Abstract
We consider the two-machine flow-shop serial-batching scheduling problem where the machines have a limited capacity in terms of the number of jobs. Two criteria are considered here. The first criterion is the number of batches to be minimized. This criterion reflects situations where processing of any batch induces a fixed cost, which leads to a total cost proportional to the number of batches. The second criterion is the makespan. This model is relevant in different production contexts, especially when considering joint production and inbound delivery scheduling. We study the complexity of the problem and propose two polynomial-time approximation algorithms with a guaranteed performance. The effectiveness of these algorithms is evaluated using numerical experiments. Exact polynomial-time algorithms are also provided for some particular cases.
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