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 three-dimensional (3-D) printing technology. We consider multiple parts facing stochastic demands and adopt procure/manufacture-to-stock versus print-ondemand 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.