A Constraint Programming Formulation of the Multi-Mode Resource-Constrained Project Scheduling Problem for the Flexible Job Shop Scheduling Problem

In this work, a constraint programming (CP) formulation of the multi-mode resource-constrained project scheduling problem (MMRCPSP) is proposed for solving the flexible job shop scheduling problem (FJSSP) under the makespan minimization criterion. The resulting CP model allows us to tackle the classical instances of the FJSSP (such as where the operations of a given job follow a linear order). It can also handle FJSSP instances where the precedence relationships between operations are defined by an arbitrary directed acyclic graph (sequencing flexibility). The performance of our approach was tested using 271 classical FJSSP instances and 50 FJSSP instances with sequencing flexibility. We establish the validity of our approach by achieving an average relative percentage deviation of 3.04% and 0.18% when compared to the best-known lower and upper bounds, respectively. Additionally, we were able to contribute to the literature with ten new lower bounds and two new upper bounds. Our CP approach is relatively simple yet competitive and can be quickly applied and adapted by new practitioners in the area.