Detailed scheduling of batch production in a cell with parallel facilities and common renewable resources

The problem of scheduling production in a cell consisting of several parallel facilities, which arises in many process industries, is addressed. The cell produces a variety of items in required quantities. The production of an item requires an operation, which may be performed on one of a subset of the parallel facilities, and it consumes some base products at given rates. There are constrained resources and structural constraints. Resetting a facility to change from one operation to another may necessitate time-consuming changeover. The problem is solved first by assuming that changeover times are negligible. This leads to forming complete schedules by combining in sequence a number of elementary production schedules (EPS), such that an objective function related to production cost is minimized. During each EPS, and therefore throughout the schedule, all constraints are respected. Subsequently, the EPSs are sequenced to minimize the number of changeovers among operations. Finally, all operations, including changeovers, are scheduled such that the makespan is minimized, while preserving precedence relationships among the operations such that the feasibility of the overall schedule is maintained. The paper presents the overall approach, the models constructed for each sub-problem and the algorithms developed to solve these models. Illustrative examples and results of computational testing are given.