Integration of Machine Scheduling and Personnel Allocation for an Industrial-Scale Analytical Services Facility

This work presents a monolithic formulation to fully integrate machine scheduling and personnel allocation for large-scale industrial problems. Our computational results, tested for 50 scenarios, show that the monolithic formulation cannot find a solution when the size of the instances grows. In order to find solutions for industrial-size problems, we propose a sequential algorithm where we first solve the machine scheduling and then use this solution to obtain the dual information to guide the personnel allocation decisions by defining the most profitable machines where employees should be allocated. This approach is an alternative to the monolithic, as it can produce high-quality solutions for computationally intensive problems involving hundreds of processes, jobs, and employees. We show that the proposed sequential approach can find solutions to instances with more than one million decision variables and constraints.