Cutting-Plane Separation Strategies for Semidefinite Programming Models to Solve the Single-Row Facility Layout Problem

The single-row facility layout problem (SRFLP) is concerned with finding the optimal linear placement of n departments with different lengths in a straight line. It is typically achieved by minimizing the cost associated with the interactions between the departments. The semidefinite programming (SDP) relaxation model that incorporates cutting planes proposed recently by Anjos, Kennings, and Vannelli was considered a breakthrough in the field. This poster will present a new SDP relaxation model, and compare the two SDP relaxations. In combination with the two SDP relaxations, we also explore different strategies to separate the cutting planes, compare their practical performance, and propose an overall best methodology for the SRFLP. This research brings the SDP relaxation model with cutting planes to a higher level by enabling the solution of larger instances.