Automated transport of multiple particles using optical tweezers requires real-time path planning to move them in coordination by avoiding collisions among themselves and with randomly moving obstacles. This paper develops a decoupled and prioritized path planning approach by sequentially applying a partially observable Markov decision process algorithm on every particle that needs to be transported. We use an iterative version of a maximum bipartite graph matching algorithm to assign given goal locations to such particles. We then employ a three-step method consisting of clustering, classification, and branch and bound optimization to determine the final collision-free paths. We demonstrate the effectiveness of the developed approach via experiments using silica beads in a holographic tweezers setup. We also discuss the applicability of our approach and challenges in manipulating biological cells indirectly by using the transported particles as grippers.