A Computational Study of Continuous and Discrete Time Formulations for a Class of Short-Term Scheduling Problems for Multipurpose Plants

Abstract

A key decision in scheduling problems is deciding when to perform certain operations, and the quality of solutions depends on how time is represented. The two main classes of time representation are discrete-time approaches (with uniform or nonuniform discretization schemes) and continuous-time approaches. In this work, we compare the performance of these two classes for short-term scheduling of multipurpose facilities with single purpose machines, constant processing times, discrete batches, material splitting, multitasking, and no batch mixing. In addition, the different discretization schemes were compared against each other. We show that, for the modeling framework proposed in this work, the selected discrete-time formulation typically obtained higher quality solutions, and required less time to solve as compared to the selected continuous-time formulation, as the continuous-time formulation exhibited detrimental trade-off between computational time and solution quality. We also show that within the s...