Stock or Print? Impact of 3-D Printing on Spare Parts Logistics

We present a general framework to study the design of spare parts logistics in the presence of 3D printing technology. We consider multiple parts facing stochastic demands, and adopt procure/manufacture-to-stock versus print-on-demand to highlight the main difference of production modes featured in traditional manufacturing and 3D printing. A multi-class priority queue with deterministic service times is employed to capture the intrinsic heterogeneity among spare parts and reflect the operational details of 3D printing. To minimize long-run average system cost, our model determines which parts to stock and which to print. We find that the optimal 3D printer's utilization increases as the additional unit cost of printing declines and the printing speed improves. The rate of increase, however, decays, demonstrating the well-known diminishing returns effect. We also find the optimal utilization to increase in part variety and decrease in part criticality, suggesting the value of 3D technology in tolerating large part variety and the value of inventory for critical parts. By examining the percentage cost savings enabled by 3D printing, we find that, while the reduction in printing cost continuously adds to the value of 3D printing in a linear fashion, the impact of the improvement of printing speed exhibits S-shaped growth. We also derive various structural properties of the problem and devise an efficient algorithm to obtain near optimal solutions. Finally, our numerical study shows that the 3D printer is in general lightly used under realistic parameter settings but results in significant cost savings, suggesting complementarity between stock and print in cost minimization.