A binary LP model to the facility layout problem

In facility layout problems, a major concern is the optimal design or remodeling of the facilities of an organization. The decision-maker’s objective is to arrange the facility in an optimal way, so that the interaction among functions (i.e. machines, inventories, persons) and places (i.e. offices, work locations, depots) is efficient. A simple pure-binary LP model … Read more

An explicit equivalent positive semidefinite program for nonlinear 0-1 programs

We consider the general nonlinear optimization problem in 0-1 variables and provide an explicit equivalent positive semidefinite program in $2^n-1$ variables. The optimal values of both problems are identical. From every optimal solution of the former one easily find an optimal solution of the latter and conversely, from every solution of the latter one may … Read more

New formulation and resolution method for the p-Center problem

The $p$-Center problem consists in locating $p$ facilities among a set of $M$ possible locations and assigning $N$ clients to them in order to minimize the maximum distance between a client and the facility to which he is allocated. We present a new integer linear programming formulation for this Min-Max problem with a polynomial number … Read more

The Steinberg Wiring Problem

In 1961 Leon Steinberg formulated a “backboard wiring” problem that has resisted solution for 40 years. Steinberg’s wiring problem is to determine the locations of 34 computer components on a 4 by 9 grid so as to minimize the total length of the wiring required to interconnect them. The problem is an example of a … Read more

An Efficient Exact Algorithm for the Vertex p-Center Problem

Inspired by an algorithm due to Minieka, we develop a simple and yet very efficient exact algorithm for the problem of locating p facilities and assigning clients to them in order to minimize the maximum distance between a client and the facility it is assigned to. After a lower bounding phase, the algorithm iteratively sets … Read more

A Family of Inequalities for the Generalized Assignment Polytope

We present a family of inequalities that are valid for the generalized assignment polytope. Although the inequalities are not facet-defining in general, they define facets of a polytope of a relaxation. We report computational results on the use of the inequalities in a branch-and-cut scheme that demonstrate their effectiveness. Citation Department of Industrial Engineering, State … Read more

A Parallel, Linear Programming Based Heuristic for Large Scale Set Partitioning Problems

We describe a parallel, linear programming and implication based heuristic for solving set partitioning problems on distributed memory computer architectures. Our implementation is carefully designed to exploit parallelism to greatest advantage in advanced techniques like preprocessing and probing, primal heuristics, and cut generation. A primal-dual subproblem simplex method is used for solving the linear programming … Read more