An alternative polynomial-sized formulation and an optimization based heuristic for the reviewer assignment problem

Peer review systems are based on evaluating a scholarly work, referred to as a proposal, by experts in that field. In such a system, we consider the reviewer assignment problem, i.e., the problem of assigning proposals to reviewers under the assumption that each reviewer returns her preferences using ordinal rankings. Motivated by the problem defined in Cook et al. (Management Science, 51:655–661, 2005), we focus on reviewer assignments so as to maximize the total number of pairwise comparisons of proposals while ensuring a balanced coverage of distinct pairs of proposals. We propose an alternative mixed integer linear programming formulation for the reviewer assignment problem. In contrast to the optimization model proposed by Cook et al. (2005), the size of our formulation is polynomial in the input size. We present a semidefinite programming relaxation of our optimization model. Furthermore, we propose an optimization based heuristic approach, in which an optimal solution of the linear programming relaxation or the semidefinite programming relaxation of our optimization model is rounded in a straightforward fashion, followed by a local improvement scheme based on pairwise exchanges of proposals. Our computational results illustrate the effectiveness of our optimization model and our heuristic approach.