Cooperative 3D printing (C3DP) is a novel approach to additive manufacturing, where multiple printhead-carrying mobile robots work together cooperatively to print a desired part. The core of C3DP is the chunk-based printing strategy in which the desired part is first split into smaller chunks, and then the chunks are assigned to individual printing robots. These robots will work on the chunks simultaneously and in a scheduled sequence until the entire part is complete. Though promising, C3DP lacks proper framework that enables automatic chunking and scheduling given the available number of robots. In this study, we develop a computational framework that can automatically generate print schedule for specified number of chunks. The framework contains 1) a random generator that creates random print schedule using adjacency matrix which represents directed dependency tree (DDT) structure of chunks; 2) a set of geometric constraints against which the randomly generated schedules will be checked for validation; and 3) a printing time evaluation metric for comparing the performance of all valid schedules. With the developed framework, we present a case study by printing a large rectangular plate which has dimensions beyond what traditional desktop printers can print. The study showcases that our computation framework can successfully generate a variety of scheduling strategies for collision-free C3DP without any human interventions.