Scheduling of semi-automatic carousels with fixed production sequences

Rotary transfer machines are widely used in different industrial sectors. A rich literature concerning their design and optimisation is available, but mainly dedicated to integrated machining systems. This machine architecture is also implemented in the aluminium gravity die casting technology where the specificity of the casting process needs an appropriate design. In particular, the constraints related to processing times and the rigidity of the production sequence impose a specific approach to schedule the production for achieving an optimal cycle time. We approach this problem with an optimisation perspective: first we propose a mixed-integer linear programming formulation for defining the sequencing and scheduling of the machine in order to obtain a specified production with minimum makespan, and discuss strategies for enumerating the variables of the formulation. Second, we describe a heuristic algorithm as an alternative to the solution of the formulation through a general-purpose solver. Eventually, we present extensive computational experiments on a set of instances generated from real data, comparing these alternative approaches.