Computational enhancements of continuous production scheduling MILPs using tightening constraints

In this paper, we propose employing tightening constraints, based on known system information, into discrete-time continuous production scheduling models to enhance their computational performance. We first establish a model with transient operations such as startups, shutdowns, and direct transitions. We propose a demand propagation algorithm (DPA), implemented as a preprocessing step, that utilizes demand information and other known system parameters to calculate parameters which are later used in a series of constraints to tighten the feasible space of the linear programming (LP) relaxation of the mixed-integer linear programming (MILP) problem. This reduces the branching required to close the optimality gap which consequently decreases solution times. We present computational results that show our proposed method can lead to over an order of magnitude reduction in solution times.