# Integration of Production Planning and Scheduling Based on RTN Representation under Uncertainties
## 1 Introduction  
Production planning and scheduling are important bases for production decisions, and play an important role in economic benefits. In the traditional control of production processes, production planning and scheduling are optimized, respectively, which has obvious disadvantages such as the infeasibility and sub-optimality of optimization results. With the rapid development of economic globalization and product demand diversification, competition among enterprises is more and more fierce. In order to arrange production reasonably and enhance competitiveness of enterprises, enterprise managers and researchers realize that single production planning or scheduling cannot satisfy the needs of production and management in enterprises. Consequently, the integration problem of production planning and scheduling is receiving more and more attention [1] in the complex and changeable economic situation [2; 3]. [PERSON] et al. [4] proposed that production planning and scheduling are complementary, and that integration of production planning and scheduling can enhance the performance of production management greatly. [PERSON] [5] formulated a holistic integrated model of production planning and scheduling, and solved the integrated model hierarchically. [PERSON] et al. [6] explored multi-period multi-workshop production planning and scheduling problems, and formulated an integrated optimization model of the production planning and scheduling based on nonlinear mixed integer programming. An alternant iterative method by hybrid genetic algorithm is employed to solve theintegrated model, which promoted the research of the integration problem of production planning and scheduling. [PERSON] et al. [PERSON] et al. (2017) stated that implementing integrated optimization of planning and scheduling can improve the quality of decision making in the process operations, and also proposed a new decomposition strategy based on two-level optimization. [PERSON] et al. [PERSON] et al. (2018) formulated a bi-level integrated model of production planning and scheduling based on State-Task Network (STN) representation, and introduced the rolling horizon optimization strategy to solve the bi-level integrated model iteratively. The feasibility and effectiveness of the proposed model are illustrated through benchmark examples. [PERSON] et al. [PERSON] et al. (2018) developed a hierarchical and integrated model considering both levels, aggregate production planning, and master production scheduling. Computational tests show that it is possible to solve the integrated model and it outperforms the existing hierarchical approach for all instances. [PERSON] et al. [PERSON] et al. (2018) proposed a new model integrating planning and scheduling to make up for the defect that the capacity limitation could not reflect the practical availability of resources, and added the constraint of resource availability. In this model, the optimization total cost of a single-level job shop was taken as the objective function, and the random approximation method was adopted as the genetic algorithm to solve the N-P problem. A reasonable and elaborate representation for production processes is an important point to establish production planning and scheduling model. In the process industry, general representation methods for production process include STN, State-Sequence Network (SSN) and Resource-Task Network (RTN). [PERSON] et al. [PERSON] et al. (2018) proposed the RTN representation method, which is a comprehensive and concise process-representation method. This representation method can describe all the resource properties in a unified manner. Any kinds of facilities and other resources are not distinctive, and considered as producible and consumable resources when the tasks are active. [PERSON] et al. [PERSON] et al.