3D printing (3DP) is a revolutionary manufacturing method that enables rapid prototyping, customization and local production of parts, hence reducing waste of resources. A new paradigm in the supply chain could be then realized by capitalizing on 3DP, that is: decentralized manufacturing, characterized by geographic dispersion and enhanced resilience to risks and disruptions, while also offering customers numerous benefits, including faster fulfilment of personalized orders. However, optimizing the allocation of customer demands is a complex challenge, especially in the context of decentralized 3DP shops operating under limited capacity constraints. By optimizing based on delivery distance, it is possible to reduce resource consumption and environmental impact while also shortening overall delivery time, thereby achieving better realization of the advantages of decentralized 3DP. This research firstly addresses the challenge of efficiently allocating customer demand to decentralized 3DP shops, optimizing delivery distances while considering capacity constraints by leveraging on mature Mixed Integer Linear Programming (MILP) based 3DP optimization techniques and innovative combination with Monte Carlo simulation. Furthermore, the study analyzes quantitatively and qualitatively the superior probability and difference in overall delivery distance between decentralized 3DP shops and hypothetical centralized 3DP hubs across various sub-scenarios with massive, randomized customer instances in the greater Cairo region in Egypt. Through this research, we aim to gain a comprehensive understanding on the advantages of decentralized 3DP on a much broader scale.