Matheuristic for additive Manufacturing scheduling problem

RODRÍGUEZ, JEANETTE; ROSSIT, DANIEL ALEJANDRO

Congreso; XI-th International Conference on Production Research Americas 2022; 2022

The Federal University of Technology ? Parana

Abstract. Scheduling problems in additive manufacturing is a problem that, despite having only one processing stage, can be much more complex than single-stage shop scheduling problems (as single-machine), since machines can process more than one part with different geometries simultaneously. Thus, to achieve efficiency, each run of the printing machine must be used to its full capacity, this implies grouping parts in a single job in such a man-ner that machine's capacity is filled. Then, the different Jobs must be sched-uled defining the processing sequence [2]. The use of the machines in terms of time will be dependent on the job, which, in turn, is dependent on those parts that have been grouped within the job. Grouping the parts into jobs rep-resents the nesting problem. Then, the resolution of the nesting problem will have a direct impact on the value of objective function of scheduling solu-tion. In this work the objective function of the makespan will be studied with parallel identical 3D printing machines. The greatest difficulty lies in the fact that the problem is NP-Hard [3], so a purely mathematical approach is insuf-ficient. To overcome this issue a matheuristic approach is developed. The method consists of developing heuristics that address the nesting problem in-corporating knowledge about the problem, such as the influence of the pa-rameters "volume” of the parts in the definition of the Jobs; and the structure of its solutions. Then, using mathematical programming, the scheduling prob-lem is solved following to optimize makespan.