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

When formulating mixed-integer linear programming (MILP) models for production scheduling, the choice of time representation is crucial, as it affects the number of constraints and variables, and thus computational complexity. While many reformulation methods exist for continuous-time models, most research on discrete-time models has focused on batch processes, with less attention being given to continuous processes. As such, we present a discrete-time production scheduling MILP model for continuous processes and reformulate it to incorporate multiple, nonuniformly spaced time grids. We first discuss the benefits of assigning different time grids to units, tasks, and materials and explain why adhering to a uniformly spaced grid, though common practice, may not always be the most effective approach. Next, we present a production scheduling model that considers transient operations. We demonstrate how to reformulate the original model by modifying subsets, parameters, and constraints to generate unique nonuniform time grids while still accurately capturing key process characteristics; these grids can be employed for specific units, tasks, materials, or any combination thereof. Our computational study demonstrates that the proposed reformulation yields notable reductions in the solution time. Moreover, when applied in an industrial setting using a rolling horizon, the models can yield higher-quality solutions.