Cutting Plane Approaches

The Sample Average Approximation Method Applied to Stochastic Routing Problems: A Computational Study

  • Shabbir Ahmed
  • Anton J. Kleywegt
  • George L. Nemhauser
  • Alexander Shapiro
  • Bram Verweij
    • Categories Cutting Plane Approaches, Stochastic Programming, Transportation Tags , , ,

    The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. … Read more

    Polynomial interior point cutting plane methods

  • John E. Mitchell
    • Categories Cutting Plane Approaches, Linear Programming, Nonsmooth Optimization Tags , , ,

    Polynomial cutting plane methods based on the logarithmic barrier function and on the volumetric center are surveyed. These algorithms construct a linear programming relaxation of the feasible region, find an appropriate approximate center of the region, and call a separation oracle at this approximate center to determine whether additional constraints should be added to the … Read more

    Branch-and-cut for the k-way equipartition problem

  • John E. Mitchell
    • Categories Cutting Plane Approaches, Polyhedra Tags , , , ,

    We investigate the polyhedral structure of a formulation of the k-way equipartition problem and a branch-and-cut algorithm for the problem. The k-way equipartition problem requires dividing the vertices of a weighted graph into k equally sized sets, so as to minimize the total weight of edges that have both endpoints in the same set. Applications … Read more

    Realignment in the NFL

  • John E. Mitchell
    • Categories Applications - OR and Management Sciences, Branch and Cut Algorithms, Cutting Plane Approaches Tags , ,

    The National Football League (NFL) in the United States will expand to 32 teams in 2002 with the addition of a team in Houston. At that point, the league will be realigned into eight divisions, each containing four teams. We describe a branch-and-cut algorithm for minimizing the sum of intradivisional travel distances. We consider first … Read more