Job sequencing and tool switching problem with non-identical parallel machines: mathematical formulations and modeling improvements

The job sequencing and tool switching problem with non-identical parallel machines (SSP-NPM) is a generalization of the job sequencing and tool switching problem (SSP), which is known to be an NP-hard optimization problem. SSP-NPM involves scheduling jobs on non-identical parallel machines while determining the associated tool sequences to minimize the makespan. In this paper, we propose an improved version of the existing position-based MILP model introduced in Calmels (2022a). Building on this, we develop a position-based arc flow model. In addition, we introduce a novel MILP formulation based on a job group representation of the problem, as used in Akhundov and Ostrowski (2024) for the SSP, which we extend to derive a job group based arc flow model. Several valid inequalities and symmetry-breaking constraints were considered to improve the proposed approaches. Lower and upper bounds were also developed to improve the proposed approaches. Computational experiments were performed using available literature and randomly generated instances to evaluate the effectiveness of the proposed approaches.