Generalized Disjunctive Programming as a Systematic Modeling Framework to Derive Scheduling Formulations

We propose linear generalized disjunctive programming (GDP) models for the short-term scheduling problem of single stage batch plants with parallel units. Three different concepts of continuous-time representation are explored, immediate and general precedence, as well as multiple time grids. The linear GDP models are then reformulated using both big-M and convex hull reformulations, and the resulting mixed-integer linear programming models compared through the solution of a set of example problems. We show that two general precedence models from the literature can be derived using a big-M reformulation for a set of disjunctions and a convex hull reformulation for another. The best performer is, however, a multiple time grid model which can be derived from the convex hull reformulation followed by simple algebraic manipulations to eliminate the disaggregated variables and reduce the sets of constraints, thus leading to a more compact and efficient formulation.