Combining the advantages of discrete- and continuous-time scheduling models: Part 1. Framework and mathematical formulations

We propose a general method for the solution of chemical production scheduling problems in network environments. The method consists of three stages. In the first stage, a discrete-time mixed-integer programming (MIP) model is solved to quickly obtain an approximate solution. In the second stage, the solution is mapped onto newly introduced unit- and material-specific continuous-time grids, using a mapping algorithm. In the third stage, a continuous-time linear programming (LP) model is solved to improve the accuracy of the mapped discrete-time solution by refining the timing of events and batch sizes. The proposed method takes advantage of the complementary strengths of discrete- and continuous-time formulations, which enables us to not only handle various processing features (e.g., intermediate deliveries and orders, time-varying resource availability and cost, variable processing times), but also obtain order of magnitude speedups in the solution of large-scale instances.