Mathematical Modelling of Non-Permutation Flow Shop Processes with Lot Streaming in the Smart Manufacturing Era

  • Daniel Rossit Engineering Department, Universidad Nacional del Sur, Bahía Blanca, Argentina and INMABB, CONICET, Bahía Blanca, Argentina
  • Fernando Tohmé INMABB, CONICET, Bahía Blanca, Argentina and Economics Department, Universidad Nacional del Sur, Bahía Blanca, Argentina
  • Rodrigo Introcaso Engineering Department, Universidad Nacional del Sur, Bahía Blanca, Argentina
  • Jeanette Rodríguez Engineering Department, Universidad Nacional del Sur, Bahía Blanca, Argentina
Keywords: Scheduling; Mathematical Modelling; Non-Permutation Flow Shop; Lot Streaming; Industry 4.0; Total Tardiness

Abstract

Industry 4.0 is leveraging the production capabilities of the industry. The deep digitalization that Industry 4.0 promotes enables to extend control skills to an exhaustive detail in the shop floors. Then, new planning strategies can be designed and implemented. We present mathematical models to represent non-permutation flow shop processes, incorporating Industry 4.0 features and customer-focused attention. Basically, we study the impact of lot streaming on the ensuing optimization problems, since the work-in-process inventory control is considerably enhanced by Industry 4.0 technologies. Thus, is possible to take advantage of subdividing the production lots into smaller sublots, as lot streaming proposes. To test this hypothesis we use a novel approach to non-permutation flow shop problems which requires a lot streaming strategy, incorporating total tardiness as objective function. Our analysis indicates that lot streaming improves results increasingly with the number of machines. We also find that the improvement is less steep with more sublots, increasing the computational cost of solutions. This indicates that it is highly relevant to fine tune the maximum number of sublots to avoid extra costs.

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References

Benavides, A. J., & Ritt, M. (2016). Two simple and effective heuristics for minimizing the makespan in non-permutation flow shops. Computers & Operations Research, 66, 160-169. https://doi.org/10.1016/j.cor.2015.08.001

Benavides, A. J., & Ritt, M. (2018). Fast heuristics for minimizing the makespan in non-permutation flow shops. Computers & Operations Research, 100, 230-243. https://doi.org/10.1016/j.cor.2018.07.017

Bicakci, P. S., & Kara, İ. (2019). A New Formulation for the Single Machine Order Acceptance and Scheduling Problem with Sequence-Dependent Setup Times. International Journal of Supply and Operations Management, 6(2), 159-167. https://dx.doi.org/10.22034/2019.2.5

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

Conway, R. W., Maxwell, W. L., & Miller, L. W. (1967). Theory of scheduling. Courier Corporation

D'Amico, F., Rossit, D. A. & Frutos, M. (2021). Lot streaming Permutation Flow shop with energy awareness. International Journal of Industrial Engineering and Management, 12(1), 25-36. http://dx.doi.org/10.24867/IJIEM-2021-1-274

Dolgui, A., Ivanov, D., Sethi, S. P., & Sokolov, B. (2019). Scheduling in production, supply chain and Industry 4.0 systems by optimal control: fundamentals, state-of-the-art and applications. International Journal of Production Research, 57(2), 411-432. https://doi.org/10.1080/00207543.2018.1442948

El Hamdi, S., Oudani, M., & Abouabdellah, A. (2019). Towards Identification of the Hierarchical Link between Industry 4.0, Smart Manufacturing and Smart Factory: Concept Cross-Comparison and Synthesis. International Journal of Supply and Operations Management, 6(3), 231-244. https://dx.doi.org/10.22034/2019.3.4

Ferraro, A., Rossit, D., Toncovich, A., & Frutos, M. (2019). Lot streaming flow shop with a heterogeneous machine. Engineering Management Journal, 31(2), 113-126. https://doi.org/10.1080/10429247.2018.1522221

Garey, M. R., Johnson, D. S., & Sethi, R. (1976). The complexity of flowshop and jobshop scheduling. Mathematics of Operations Research, 1(2), 117-129. https://doi.org/10.1287/moor.1.2.117

Graham, R. L., Lawler, E. L., Lenstra, J. K., & Kan, A. R. (1979). Optimization and approximation in deterministic sequencing and scheduling: a survey. In Annals of discrete mathematics 5, 287-326. https://doi.org/10.1016/S0167-5060(08)70356-X

Grassi, A., Guizzi, G., Santillo, L. C., & Vespoli, S. (2020). A semi-heterarchical production control architecture for industry 4.0-based manufacturing systems. Manufacturing Letters, 24, 43-46. https://doi.org/10.1016/j.mfglet.2020.03.007

Ivanov, D., Dolgui, A., Sokolov, B., Werner, F., & Ivanova, M. (2016). A dynamic model and an algorithm for short-term supply chain scheduling in the smart factory industry 4.0. International Journal of Production Research, 54(2), 386-402. https://doi.org/10.1080/00207543.2014.999958

Jain, A. S., & Meeran, S. (2002). A multi-level hybrid framework applied to the general flow-shop scheduling problem. Computers & Operations Research,29(13), 1873-1901. https://doi.org/10.1016/S0305-0548(01)00064-8

Johnson, S. M. (1954). Optimal two‐and three‐stage production schedules with setup times included. Naval research logistics quarterly, 1(1), 61-68. https://doi.org/10.1002/nav.3800010110

Koulamas, C. (1998). A new constructive heuristic for the flowshop scheduling problem. European Journal of Operational Research, 105(1), 66-71. https://doi.org/10.1016/S0377-2217(97)00027-1

Lee, J., Bagheri, B., & Kao, H. A. (2015). A cyber-physical systems architecture for industry 4.0-based manufacturing systems. Manufacturing letters, 3, 18-23. https://doi.org/10.1016/j.mfglet.2014.12.001

Liao, C. J., Liao, L. M., & Tseng, C. T. (2006). A performance evaluation of permutation vs. non-permutation schedules in a flowshop. International Journal of Production Research, 44(20), 4297-4309. https://doi.org/10.1080/00207540600595892

Liao, L. M., & Huang, C. J. (2010). Tabu search for non-permutation flowshop scheduling problem with minimizing total tardiness. Applied Mathematics and Computation, 217(2), 557-567. https://doi.org/10.1016/j.amc.2010.05.089

Nagarajan, V., & Sviridenko, M. (2009). Tight bounds for permutation flow shop scheduling. Mathematics of Operations Research, 34(2), 417-427. https://doi.org/10.1287/moor.1080.0368

Pan, Q. K., Tasgetiren, M. F., Suganthan, P. N., & Chua, T. J. (2011). A discrete artificial bee colony algorithm for the lot-streaming flow shop scheduling problem. Information sciences, 181(12), 2455-2468. https://doi.org/10.1016/j.ins.2009.12.025

Perez, A. T. E., Rossit, D. A., Tohme, F., & Vásquez, Ó. C. (2022). Mass customized/personalized manufacturing in Industry 4.0 and blockchain: Research challenges, main problems, and the design of an information architecture. Information Fusion, 79, 44-57. https://doi.org/10.1016/j.inffus.2021.09.021

Pinedo, M. (2012). Scheduling (Vol. 29). New York: Springer.

Potts, C. N., Shmoys, D. B., & Williamson, D. P. (1991). Permutation vs. non-permutation flow shop schedules. Operations Research Letters, 10(5), 281-284. https://doi.org/10.1016/0167-6377(91)90014-G

Rebaine, D. (2005). Flow shop vs. permutation shop with time delays.Computers & Industrial Engineering, 48(2), 357-362. https://doi.org/10.1016/j.cie.2005.01.019

Rossi, A., & Lanzetta, M. (2014). Native metaheuristics for non-permutation flowshop scheduling. Journal of Intelligent Manufacturing, 25(6), 1221-1233. https://doi.org/10.1007/s10845-012-0724-8

Rossit, D., Tohmé, F., Frutos, M., Bard, J., & Broz, D. (2016). A non-permutation flowshop scheduling problem with lot streaming: A Mathematical model. International Journal of Industrial Engineering Computations, 7(3), 507-516. http://dx.doi.org/10.5267/j.ijiec.2015.11.004

Rossit, D. A., Tohmé, F., & Frutos, M. (2018a). The non-permutation flow-shop scheduling problem: a literature review. Omega, 77, 143-153. https://doi.org/10.1016/j.omega.2017.05.010

Rossit, D. A., Vásquez, Ó. C., Tohmé, F., Frutos, M., & Safe, M. D. (2018b). The dominance flow shop scheduling problem. Electronic Notes in Discrete Mathematics, 69, 21-28. https://doi.org/10.1016/j.endm.2018.07.004

Rossit, D. A., Vásquez, Ó. C., Tohmé, F., Frutos, M., & Safe, M. D. (2021a). A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems. European Journal of Operational Research, 289(3), 841-854. https://doi.org/10.1016/j.ejor.2019.07.055

Rossit, D. A., Toncovich, A., Rossit, D. G. & Nesmachnow, S. (2021b). Solving a flow shop scheduling problem with missing operations in an Industry 4.0 production environment. Journal of Project Management, 6(1), 33-44. http://dx.doi.org/10.5267/j.jpm.2020.10.001

Rudek, R. (2011). Computational complexity and solution algorithms for flowshop scheduling problems with the learning effect. Computers & Industrial Engineering, 61(1), 20-31. https://doi.org/10.1016/j.cie.2011.02.005

Sarin, S. C., & Jaiprakash, P. (2007). Flow shop lot streaming. Springer Science & Business Media.

Stanković, A., Petrović, G., Ćojbašić, Ž., & Marković, D. (2020). An application of metaheuristic optimization algorithms for solving the flexible job-shop scheduling problem. Operational Research in Engineering Sciences: Theory and Applications, 3(3), 13-28. https://doi.org/10.31181/oresta20303013s

Strusevich, V. A., & Zwaneveld, C. M. (1994). On non-permutation solutions to some two machine flow shop scheduling problems. Zeitschrift für Operations Research, 39(3), 305-319. https://doi.org/10.1007/BF01435460

Tandon, M., Cummings, P. T., & LeVan, M. D. (1991). Flowshop sequencing with non-permutation schedules. Computers & chemical engineering, 15(8), 601-607. https://doi.org/10.1016/0098-1354(91)80014-M

Trietsch, D., & Baker, K. R. (1993). Basic techniques for lot streaming. Operations Research, 41(6), 1065-1076. https://doi.org/10.1287/opre.41.6.1065

Wang, Y., Ma, H. S., Yang, J. H., & Wang, K. S. (2017). Industry 4.0: a way from mass customization to mass personalization production. Advances in Manufacturing, 5(4), 311-320. https://doi.org/10.1007/s40436-017-0204-7

Xu, L. D., Xu, E. L., & Li, L. (2018). Industry 4.0: state of the art and future trends. International Journal of Production Research, 56(8), 2941-2962. https://doi.org/10.1080/00207543.2018.1444806

Ying, K. C., Gupta, J. N., Lin, S. W., & Lee, Z. J. (2010). Permutation and non-permutation schedules for the flowline manufacturing cell with sequence dependent family setups. International Journal of Production Research, 48(8), 2169-2184. https://doi.org/10.1080/00207540802534707

Ziaee, M. (2013). General flowshop scheduling problem with the sequence dependent setup times: A heuristic approach. Information Sciences, 251, 126-135. https://doi.org/10.1016/j.ins.2013.06.025

Published
2022-03-25
How to Cite
Rossit, D., Tohmé, F., Introcaso, R., & Rodríguez, J. (2022). Mathematical Modelling of Non-Permutation Flow Shop Processes with Lot Streaming in the Smart Manufacturing Era. Operational Research in Engineering Sciences: Theory and Applications, 5(1), 169-184. https://doi.org/10.31181/oresta250322166r