One of the promises of three-dimensional (3D) printing technology is that it would allow warehouses to store inventory as digital files instead of physical items. The strategy could save valuable shelf space and enable companies to deliver goods at the near-instantaneous speed of email, instead of waiting for trucks and airplanes to transport the goods.

But exactly which parts should you store in physical form, and which as digital blueprints? Even 3D printing takes time, so creating an item on demand might not be fast enough to meet an emergency need.

Jeannette Song, an operations professor at Duke University's Fuqua School of Business, has now created a mathematical model to help companies balance the cost of storing spare parts with the need to have them instantly available, the school said. Song's model, which helps users determine which parts to keep on hand and which to print, is described in the paper "Stock or Print? Impact of 3D Printing on Spare Parts Logistics," recently published in the journal Management Science.

The paper concludes that a hybrid approach is optimal for most companies, allowing them to avoid the risk of abandoning all their spare-parts inventory, while still saving money by printing certain parts on demand. "The big decision is how you rationalize all these parts, which ones to stock and which ones to print," Song said in a release. "In most cases, we find a 3D printer would not be used very much at all, but the firm saves a massive amount of inventory."