(733f) Discrete-Time Mixed-Integer Programming Models for Simultaneous Batching and Scheduling in Sequential Environments
In this work, we develop two novel discrete-time mixed integer programming models for simultaneous batching and scheduling in multipurpose facilities with storage constraints. The proposed models adopt two different modeling approaches. The first is based on explicit labeling of the batches of an order. Although each batch is labeled and scheduled individually, they are linked through the order satisfaction constraint, as well as the unit utilization constraint. The second is based on identifying possible unit routings for each order and the corresponding batch size intervals. After batch intervals are identified, the problem becomes an assignment problem where batches of a given order are assigned to different batch size intervals to meet demand. Since it is not trivial to identify unit routings and batch size intervals, we develop an algorithm which only need to be run once for each facility. In addition, we propose extensions for both models that allow us to consider limited shared utilities (both fixed and time-varying) and storage with capacity limits.
We provide illustrative examples to showcase the impact of simultaneously considering (1) batching decisions, (2) limited shared resources, and (3) storage with capacity limits on the final schedule. Finally, we carry out a computational study to understand how instance characteristics, such as expected number of batches per order and uniformity in unit capacities, impact the effectiveness of the proposed models. We show that due to the different modeling approaches adopted, their performance shows a clear trend with respect to instance characteristics. Hence, carefully selecting the model allows us to effectively solve large-scale instances.
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