Material Transfer Operations in Batch Scheduling. A Critical Modeling Issue

An effective short-term scheduling formulation must simultaneously deal with several problem difficulties commonly arising in batch processes operations. One of the key features to be considered is the representation of the material transfer operations between process stages. A nonzero time as well as certain conditions and resources are always required to move the material from one processing stage to the next one according to the specified product recipe. The transfer task consumes a period of time during which a proper synchronization of the equipment units supplying and receiving the material is enforced. Synchronization implies that during the execution of the transfer task, one unit will be supplying the material whereas the other one will be receiving it and consequently, no other task can be simultaneously performed in both units. Most of the existing mixed-integer linear programming (MILP) optimization approaches have traditionally dealt with the batch scheduling problem assuming zero transfer times, and consequently no synchronization, between consecutive processing stages. Simplification relying on negligible transfer times may work properly for the scheduling of multiproduct batch plants with similar product recipes; however, it is demonstrated in this work that ignoring the important role of transfer times may seriously compromise the feasibility of the scheduling whenever shared units and storage tanks, material recycles, or bidirectional flows of products are to be considered. To overcome the serious limitations of current MILP-based scheduling approaches, a general precedence-based framework accounting for nonzero transfer times is introduced. Also, two alternative methods that avoid generating unfeasible schedules are proposed and tested in different case studies.