Within the context of solving Mixed-Integer Linear Programs by a Branch-and-Cut algorithm, we propose a new strategy for branching. Computational experiments show that, on the majority of our test instances, this approach enumerates fewer nodes than traditional branching. On average, on instances that contain both integer and continuous variables the number of nodes in the … Read more
Integer programs defined by two equations with two free integer variables and nonnegative continuous variables have three types of nontrivial facets: split, triangle or quadrilateral inequalities. In this paper, we compare the strength of these three families of inequalities. In particular we study how well each family approximates the integer hull. We show that, in … Read more
We investigate the problem of simultaneously determining the location of facilities and the design of vehicle routes to serve customer demands under vehicle and facility capacity restrictions. We present a set-partitioning-based formulation of the problem and study the relationship between his formulation and the graph-based formulations that have been used in previous studies of this … Read more
Recently, Andersen et al.(2007), Borozan and Cornuejols (2007) and Cornuejols and Margot(2007) characterized extreme inequalities of a system of two rows with two free integer variables and nonnegative continuous variables. These inequalities are either split cuts or intersection cuts (Balas (1971)) derived using maximal lattice-free convex sets. In order to use these inequalities to obtain … Read more
This paper shows how valid inequalities based on the mixing set can be used in a mixed integer programming (MIP) solver. It discusses the relation of mixing inequalities to flow path and mixed integer rounding in- equalities and how currently used separation algorithms already generate cuts implicitly that can be seen as mixing cuts. Further … Read more
In this paper we study an exact separation algorithm for mixed knapsack sets with the aim of evaluating its effectiveness in a cutting plane algorithm for Mixed-Integer Programming. First proposed by Boyd in the 90’s, exact knapsack separation has recently found a renewed interest. In this paper we present a “lightweight” exact separation procedure for … Read more
We describe a rudimentary branch-and-cut algorithm for solving integer bilevel linear programs that extends existing techniques for standard integer linear programs to this very challenging computational setting. The algorithm improves on the branch-and-bound algorithm of Moore and Bard in that it uses cutting plane techniques to produce improved bounds, does not require specialized branching strategies, … Read more
As a traditional model in the operations research and management science domain, lot-sizing problem is embedded in many application problems such as production and inventory planning and has been consistently drawing attentions from researchers. There is significant research progress on polynomial time algorithm developments for deterministic uncapacitated lot-sizing problems based on Wagner-and-Whitin property. However, in … Read more
The value function of a mixed-integer linear program (MILP) is a function that returns the optimal solution value as a function of the right-hand side. In this paper, we analyze the structure of the value function of a MILP with a single constraint. We show that the value function is uniquely determined by a finite … Read more
Parsimonious haplotype estimation from aligned Single Nucleotide Polymorphism (SNP) fragments consists of finding the minimum number of haplotypes necessary to explain a given set of genotypes. This problem is known to be NP-Hard. Here we describe a new integer linear-programming model to tackle this problem based on the concept of class representatives, already used for … Read more