The inventory level has a significant influence on the cost of process scheduling. The stochastic cutting stock problem (SCSP) is a complicated inventory-level scheduling problem due to the existence of random variables. In this study, we applied a model-free on-policy reinforcement learning (RL) approach based on a well-known RL method, called the Advantage Actor-Critic, to solve a SCSP example. To achieve the two goals of our RL model, namely, avoiding violating the constraints and minimizing cost, we proposed a two-stage discount factor algorithm to balance these goals during different training stages and adopted the game concept of an episode ending when an action violates any constraint. Experimental results demonstrate that our proposed method obtains solutions with low costs and is good at continuously generating actions that satisfy the constraints. Additionally, the two-stage discount factor algorithm trained the model faster while maintaining a good balance between the two aforementioned goals.