Discrete and continuous-time formulations for dealing with break periods: Preemptive and non-preemptive scheduling

Abstract

This paper presents new mixed-integer linear programming (MILP) approaches for handling preemption both in discrete and continuous-time scheduling formulations. Preemption refers to the capability of interrupting the execution of a task when encountering a pre-defined break period, assuming that the task continues immediately after the end of such time window. We rely on Generalized Disjunctive Programming to derive the constraints for the continuous-time formulations and on a compact convex hull reformulation to make them computationally efficient. We investigate both the general precedence and multiple time grids representation concepts. Generalization of the discrete-time formulation is simpler, involving a change in the model parameters. Validation and comparison of the mathematical formulations is done through the solution of sixteen benchmark problems, involving instances with one to four sets of breaks. The results show that the general precedence formulation is computationally more effective for flexible flowshops, being outperformed by the discrete-time approach when considering common rather than machine-dependent breaks. For single stage plants with parallel units, the continuous multiple time grid formulation prevails.