In this article, we study the NP-Hard combinatorial optimization problem of the minimum initial marking (MIM) computation in labeled Petri net (L-PN) while considering a sequence of labels to minimize the resource consumption in a flexible manufacturing system (FMS), and we propose an approach based on the ant colony optimization (ACO) precisely the extension Rank-based ACO to optimal resource allocation and scheduling in FMS. The ACO meta-heuristic is inspired by the behavior of ants in foraging based on pheromones deposit. The numerical results show that the proposed algorithm obtained much better results than previous studies.