Scheduling with lot streaming in a two-machine re-entrant flow shop

  • Ferda Can Cetinkaya Department of Industrial Engineering, Çankaya University, Ankara, Turkey
  • Mehmet Duman NERITA, Near East University, TRNC, Mersin 10, Turkey
Keywords: scheduling, lot streaming, re-entrant flow shop, makespan

Abstract

Lot streaming is splitting a job-lot of identical items into several sublots (portions of a lot) that can be moved to the next machines upon completion so that operations on successive machines can be overlapped; hence, the overall performance of a multi-stage manufacturing environment can be improved. In this study, we consider a scheduling problem with lot streaming in a two-machine re-entrant flow shop in which each job-lot is processed first on Machine 1, then goes to Machine 2 for its second operation before it returns to the primary machine (either Machine 1 or Machine 2) for the third operation. For the two cases of the primary machine, both single-job and multi-job cases are studied independently. Optimal and near-optimal solution procedures are developed. Our objective is to minimize the makespan, which is the maximum completion time of the sublots and job lots in the single-job and multi-job cases, respectively. We prove that the single-job problem is optimally solved in polynomial-time regardless of whether the third operation is performed on Machine 1 or Machine 2. The multi-job problem is also optimally solvable in polynomial time when the third operation is performed on Machine 2. However, we prove that the multi-job problem is NP-hard when the third operation is performed on Machine 1. A global lower bound on the makespan and a simple heuristic algorithm are developed. Our computational experiment results reveal that our proposed heuristic algorithm provides optimal or near-optimal solutions in a very short time.

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References

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Published
2021-12-11
How to Cite
Cetinkaya, F. C., & Duman, M. (2021). Scheduling with lot streaming in a two-machine re-entrant flow shop. Operational Research in Engineering Sciences: Theory and Applications, 4(3), 142-175. https://doi.org/10.31181/oresta111221142c