In this paper, we consider the Job Sequencing and Tool Switching Problem with Non-identical Parallel Machines (SSP-NPM), which arises in a flexible manufacturing context. The SSP-NPM is a generalization of the classical Job Sequencing and Tool Switching Problem, which is an NP-hard problem. In the SSP-NPM, a set of unrelated parallel machines is available to process a set of jobs. Each job, in turn, requires a set of tools to be loaded on the machine during its processing. Since each machine has a limited storage capacity, tool switches, that lead in setup times, are needed in order to make it possible to process all jobs. To solve the problem, we propose an arc-flow (AF) model that associated flows on a capacitated network with schedules. Preliminary experiments show that the AF model is able to solve small-sized benchmark instances. Future research concers the improvement of the formulation by proposing valid inequalities and preprocessing procedures to reduce the AF size and developing matheuristics/exact/decomposition methods to efficiently solve the SPP-NPM.