A lower bound for a finite-scenario chance-constrained problem is given by the quantile value corresponding to the sorted optimal objective values of scenario subproblems. This quantile bound can be improved by grouping subsets of scenarios at the expense of larger subproblems. The quality of the bound depends on how the scenarios are grouped. We formulate a mixed-integer bilevel program that o...

The Discrete Ordered Median Problem (DOMP) generalizes classical discrete location problems, such as the N -median, N -center and Uncapacitated Facility Location problems. It was introduced by Nickel [16], who formulated it as both a nonlinear and a linear integer program. We propose an alternative integer linear programming formulation for the DOMP, discuss relationships between both integer l...

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 In spite of the many special purpose heuristics for specific classes of integer programming (IP) problems, there are few developments that focus on general purpose integer programming heuristics. This stems partly from the perception that general purpose methods are likely to be less effective than specialized procedures for specific problems, and partly from the perception that there is no u...

We propose to solve the break minimization problem in sports scheduling by transforming it into a maximum cut problem in an undirected graph and applying a branch-and-cut algorithm. Our approach outperforms previous approaches with constraint programming and integer programming techniques.

Given a connected node-weighted (di)graph, with a root node r, and a (possibly empty) set of nodes R, the Rooted Maximum NodeWeight Connected Subgraph Problem (RMWCS) is the problem of finding a connected subgraph rooted at r that connects all nodes in R with maximum total weight. In this paper we consider the RMWCS as well as its budget-constrained version, in which also non-negative costs of ...

Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem to an equivalent nonconvex quadratic programming problem, interior point methods for solving network flow probl...

We consider the problem of designing a two level telecommunications network at minimum cost. The decisions involved are the locations of concentrators, the assignments of user nodes to concentrators and the installation of links connecting concentrators in a reliable backbone network. We define a reliable backbone network as one where there exist at least 2-edge disjoint paths between any pair ...

After thirty years of doing other things, I am once again doing some research on integer programming. It has been interesting and exciting for me to see what has changed during those thirty years. The practical side of integer programming has developed far more than I would have ever anticipated. Problems of a size and complexity that we would never have thought of attempting thirty years ago a...

An interior-point algorithm within a branch-and-bound framework for solving nonlinear mixed integer programs is described. In contrast to solving the relaxation to optimality at each tree node, the relaxation is only solved to near-optimality. Analogous to using advanced bases for warmstart solutions in the case of linear MIP, a \dynamic" collection of warmstart vectors is kept. Computational r...