Production logistics has an important role as a chain that connects the components of the production system. The most important goal of production logistics plans is to keep the flow of the production system well. However, compared to the production system, the level of planning, management, and digitalization of the production logistics system is not high enough, so it is difficult to respond flexibly when unexpected situations occur in the production logistics system. Optimization and heuristic algorithms have been proposed to solve this problem, but due to their inflexible nature, they can only achieve the desired solution in a limited environment. In this paper, the relationship between the production and production logistics system is analyzed and stochastic variables are introduced by modifying the pickup and delivery problem with time windows (PDPTW) optimization model to establish a flexible production logistics plan. This model, taking into account stochastic variables, gives the scheduler a new perspective, allowing them to have new insights based on the mathematical model. However, since the optimization model is still insufficient to respond to the dynamic environment, future research will cover how to derive meaningful results even in a dynamic environment such as a machine learning model.