Mathematical Models for Minimizing Total Tardiness on Parallel Additive Manufacturing Machines

Abstract

In this research we tackle the scheduling problem in additive manufacturing for unrelated parallel machines. Both the nesting and scheduling aspects are considered. Parts have several alternative build orientations. The goal is to minimize the total tardiness of parts. We propose a mixed-integer linear programming model which considers the nesting subproblem as a 2D bin-packing problem, as well as a model which simplifies the nesting subproblem to a 1D bin-packing problem. The computational efficiency and properties of the proposed models are investigated by numerical experiments. Results show that the total tardiness optimization significantly increases the complexity of the problem, only the simple instances are solved optimally, whereas the makespan variant is able to solve all testing instances. Using the 1D bin-packing simplification allows for solving more instances to optimality, but with a risk of obtaining nesting-infeasibility. We also observed the compromise between the total tardiness and makespan objectives, which originates from the dilemma of “packing more parts to benefit from the common machine setup/recoating time” or “packing less parts to maintain the flexibility for handling distributed duedates”.