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

Abstract

We present a general framework to study the design of spare parts logistics in the presence of three-dimensional (3-D) 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 3-D printing. To minimize long-run average system cost, our model determines which parts to stock and which to print. We find that the optimal 3-D 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 3-D technology in tolerating large part variety and the value of inventory for critical parts. By examining the percentage cost savings enabled by 3-D printing, we find that, although the reduction in printing cost continuously adds to the value of 3-D 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 3-D 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. This paper was accepted by Victor Martínez-de-Albéniz, operations management.