1 xQx as a Modeling and Solution Framework for the Linear Ordering Problem Mark Lewis a , Bahram Alidaee b , Fred Glover c , Gary Kochenberger d,* a School of Professional Studies, Missouri Western State University, St. Joseph, MO b Hearin Center for Enterprise Science, School of Business, University of Mississippi, University, MS c Leeds School of Business, University of Colorado, Boulder, CO d School of Business, University of Colorado, Denver, CO (September, 2005) Abstract. This paper illustrates how large instances of the linear ordering problem can be effectively modeled and solved as unconstrained quadratic binary programs (UQP). Computational experience comparing a basic tabu search code for UQP to the state-of- the-art commercial code (CPLEX) demonstrates the viability and attractiveness of our approach. Key words: Linear ordering; integer programming; metaheuristics MSC Classification: 90C10, 90C20, 90C59 * Corresponding author. Email addresses: mlewis14@missouriwestern.edu, balidaee@bus.olemiss.edu, fred.glover@colorado.edu, Gary.kochenberger@cudenver.edu _______________________________________________________________________ 1. Introduction The linear ordering problem (LOP) is well-known for its diversity of application as well as its computational challenge. This important problem, which is known to be NP-hard, has attracted considerable attention in the literature. In this paper we present a general method for solving 0-1 integer linear programs, apply this general approach to LOP and show its attractiveness by comparison to an industry standard commercial solver. Applications of the linear ordering model have been reported in a wide variety of problem settings including economics, logistics, social sciences, and discrete