A math-heuristic approach for scheduling the production and delivery of a mobile additive manufacturing hub

This paper investigates an innovative printing-while-delivering paradigm within a mobile additive manufacturing (MAM) hub. Different from the conventional production-first-delivery-second (PFDS) mode, the MAM hub, comprising a 3D printer and a truck, can seamlessly integrate the production and delivery processes. Throughout the delivery process of the MAM hub, the embedded 3D printer within the truck concurrently prints products for customers in batches. This capability significantly diminishes customer dissatisfaction caused by time delays between order placement and product receipt, which requires coordinating the delivery routing of truck and the production scheduling of 3D printer. To tackle this problem, a mixed integer programming model is firstly established to minimize the required time of the MAM hub returning to depot after completing all deliveries. Then, a math-heuristic approach combining the genetic algorithm and branch-and-bound is devised to solve the mathematical model efficiently. The delivery sequence of truck is represented as a chromosome in the genetic algorithm; while, for each delivery sequence, the optimal production scheduling of 3D printer is obtained by branch-and-bound based on the theoretical analysis about the relationship between production and delivery sequences. In the numerical experiments, the proposed math-heuristic algorithm produces results identical to CPLEX solver outcomes in small-scale cases. For larger instances, it outperforms traditional genetic algorithms by 3.39% to 19.54%. The proposed batch printing mode consistently surpasses the non-batch mode by 10% to 25%. Moreover, compared to PFDS, the printing-while-delivering paradigm reduces trip time by over 40%. Finally, we analyze the effects of customer quantity, distribution radius, and printing time on the objective, providing management insights about optimal production and delivery strategy. The research finding not only aids in scheduling the MAM hub but also holds the potential to address other applications characterized by simultaneous production and delivery requirements.