Mixed Integer Linear Programming for a Real-World Parallel Machine Scheduling Problem with Workforce and Precedence Constraints

In this work, we consider a real-world scheduling problem occurring in the engineering test laboratory of a multinational company producing hydraulic components for motion systems. Similar problems have been solved in the literature under the framework of resource constrained parallel machine scheduling problems. In our work, the tests on the hydraulic components are the jobs to be scheduled. Each job must be processed on a machine and requires an additional human resource to prepare the machine and supervise the job. Machine and workforce eligibility constraints are also included. Release and due dates are given for jobs. The aim is to minimize the total weighted tardiness. Each job has a processing time expressed in working days that depends on the machine and requires a fixed number of hours per day for its assigned worker. Moreover, precedence and contiguity relations between jobs must be respected. We propose a Mixed Integer Linear Programming formulation to model the problem and demonstrate its effectiveness on both real-world and randomly generated instances.