Employing Multiple Nonuniform Discrete-Time Grids for Continuous Production Scheduling MILPs

Area of Science:

• Operations Research
• Chemical Engineering
• Industrial Engineering

Background:

• Mixed-integer linear programming (MILP) is essential for production scheduling.
• Current discrete-time models often focus on batch processes, neglecting continuous ones.
• Uniformly spaced time grids can increase computational complexity in MILP models.

Purpose of the Study:

• To develop a discrete-time MILP model for continuous process scheduling.
• To reformulate existing models to incorporate multiple, nonuniformly spaced time grids.
• To improve the efficiency and solution quality of production scheduling.

Main Methods:

• Developed a discrete-time MILP model for continuous processes.
• Reformulated the model to allow for nonuniform time grids for units, tasks, and materials.
• Modified subsets, parameters, and constraints to generate unique time grids.
• Incorporated transient operations into the scheduling model.

Main Results:

• The proposed reformulation significantly reduces solution time for MILP production scheduling models.
• Nonuniformly spaced time grids accurately capture key process characteristics.
• Application in a rolling horizon setting yielded higher-quality solutions.

Conclusions:

• Discrete-time MILP models for continuous processes benefit from nonuniform time grids.
• The reformulation enhances computational efficiency and solution quality in production scheduling.
• This approach offers practical advantages for industrial scheduling applications.