Scheduling in additive manufacturing problems

Abstract

Scheduling problems in additive manufacturing is a problem that can involve considerably morecomplexity than single-stage scheduling problems, since machines can process more than one partwith different geometries simultaneously [1]. To achieve efficiency in terms of the used capacity of themachine, it is necessary to group as many parts as possible in a single job. Since the use of themachines in terms of time depends on the job being processed, how parts are grouped within eachjob comes critical. This implies that the resolution of the nesting problem will have a direct impact onthe objective function of the jobs Schedule. In this work, the objective function to be minimized is theTotal Completion time, wich is obtained by the sum of the completion time of each job. The biggestdifficulty is that the problem is NP-Hard [2], so a purely mathematical approach is insufficient. For thisreason, a hybrid method is proposed that allows linking the benefits of an approach based onmathematical programming but enhanced by heuristic methods. In this way, heuristics are developedthat address the nesting problem incorporating knowledge about the nature of the problem, such asthe influence of the parameters “height” and volume” of the parts in the definition of the Jobs; and thestructure of its solutions. Then, using mathematical programming, solve the scheduling in paralleladditive manufacturing machines. For the nesting stage, several heuristics were proposed andcompared, showing that those heuristics that best captured the influence of the parameterscontributed more to solving the problem.