Combinatorial Benders decomposition for single machine scheduling in additive manufacturing with two-dimensional packing constraints

Abstract

This paper addresses a single-machine scheduling problem in additive manufacturing (AM). We focus on the direct metal laser sintering (DMLS) technology of an AM process, where parts can be produced simultaneously in a batch. In this problem, we consider simultaneously the assignment of parts to batches and the packing of parts onto two-dimensional surfaces of the build chamber to minimize the makespan objective. To solve this problem, a mixed integer linear programming model is formulated, and an approximation algorithm is proposed, followed by an exact algorithm based on combinatorial Benders decomposition method with various Benders cuts and acceleration strategies (Algorithm CBD). Finally, we conduct a comprehensive computational study to verify the efficiency of our proposed Algorithm CBD. The computational results show that our proposed Algorithm CBD can effectively solve the test instances with different sizes.