Job shop deadlock-free scheduling using Mixed Integer Programming and rank matrices

The goal of this paper is to propose a novel mixed integer programming (MIP) formulation for the deadlock-free job shop scheduling problem with limited capacity buffers. Two scenarios are considered; the presence of a central buffer, and unit capacity input buffers for the machines. Due to the complexity of the problem, an operations insertion heuristic based on rank matrices is also proposed to solve the problem. In this heuristic, rank matrices are used to generate the schedules and to check for deadlock situations and machine blocking considering the presence of a central buffer. To evaluate the performances of the mathematical models and the heuristic, comparisons to other approaches reported in literature are conducted.