Lower and upper bounds for scheduling a real-life assembly problem with precedences and resource constraints

In this work, we consider a real-life scheduling problem involving the production of off-road vehicles using a three-level assembly process, subject to precedence, machines, and resource constraints. This problem shares multiple characteristics with other scheduling problems such as the Parallel Machine Scheduling and Flexible Flow Shop Problems. However, it also comprises less investigated aspects such as a specific job precedence structure resulting in a directed rooted in-tree and a global resource constraint limiting the number of simultaneously active machines. We present a straightforward adaptation of a time-indexed mathematical formulation to the problem and introduce a new lower-bounding procedure. To solve the problem, we propose constructive heuristics based on classical priority rules and adaptations of job sequencing heuristics. We also propose CORE, a specialized approach tailored to leverage the problem structure. All the algorithms are extensively evaluated on two benchmark sets, various shop floor configurations, and eight real-life scenarios. Our results reveal the general effectiveness of job sequencing approaches and demonstrate the overall superiority of CORE.