The Study Of Time Representations For Chemical Production Scheduling Models

Optimal scheduling is a decision-making process that is widely used in the field of chemical industry and it has been extensively investigated in the Process Systems En-gineering(PSE)community.Most of the existing mathematical programming models for scheduling can be classified into two categories in terms of the time representa-tion:continuous-time(CT)and discrete-time(DT).The CT and DT approaches have their own strengths and weaknesses,and are suitable for different types of scheduling problems.In order to accommodate more production problems and address the issue of computational complexity,a mixed-time(MT)representation has also been stud-ied in the literature,which integrates the DT and the CT representations.This thesis compares the different time representations for scheduling of continuous and batch processes.The thesis also establishes a new and more general MT modeling frame-work that uses discrete time grids and continuous time variables to describe time.The main research contents of this thesis is as follows:1.For the scheduling of a continuous process involving parallel units and multi-grade products,with the goal of minimizing energy consumption,a CT mixed-integer linear programming(MILP)formulation is proposed.The model describes various operating constraints,including three delivery modes for final products,namely,con-tinuous delivery,fixed time delivery,and flexible time delivery,as well as sequence-dependent transition,run-length constraints,and boundary constraints.The CT for-mulation is compared with an existing DT formulation in terms of model scale and solution accuracy.2.Based on the comparison of DT and CT formulations,this work improves the existing MT representation and proposed a more general one.A discrete time grid is defined as a reference and all event points are not restricted at these fixed grid points.In addition,continuous time variables are defined and various time-related constraints can be described,which enables accuracy and flexibility of the model.At the same time,the product demand is allocated to each time interval,and material balance is considered on grid points to avoid introducing additional variables.3.The MT modeling framework is applied to the scheduling of the previous continuous process.Based on the discrete time grid and time variables,the transition constraints and energy consumption are described,and operating constraints are refor-mulated.The comparison to the CT model proposed previously and a DT model is demonstrated and the advantages of MT representation are analyzed.4.The MT representation presented in this work can also be used to formulate scheduling problems of batch processes.A network-based batch process is considered with fixed processing times for different tasks.The MILP model is established based on the MT representation.The unit allocation and capacity,time constraints,material balance are modeled and the objective is to minimize the total consumption.The MT model is compared with a traditional DT model for batch processes.