mixed-integer programming

Scenario-Tree Decomposition: Bounds for Multistage Stochastic Mixed-Integer Programs

  • Oleg A. Prokopyev
  • Andrew J. Schaefer
  • Gabriel L. Zenarosa
    • Categories Integer Programming, Parallel Algorithms, Stochastic Programming Tags , ,

    Multistage stochastic mixed-integer programming is a powerful modeling paradigm appropriate for many problems involving a sequence of discrete decisions under uncertainty; however, they are difficult to solve without exploiting special structures. We present scenario-tree decomposition to establish bounds for unstructured multistage stochastic mixed-integer programs. Our method decomposes the scenario tree into a number of smaller … Read more

    Binary Decision Rules for Multistage Adaptive Mixed-Integer Optimization

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

    Decision rules provide a flexible toolbox for solving the computationally demanding, multistage adaptive optimization problems. There is a plethora of real-valued decision rules that are highly scalable and achieve good quality solutions. On the other hand, existing binary decision rule structures tend to produce good quality solutions at the expense of limited scalability, and are … Read more

    On the Value Function of a Mixed Integer Linear Optimization Problem and an Algorithm for its Construction

  • Anahita Hassanzadeh
  • Ted K. Ralphs
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , ,

    This paper addresses the value function of a general mixed integer linear optimization problem (MILP). The value function describes the change in optimal objective value as the right-hand side is varied and understanding its structure is central to solving a variety of important classes of optimization problems. We propose a discrete representation of the MILP … Read more

    Solving Bilevel Mixed Integer Program by Reformulations and Decomposition

  • Yu An
  • Bo Zeng
    • Categories (Mixed) Integer Linear Programming, Complementarity and Variational Inequalities Tags , , ,

    In this paper, we study bilevel mixed integer programming (MIP) problem and present a novel computing scheme based on reformulations and decomposition strategy. By converting bilevel MIP into a constrained mathematical program, we present its single-level reformulations that are friendly to perform analysis and build insights. Then, we develop a decomposition algorithm based on column-and-constraint … Read more

    Analysis of mixed integer programming formulations for single machine scheduling problems with sequence dependent setup times and release dates

  • Carlos R. V. Carvalho
  • Mauricio Cardoso de Souza
  • Thiago Henrique Nogueira
  • Martín Gómez Ravetti
    • Categories Scheduling Tags , , ,

    In this article, six different mixed integer programming (MIP) formulations are proposed and analyzed. These formulations are based on the knowledge of four different paradigms for single machine scheduling problems (SMSP) with sequence dependent setup times and release dates. Each formulation reflects a specific concept on how the variables and parameters are defined, requiring particular … Read more

    Tight MIP Formulations of the Power-Based Unit Commitment Problem

  • Claudio Gentile
  • Germán Morales-España
  • Andres Ramos
    • Categories (Mixed) Integer Linear Programming, Scheduling Tags , , , , ,

    This paper provides the convex hull description for the basic operation of slow- and quick-start units in power-based unit commitment (UC) problems. The basic operating constraints that are modeled for both types of units are: 1) generation limits and 2) minimum up and down times. Apart from this, the startup and shutdown processes are also … Read more

    A Tight MIP Formulation of the Unit Commitment Problem with Start-up and Shut-down Constraints

  • Claudio Gentile
  • Germán Morales-España
  • Andres Ramos
    • Categories (Mixed) Integer Linear Programming, Scheduling Tags , ,

    This paper provides the convex hull description for the following basic operating constraints of a single power generation unit in Unit Commitment (UC) problems: 1) generation limits, 2) startup and shutdown capabilities, and 3) minimum up and down times. Although the model does not consider some crucial constraints, such as ramping, the proposed constraints can … Read more

    Power-Capacity and Ramp-Capability Reserves for Wind Integration in Power-Based UC

  • Ross Baldick
  • Germán Morales-España
  • Javier García-González
  • Andres Ramos
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , , , ,

    This paper proposes a power-based network-constrained unit commitment (UC) model as an alternative to the traditional deterministic UCs to deal with wind generation uncertainty. The formulation draws a clear distinction between power-capacity and ramp-capability reserves to deal with wind production uncertainty. These power and ramp requirements can be obtained from wind forecast information. The model … Read more

    On Global Optimization

  • Isaac Siwale
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Multi-Criteria Optimization Tags , , , ,

    This paper presents a relatively “unfettered” method for finding global optima to constrained nonlinear programs. The method reformulates the given program into a bi-objective mixed-integer program that is then solved for the Nash equilibrium. A numerical example (whose solution provides a new benchmark against which other algorithms may be assessed) is included to illustrate the … Read more

    n-step cycle inequalities: facets for continuous n-mixing set and strong cuts for multi-module capacitated lot-sizing problem

  • Manish Bansal
  • Kiavash Kianfar
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches, Production and Logistics Tags , , , , ,

    In this paper, we introduce a generalization of the continuous mixing set (which we refer to as the continuous n-mixing set). This set is closely related to the feasible set of the multi-module capacitated lot-sizing (MML) problem with(out) backlogging. We develop new classes of valid inequalities for this set, referred to as n’-step cycle inequalities, … Read more