# Integration of Production Planning and Scheduling Based on RTN Representation under Uncertainties
## 1 Introduction
(2018) extended the concept of RTN to provide a unified mathematical formulation of the problem of determining the optimal operating conditions of a mixed production facility, comprising a multipurpose plant for both batch and continuous operations. Alternative approaches for solving the general problem were discussed, and some preliminary numerical results were presented. [PERSON] et al. [PERSON] et al. (2018) proposed an improved general mathematical programming formulation for optimal scheduling of batch processes based on the RTN representation. The proposed models led to simpler and less degenerate mathematical models. These models can be solved in significantly less CPU time, when compared to other RTN continuous-time formulations. [PERSON] et al. [PERSON] et al. (2018) proposed an improved mixed integer linear programming model for short-term scheduling of multipurpose batch plants under maximization of profit based on RTN representation and unit-specific events. To solve the model, a hybrid method based on line-up competition algorithm and linear programming was presented. Simulation results show that the proposed model and hybrid method were effective for short-term scheduling of multipurpose batch plants. Some research achievements on the production planning and scheduling problem based on RTN representation were proposed, however, the majority of these achievements are under determinate condition, and do not involve uncertain factors [PERSON] et al. (2018); [PERSON] et al. (2018). [PERSON] et al. [PERSON] et al. (2018) believed that distributionally robust optimization (DRO) is a new and effective method to deal with the imprecise probability distribution of uncertain parameters in the decision-making process. They proposed an effective DRO framework to solve the production planning and scheduling problem in the uncertain demand environment. Based on this, they considered the multi-stage sequential decision structure in the operation process. [PERSON] et al. [PERSON] et al. (2018) proposed an adaptive strategy applicable to the multi-stage setting of the two-stage planning and robust optimization model, and an approximate heuristic algorithm based on multistage stochastic programming and adjustable robust optimization. The simulation results show that the strategies are promising in solving large-scale problems: the approximate strategy based on adjustable robust optimization has, on average, 6.72% better performance and is 7.9 times faster than the deterministic model. Production planning and scheduling problem based on RTN representation considering uncertain factors as constraints in production process, is rare. This paper formulates the multi-period bi-level integrated model of production planning and scheduling, considers the demand and utility uncertainties for the production planning and scheduling problem based on RTN presentation. A deterministic model with two layers of planning and scheduling is formulated firstly. In the deterministic model, uncertainties of demand and utility are treated as deterministic parameters in the planning layer and scheduling layer respectively. Then the chance constrained programming [19] and fuzzy theory [20; 21] are introduced into the planning layer model and scheduling layer model, respectively, to describe the uncertainties of demand and utility [22; 23]. The planning layer model is formulated by the discrete-time modeling method [24]. The scheduling layer model is formulated by the unit-specific event-based continuous-time modeling method. Rolling horizon optimization strategy [25] is utilized to solve the bi-level integrated model iteratively. The simulation results show that the model and algorithm can accurately describe the uncertain factors, decrease the effects of uncertain factors on optimization results, and more accurately reflect the actual production processes. This paper is organized as follows: Section 1 introduces the research status of production planning and scheduling integration.