Scheduling 3D printers with multiple printing alternatives

摘要

We examine a 3D printer scheduling problem with products that have multiple printing alternatives for makespan minimization. When 3D printers are used as processing machines, products can be printed in either a complete form or as parts, which are assembled later, and the printed parts can also have different forms. Hence, products have multiple printing alternatives, each of which consists of different types and numbers of parts, and the total printing time of a product depends on the printing alternatives. Therefore, we need to select the best printing alternative for each product and assign the corresponding parts to 3D printers efficiently so that the makespan of producing all of the products can be minimized. We first propose a mathematical model and then develop a genetic algorithm to address this problem. We experimentally show that the average difference between the makespan from the genetic algorithm and its lower bound is less than 2%, even for 50 jobs with 10 3D printers.