In this paper, we develop a new heuristic procedure for the linear ordering problem (LOP). This NP-hard problem has a significant number of applications in practice. The LOP, for example, is equivalent to the so-called triangulation problem for input–output tables in economics. In this paper, we concentrate on matrices that arise in the context of this real-world application. The proposed algorithm is based on the tabu search methodology and incorporates strategies for search intensification and diversification. For search intensification, we experiment with path relinking, a strategy proposed several years ago in connection with tabu search, which has been rarely used in actual implementations. Extensive computational experiments with input–output tables show that the proposed procedure outperforms the best heuristics reported in the literature. Furthermore, the experiments also show the merit of achieving a balance between intensification and diversification in the search. Scope and purpose The linear ordering problem (LOP) has a wide range of applications in several fields. Perhaps, the best know application of the LOP occurs in the field of economics. In this application, the economy (regional or national) is first subdivided into sectors. Then, an input/output matrix is created, in which the entry ( i, j ) represents the flow of money from sector i to sector j. Economists are often interested in ordering the sectors so that suppliers tend to come first followed by consumers. This is achieved by permuting the rows and columns of the matrix so that the sum of entries above the diagonal is maximized, which is the objective of the LOP. In group decision making, for example, the linear ordering problem can be used to provide a ranking by paired comparison (or aggregation of individual preferences). A matrix entry ( i, j ) in this context may represent the strength of the preference that the group shows for option i over option j. Since the data may be inconsistent, there may not be a direct way of finding an ordering for the options. The solution to the corresponding LOP emerges as viable alternative for ranking the options under consideration. Due to its combinatorial nature, the linear ordering problem has been shown to be hard (computationally speaking While other computationally hard problems have captured the attention of researcher for many years (e.g., the travelling salesman problem), developing efficient solution procedure for the LOP has been somewhat neglected. The goal of our paper is two-fold: (1) to develop an efficient heuristic procedure for this problem, and (2) to experiment with the use of specialized strategies for search intensification and diversification, within the context of the search methodology that we have chosen to apply.