COmputational INfrastructure for Operations Research Lehigh University This document will serve as a simple example for using COIN/BCP to solve an integer linear program (ILP) using branch and price (BP). Topic: Integer Linear Program, Column Generation Modules: BCP, OSI, Coin, CLP Source: AAP BP.tar.gz Data: AAP Data included in AAP BP.tar.gz Author: Matthew Galati Document: AAP BP: A COIN/BCP...

The development of new mathematical theory and its application in software systems for the solution of hard optimization problems have a long tradition in mathematical programming. In this tradition we implemented ABACUS, an object-oriented software framework for branch-and-cut-and-price algorithms for the solution of mixed integer and combinatorial optimization problems. This paper discusses s...

This paper presents an optimization model for the selection of sets of clients that will receive an offer for one or more products during a promotion campaign. We show that the problem is strongly NP-hard and that it is unlikely that a constant-factor approximation algorithm can be proposed for solving this problem. We propose an alternative set-covering formulation and develop a branch-and-pri...

Branch-and-price is a generalization of linear programming (LP) based branch-and-bound specifically designed to handle integer programming (IP) formulations that contain a huge number of variables. The basic idea of branch-and-price is simple. Columns are left out of the LP relaxation because there are too many columns to handle efficiently and most of them will have their associated variable e...

A short introduction to Integer Programming (IP). Problems leading to IP models. Some modelling tricks and reformulations. Geometry of linear IP. TUM matrices. Brief notes on polyhedral analysis. Separation theory. Chvatal cut hierarchy, Gomory cuts, Disjunctive cuts, RLT cut hierarchy. Iterative methods: Branch-and-Bound, Cutting Plane, Branch-and-Cut, Branch-and-Price. Lower bounds: Lagrangia...

In the Variable Cost and Size Bin Packing Problem with optional items, a set of items characterized by volume and profit and a set of bins of different types characterized by volume and cost are given. The goal consists in selecting those items and bins which optimize an objective function which combines the cost of the used bins and the profit of the selected items. We propose two methods to t...

To improve the current real-world deployments of Stackelberg security games (SSGs), it is critical now to efficiently incorporate models of adversary bounded rationality in large-scale SSGs. Unfortunately, previously proposed branch-and-price approaches fail to scale-up given the non-convexity of such models, as we show with a realization called COCOMO. Therefore, we next present a novel cuttin...

Cadaveric liver transplantation is the only viable therapy for end-stage liver disease patients without a living donor. However, this type of transplantation is hindered in the United States by donor scarcity and rapid viability decay. Given these difficulties, the current U.S. liver transplantation and allocation policy attempts to balance allocation likelihood and geographic proximity by allo...