Continuous Production Scheduling MILP Formulations Using Record Keeping Variables

Most solution methods for mixed-integer linear programming (MILP) production scheduling models have been developed for batch processes. In this paper, we employ integer variables, referred to as record keeping variables (RKVs), into discrete-time continuous production scheduling MILP models that facilitate efficient branching and lead to substantial reductions in solution time. We first introduce different types of RKVs and determine which class of RKVs is the most effective. Second, we explore branching priorities and demonstrate that prioritizing branching on RKVs, relative to other binary variables, leads to further computational improvements. Next, we analyze system attributes, such as task and unit utilization, to determine if prioritizing branching on specific RKVs leads to additional computational enhancements. Our computational results show that the proposed reformulations, in combination with implementing branching priorities, lead to significant computational improvements of continuous production scheduling MILP models.