The study of time representations for chemical production scheduling models

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Shao, Fanglin
Scheduling , MILP
Optimal scheduling has been extensively investigated in the Process Systems Engineering (PSE) community. Most of the existing mathematical programming models for scheduling can be classified into two categories in terms of the time representation: 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 studied 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 framework that uses discrete time grids and continuous time variables to describe time. The main research contents of this thesis are as follows: 1. For the scheduling of a continuous process 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, as well as sequence-dependent transition, processing time constraints, and boundary constraints. The CT formulation is compared with an existing DT formulation in terms of model scale and solution accuracy. 2. A new MT presentation based model is proposed for the continuous process scheduling problem. In this model, a discrete time grid is adopted as a reference and the event points are not restricted to the fixed grid points. In addition, continuous time variables are introduced to represent the deviation of event points to the discrete time grid. The MT model is more precise in modeling time and often includes fewer integer variables than the CT model. 3. The MT representation is also applied to the scheduling of a batch process, which has multiple tasks with fixed processing times. The MILP model includes unit allocation and capacity constraints, time balance constraints, and an objective to minimize the total cost. The computational results demonstrate the advantage of the MT model over the DT model for the batch process.
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