yevgeniy Vorobeychik
    • Categories 0-1 Programming, Applications - OR and Management Sciences, Meta Heuristics Tags , , , ,

    This paper investigates problems of disease prevention and epidemic control (DPEC), in which we optimize two sets of decisions: (i) vaccinating individuals and (ii) closing locations, given respective budgets with the goal of minimizing the expected number of infected individuals after intervention. The spread of diseases is inherently stochastic due to the uncertainty about disease … Read more

    Optimization Models for Differentiating Quality of Service Levels in Probabilistic Network Capacity Design Problems

  • Zhihao Chen
  • Siqian Shen
    • Categories Network Optimization, Stochastic Programming, Transportation

    This paper develops various chance-constrained models for optimizing the probabilistic network design problem (PNDP), where we differentiate the quality of service (QoS) and measure the related network performance under uncertain demand. The upper level problem of PNDP designs continuous/discrete link capacities shared by multi-commodity flows, and the lower level problem differentiates the corresponding QoS for … Read more

    On Solving a Hard Quadratic 3-Dimensional Assignment Problem

  • Hans D Mittelmann
  • Domenico Salvagnin
    • Categories Branch and Cut Algorithms, Telecommunications Tags , ,

    We address the exact solution of a very challenging (and previously unsolved) instance of the quadratic 3-dimensional assignment problem, arising in digital wireless communications. The paper describes the techniques developed to solve this instance to proven optimality, from the choice of an appropriate mixed-integer programming formulation, to cutting planes and symmetry handling. Using these techniques … Read more

    Two-Stage Decomposition Algorithms for Single Product Maritime Inventory Routing

  • Ahmet Keha
  • George L. Nemhauser
  • Dimitri J. Papageorgiou
  • Joel Sokol
    • Categories Production and Logistics, Supply Chain Management, Transportation Tags , , , , ,

    We present two decomposition algorithms for single product deep-sea maritime inventory routing problems (MIRPs) that possess a core substructure common in many real-world applications. The problem involves routing vessels, each belonging to a particular vessel class, between loading and discharging ports, each belonging to a particular region. Our algorithms iteratively solve a MIRP by zooming … Read more

    Existence of Competitive Equilibrium in Piecewise Linear and Concave Exchange Economies and the non-symmetric Nash Bargaining Solution

  • Somdeb Lahiri
    • Categories Finance and Economics, Game Theory Tags , , , ,

    In this paper we show that for concave piecewise linear exchange economies every competitive equilibrium satisfies the property that the competitive allocation is a non-symmetric Nash bargaining solution with weights being the initial income of individual agents evaluated at the equilibrium price vector. We prove the existence of competitive equilibrium for concave piecewise linear exchange … Read more

    A Convex Optimization Approach for Computing Correlated Choice Probabilities with Many Alternatives

  • Selin Damla Ahipasaoglu
  • Karthik Natarajan
  • Xiaobo Li
    • Categories Applications - OR and Management Sciences, Robust Optimization, Semi-definite Programming Tags , ,

    A popular discrete choice model that incorporates correlation information is the Multinomial Probit (MNP) model where the random utilities of the alternatives are chosen from a multivariate normal distribution. Computing the choice probabilities is challenging in the MNP model when the number of alternatives is large and simulation is used to approximate the choice probabilities. … Read more

    Design of Near Optimal Decision Rules in Multistage Adaptive Mixed-Integer Optimization

  • Dimitris Bertsimas
  • Angelos Georghiou
    • Categories Applications - OR and Management Sciences, Integer Programming, Robust Optimization Tags , ,

    In recent years, decision rules have been established as the preferred solution method for addressing computationally demanding, multistage adaptive optimization problems. Despite their success, existing decision rules (a) are typically constrained by their a priori design and (b) do not incorporate in their modeling adaptive binary decisions. To address these problems, we first derive the … Read more