Using 3D-printing in disaster response: the two-stage stochastic 3D-printing knapsack problem

In this paper, we will shed light on when to pack and use 3D-printers in disaster response operations. For that, we introduce a new type of problem, which we call the two-stage stochastic 3D-printing knapsack problem. We provide a two-stage stochastic programming formulation for this problem, for which both the first and the second stage are NP-hard integer linear programs. We reformulate this formulation to an equivalent integer linear program, which can be efficiently solved by standard solvers. Our numerical results illustrate that for most situations using a 3D-printer is beneficial. Only in extreme circumstances, where the quality of printed items is extremely low, the size of the 3D-printer is extremely large compared to the knapsack size, when there is no time to print the items, or when demand for items is low, packing no 3D-printers is the best option.