An improved mixed integer linear formulation and lower bounds for minimizing makespan on a flow shop with batch processing machines

This paper considers a flow shop scheduling problem with batch processing machines. Each batch processing machine has a limited capacity and can process a group of jobs, each of them having a different known capacity requirement, simultaneously. Job processing time on each machine is known and arbitrary. The processing time of a batch on each machine is the longest processing time of all jobs in the batch. We improve the only existing mixed integer linear formulation (MILF) of the problem through significant reduction in size complexity of the model. Results justify that the improved MILF is clearly more efficient in reducing the required time for obtaining optimal makespan of small-size problems, in comparison with the existing MILF. Motivated by relaxing variety of the problem assumptions, several valid lower bounds on the optimal makespan are also proposed that can furtheraccelerate obtaining optimal solution through proposed MILF. Robustness evaluation of each bound under the different problem settings is reported through computations.