Applying machine learning for the anticipation of complex nesting solutions in hierarchical production planning

In hierarchical production planning, the consideration of interdependencies between superior top-level decisions and subordinate base-level decisions is essential. In this respect, the anticipation of base-level reactions is highly recommended. In this paper, we consider an example from the metal-processing industry: a serial-batch scheduling problem constitutes the top-level problem and a complex nesting problem constitutes the base-level problem. The top-level scheduling decision includes a batching decision, i.e., the determination of a set of small items to be cut out of a large slide. Thus, to evaluate the feasibility of a batch, the base-level nesting problem must be solved. Because solving nesting problems is time consuming even when applying heuristics, it is troublesome to solve it multiple times during solving the top-level scheduling problem. Instead, we propose an approximative anticipation of base-level reactions by machine learning to approximate batch feasibility. To that, we present a prediction framework to identify the most promising machine learning method for the prediction (regression) task. For applying these methods, we propose new feature vectors describing the characteristics of complex nesting problem instances. For training, validation, and testing, we present a new instance generation procedure that uses a set of 6,000 convex, concave, and complex shapes to generate 88,200 nesting instances. The testing results show that an artificial neural network achieves the lowest expected loss (root mean squared error). Depending on further assumptions, we can report that the approximate anticipation based on machine learning predictions leads to an appropriate batch feasibility decision for 98.8% of the nesting instances.