On the block layout shortest loop design problem

Abstract

This article verifies a formulation presented by Asef-Vaziri, Laporte, and Sriskandarajah (2000) for the block layout shortest loop design problem. An error in the set of connectivity constraints of the formulation is corrected and then it is shown that a new set of constraints is needed to guarantee that every solution satisfying the corrected formulation determines a complete loop; i.e., a loop covering each production cell of the block layout. Finally, a cutting-plane algorithm is developed to solve the corrected formulation. The proposed algorithm solves instances with sizes of up to 100 departments in less than 3 seconds. This shows that the algorithm outperforms the best algorithm proposed in the literature, which can solve instances with sizes of up to 80 in less than 60 seconds.