Mixed-Integer Programming Models for Two Metal Additive Manufacturing Methods

Since the beginning of its development in the 1950s, mixed-integer programming (MIP) has been used for a variety of practical application problems, such as sequence optimization. Exact solution techniques for MIPs, most prominently branch-and-cut techniques, have the advantage (compared to heuristics such as genetic algorithms) that they can generate solutions with optimality certificates. The novel process of additive manufacturing opens up a further perspective for their use. With the two common techniques, Wire-Arc Additive Manufacturing and Laser Powder Bed Fusion, the sequence in which a given component geometry must be manufactured can be planned. In particular, the heat transfer within the component must be taken into account here, since excessive temperature gradients can lead to internal stresses and warpage after cooling. In order to integrate the temperature, heat transfer models (heat conduction, heat radiation) are integrated into a sequencing model. This leads to the problem class of MIPDECO: MIPs with partial differential equations as further constraints. We present these model approaches for both manufacturing techniques and carry out test calculations for sample geometries in order to demonstrate the feasibility of the approach.