Process Planning and Scheduling (PPS) is an essential and practical topic but a very intractable problem in manufacturing systems. Many research use iterative methods to solve such problems; however, they cannot achieve satisfactory results in both quality and computational speed. Other studies formulate scheduling problems as a graph coloring problem (GCP) or its extensions, but these formulations are limited to certain types of scheduling problems. In this paper, we propose a novel approach to formulate a general type of the PPS problem with resource allocation and process planning integrated towards a typical objective, minimizing the makespan. The PPS problem is formulated into an undirected weighted conflicting graph, where nodes represent operations and their resources; edges represent constraints, and weight factors are guidelines for the node selection at each time slot. Then, the Maximum Weighted Independent Set (MWIS) problem can be solved to find the best set of operations with their desired resources for each discrete time slot. This proposed approach solves the PPS problem directly with minimum iterations. We establish that the proposed approach always returns a feasible optimum or near-optimum solution to the PPS problem. The different weight configurations of the proposed approach for solving the PPS problem are tested on a real-world PPS example and further designated test instances to evaluate the scalability, accuracy, and robustness.