Extensions of the dual-resource constrained flexible job-shop scheduling problem

The shift in focus of manufacturing systems to high-mix and low-volume production poses a challenge to both efficient scheduling of manufacturing operations and effective assessment of production capacity. This thesis considers the problem of scheduling a set of jobs that require machine and worker resources to complete their manufacturing operations. Although planners in manufacturing contexts typically focus solely on machines, schedules that only consider machining requirements may be problematic during implementation because machines need skilled workers and cannot run unsupervised. The model used in this research will be beneficial to these environments as planners would be able to determine more realistic assignments and operation sequences to minimize the total time required to complete all jobs. This thesis presents a mathematical formulation for concurrent scheduling of machines and workers that can optimally schedule a set of jobs while accounting for changeover times between operations. The mathematical formulation is based on disjunctive constraints that capture the conflict between operations when trying to schedule them to be performed by the same machine or worker. An additional formulation extends the previous one to consider how cross-training may impact the production capacity and, for a given budget, provide training recommendations for specific workers and operations to reduce the makespan. If training a worker is advantageous to increase production capacity, the model recommends the best time window to complete it such that overlaps with work assignments are avoided. It is assumed that workers can perform tasks involving the recently acquired skills as soon as training is complete. As an alternative to the mixed-integer programming formulations, this thesis provides a math-heuristic approach that fixes the order of some operations based on Largest Processing Time (LPT) and Shortest Processing Time (SPT) procedures, while allowing the exact formulation to find the optimal schedule for the remaining operations. Computational experiments include the use of the solution for the no-training problem as a starting feasible solution to the training problem. Although the models provided are general, the manufacturing of Printed Circuit Boards are used as a case study.