A MILP formulation for a batch scheduling problem on parallel machines in the aircraft industry

In the aircraft industry structural components, referred to as part numbers (PN), have to be subject to an heat treatment in capacitated burn-in furnaces for a pre-defined period (exposure time) in order to provide them with specific physic and chemical features (e.g. hardness, corrosion resistance, conductivity). Two or more part numbers can be grouped in a batch and treated simultaneously in the same furnace if it is possible to individuate a common exposure time. In order to minimize the total completion time (makespan) of the process it needs to determine the appropriate grouping of the part numbers into batches (batching problem) to be processed by each furnace (scheduling problem). The problem can be modeled as a batch scheduling problem on parallel machines where the batching and the scheduling problem are considered at the same time. Starting from a real case study, we present an original integer linear programming formulation in the case of two capacitated parallel machines and we provide the results obtained on two real instances coming from the aircraft industry.