A Two-Stage Stochastic Integer Programming Approach to Integrated Staffing and Scheduling with Application to Nurse Management

  • Kibaek Kim
  • Sanjay Mehrotra
    • Categories (Mixed) Integer Nonlinear Programming, Scheduling, Stochastic Programming Tags , , , , ,

    We study the problem of integrated staffing and scheduling under demand uncertainty. The problem is formulated as a two-stage stochastic integer program with mixed-integer recourse. The here-and-now decision is to find initial staffing levels and schedules, well ahead in time. The wait-and-see decision is to adjust these schedules at a time epoch closer to the … Read more

    Models and Solution Techniques for Production Planning Problems with Increasing Byproducts

  • Jeff Linderoth
  • James R. Luedtke
  • Srikrishna Sridhar
    • Categories Applications - OR and Management Sciences, Chemical Engineering, Facility Planning and Design Tags , ,

    We consider a production planning problem where the production process creates a mixture of desirable products and undesirable byproducts. In this production process, at any point in time the fraction of the mixture that is an undesirable byproduct increases monotonically as a function of the cumulative mixture production up to that time. The mathematical formulation … Read more

    A strongly polynomial algorithm for linear optimization problems having 0-1 optimal solutions

  • Sergei Chubanov
    • Categories Linear Programming Tags ,

    We present a strongly polynomial algorithm for linear optimization problems of the form min{cx|Ax = b, x >= 0} having 0-1 vectors among their optimal solutions. The algorithm runs in time O(n^4*max\{m,log n}), where n is the number of variables and m is the number of equations. The algorithm also constructs necessary and sufficient optimality … Read more

    Lagrangian-Conic Relaxations, Part I: A Unified Framework and Its Applications to Quadratic Optimization Problems

  • Naohiko Arima
  • Sunyoung Kim
  • Masakazu Kojima
  • Kim-Chuan Toh
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , , ,

    In Part I of a series of study on Lagrangian-conic relaxations, we introduce a unified framework for conic and Lagrangian-conic relaxations of quadratic optimization problems (QOPs) and polynomial optimization problems (POPs). The framework is constructed with a linear conic optimization problem (COP) in a finite dimensional vector space endowed with an inner product, where the … Read more

    A Robust Additive Multiattribute Preference Model using a Nonparametric Shape-Preserving Perturbation

  • Jian Hu
  • Sanjay Mehrotra
  • Yung-wen Liu
    • Categories Multi-Criteria Optimization, Robust Optimization Tags , , , ,

    This paper develops a multiattribute preference ranking rule in the context of utility robustness. A nonparametric perturbation of a given additive reference utility function is specified to solve the problem of ambiguity and inconsistency in utility assessments, while preserving the additive structure and the decision maker’s risk preference under each criterion. A concept of robust … Read more

    New active set identification for general constrained optimization and minimax problems

  • Jinbao Jian
  • Yi Liu
    • Categories Constrained Nonlinear Optimization

    The purpose of this paper is to discuss the problem of identifying the active constraints for general constrained nonlinear programming and constrained minimax problems at an isolated local solution. Facchinei et al. [F. Facchinei, A. Fischer, and C. Kanzow, On the accurate identification of active constraints, SIAM J. Optim., 9(1998), 14-32] proposed an effective technique … Read more

    Generalized Gauss Inequalities via Semidefinite Programming

  • Paul J. Goulart
  • Daniel Kuhn
  • Bart Paul Gerard Van Parys
    • Categories Convex Optimization, Statistics, Stochastic Programming Tags , ,

    A sharp upper bound on the probability of a random vector falling outside a polytope, based solely on the first and second moments of its distribution, can be computed efficiently using semidefinite programming. However, this Chebyshev-type bound tends to be overly conservative since it is determined by a discrete worst-case distribution. In this paper we … Read more

    Solving piecewise linear equations in abs-normal form

  • Jens-Uwe Bernt
  • Andreas Griewank
  • Manuel Radons
  • Tom Streubel
    • Categories Nonsmooth Optimization Tags , , , , , ,

    With the ultimate goal of iteratively solving piecewise smooth (PS) systems, we consider the solution of piecewise linear (PL) equations. PL models can be derived in the fashion of automatic or algorithmic differentiation as local approximations of PS functions with a second order error in the distance to a given reference point. The resulting PL … Read more

    Robust optimization based self scheduling of hydro-thermal Genco in smart grids

  • Alireza Soroudi
    • Categories Robust Optimization Tags ,

    This paper proposes a robust optimization model for optimal self scheduling of a hydro-thermal generating company. The proposed model is suitable for price taker Gencos which seeks the optimal schedule of its thermal and hydro generating units for a given operating horizon. The uncertainties of electricity prices are modeled using robust optimization approach to make … Read more

    Directional Sensor Control: Heuristic Approaches

  • Edwin K.P. Chong
  • Hans D Mittelmann
  • Shankarachary Ragi
    • Categories Control Applications, Meta Heuristics Tags , , ,

    We study the problem of controlling multiple 2-D directional sensors while maximizing an objective function based on the information gain corresponding to multiple target locations. We assume a joint prior Gaussian distribution for the target locations. A sensor generates a (noisy) measurement of a target only if the target lies within the field-of-view of the … Read more