On the multiresource flexible job‐shop scheduling problem with arbitrary precedence graphs

This paper aims at linking the work presented in Dauzère‐Pérès et al. (1998) and more recently in Kasapidis et al. (2021) on the multiresource flexible job‐shop scheduling problem with nonlinear routes or equivalently with arbitrary precedence graphs. In particular, we present a mixed integer linear programming (MIP) model and a constraint programming (CP) model to formulate the problem. We also compare the theorems introduced in Dauzère‐Pérès et al. (1998) and Kasapidis et al. (2021) and propose a new theorem extension. Computational experiments were conducted to assess the efficiency and effectiveness of all propositions. Lastly, the proposed MIP and CP models are tested on benchmark problems of the literature and comparisons are made with state‐of‐the‐art algorithms.