Skip to main content
SpringerLink
Log in

The evolution of schematic representations of flow shop scheduling problems

  • Published:
Journal of Scheduling Aims and scope Submit manuscript

Abstract

The schematic representation of schedules has been a useful tool for researchers; in this paper, we review existing network-based schematics for flow shop models. We also propose new schematics for flow shops with blocking, synchronous transfers, no-wait processing, no-idle time and limited buffer space. Using schematics, we explain some of the past findings and present new results. We also explain flow shop anomalies/paradoxes. Finally, we propose schematics for four flow shop models using the concept of string analog.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Adiri, I., & Poholyres, D. (1982). Flow-shop/no-idle or no-wait scheduling to minimize the sum of completion times. Naval Research Logistics Quarterly, 29, 495–504.

    Article  Google Scholar 

  • Akers, S. B. (1956). Letter to the editor—A graphical approach to production scheduling problems. Operations Research, 4(2), 244–245.

    Article  Google Scholar 

  • Bagchi, T., Gupta, J. N. D., & Sriskandarajah, C. (2006). A review of TSP based approaches for flows hop scheduling. European Journal of Operational Research, 169, 816–854.

    Article  Google Scholar 

  • Bokor, O., Szenik, G., & Kocsis, T. (2011). Application of evaluation lines in the analysis of time-type data of project plans. In C. Egbu & E. C. W. Lou (Eds.), Proceedings of the 27th annual ARCOM conference (pp. 819–827). Bristol: Association of Researchers in Construction Management.

    Google Scholar 

  • Chang, J. H., & Chiu, H. N. (2005). A comprehensive review of lot streaming. International Journal of Production Research, 43(8), 1515–1536.

    Article  Google Scholar 

  • Chen, J., & Steiner, G. (1997). Approximation methods for discrete lot streaming in flow shops. Operations Research Letters, 21(3), 139–145.

    Article  Google Scholar 

  • Cheng, T. E., Gupta, J. N. D., & Wang, G. (2000). A review of flow shop scheduling research with setup times. Production and Operations Management, 9(3), 262–282.

    Article  Google Scholar 

  • Cheng, M., Mukherjee, N. J., & Sarin, S. C. (2013). A review of lot streaming. International Journal of Production Research, 51(23–24), 7023–7046.

    Article  Google Scholar 

  • Conway, R., Maxwell, W., McClain, J. O., & Thomas, L. J. (1988). The role of work-in-process inventory in serial production lines. Operations Research, 36(2), 229–241.

    Article  Google Scholar 

  • Conway, R. W., Maxwell, W. L., & Miller, L. W. (1967). Theory of scheduling. Reading, MA: Addison-Wesley.

    Google Scholar 

  • Dudek, R. A., Panwalkar, S. S., & Smith, M. L. (1992). The lessons of flow shop scheduling research. Operations Research, 40(1), 7–13.

    Article  Google Scholar 

  • Eiselt, H. A., & Sandblom, C. L. (2013). Decision analysis, location models, and scheduling problems. Cham: Springer.

    Google Scholar 

  • Emmons, H., & Vairaktarakis, G. (2012). Flow shop scheduling: theoretical results, algorithms, and applications (Vol. 182). Cham: Springer.

    Google Scholar 

  • Fernandez-Viagas, V., Ruiz, R., & Framinan, J. M. (2017). A new vision of approximate methods for the permutation flow shop to minimize makespan: State-of-the-art and computational evaluation. European Journal of Operational Research, 257, 707–721.

    Article  Google Scholar 

  • Fondahl, J. W. (1962). A non-computer approach to the critical path method for the construction industry. Technical Report No. 9, Construction Institute, Department of Civil Engineering, Stanford University, CA.

  • Gantt, H. L. (1903). A graphical daily balance in manufacture. Transactions of the American Society of Mechanical Engineers, XXIV, 1322–1336.

    Google Scholar 

  • Garey, M. R., Johnson, D. S., & Sethi, R. (1976). The complexity of flow shop and job shop scheduling. Mathematics of Operations Research, 1(2), 117–129.

    Article  Google Scholar 

  • Gupta, J. N. D. (1979). A review of flow shop scheduling research. In Larry Ritzman, et al. (Eds.), Disaggregation: Problems in manufacturing and service organizations. Boston, MA: Martinus Nijhoff Publications.

    Google Scholar 

  • Gupta, J. N. D., & Stafford, E. F., Jr. (2006). Flow shop scheduling research after five decades. European Journal of Operational Research, 169, 375–381.

    Google Scholar 

  • Hall, N. G., & Sriskandarajah, C. (1996). A survey of machine scheduling problems with blocking and no-wait in process. Operations Research, 44(3), 510–525.

    Article  Google Scholar 

  • Hejazi, S. R., & Saghafian, S. (2005). Flow shop-scheduling problems with makespan criterion: A review. International Journal of Production Research, 43, 2895–2929.

    Article  Google Scholar 

  • Herrmann, J. W. (2010). The perspectives of Taylor, Gantt, and Johnson: How to improve production scheduling. International Journal of Operations and Quantitative Management, 16(3), 243–254.

    Google Scholar 

  • Johnson, S. M. (1954). Optimal two- and three-stage production schedules with setup times included. Naval Research Logistics, 1(1), 61–68.

    Article  Google Scholar 

  • Kalczynski, P. J., & Kamburowski, J. (2007). On no-wait and no-idle flow shops with makespan criterion. European Journal of Operational Research, 178(3), 677–685.

    Article  Google Scholar 

  • Kamburowski, J. (2004). More on three-machine no-idle flow shops. Computers & Industrial Engineering, 46(3), 461–466.

    Article  Google Scholar 

  • Kis, T., & Pesch, E. (2005). A review of exact solution methods for the non-preemptive multiprocessor flow shop problem. European Journal of Operational Research, 164, 592–608.

    Article  Google Scholar 

  • Kuhpfahl, J. (2016). Job shop scheduling—Formulation and modeling. In J. Kuhpfahl (Ed.), Job shop scheduling with consideration of due dates (pp. 9–23). Wiesbaden: Springer Gabler.

    Chapter  Google Scholar 

  • Lee, C. Y., & Chen, Z. L. (2001). Machine scheduling with transportation considerations. Journal of Scheduling, 4(1), 3–24.

    Article  Google Scholar 

  • Linn, R., & Zhang, W. (1999). Hybrid flow shop scheduling: A survey. Computers & Industrial Engineering, 37, 57–61.

    Article  Google Scholar 

  • Mascis, A., & Pacciarelli, D. (2000). Machine scheduling via alternative graphs. University of Rome, Rome, Italy, Technical Report DIA-46-2000.

  • McCormick, S. T., Pinedo, M. L., Shenker, S., & Wolf, B. (1989). Sequencing in an assembly line with blocking to minimize cycle time. Operations Research, 37(6), 925–935.

    Article  Google Scholar 

  • Minella, G., Ruiz, R., & Ciavotta, M. (2008). A review and evaluation of multi objective algorithms for the flow shop scheduling problem. INFORMS Journal on Computing, 20, 451–471.

    Article  Google Scholar 

  • Minty, G. J. (1957). Letter to the editor—A comment on the shortest-route problem. Operations Research, 5(5), 724.

    Article  Google Scholar 

  • Neufeld, J. S., Gupta, J. N. D., & Buscher, U. (2016). A comprehensive review of flow shop group scheduling literature. Computers & Operations Research, 70, 56–74.

    Article  Google Scholar 

  • Nowicki, E. (1999). The permutation flow shop with buffers: A tabu search approach. European Journal of Operational Research, 116(1), 205–219.

    Article  Google Scholar 

  • Nowicki, E., & Smutnicki, C. (1996). A fast tabu search algorithm for the permutation flow-shop problem. European Journal of Operational Research, 91(1), 160–175.

    Article  Google Scholar 

  • Panwalkar, S. S. (1991). Scheduling of a two-machine flow shop with travel time between machines. Journal of the Operational Research Society, 42, 609–613.

    Article  Google Scholar 

  • Papadimitriou, C. H., & Kanellakis, P. C. (1980). Flow shop scheduling with limited temporary storage. Journal of the ACM, 27(3), 533–549.

    Article  Google Scholar 

  • Pinedo, M. (2008). Scheduling, theory, algorithms, and systems. New York: Springer.

    Google Scholar 

  • Reisman, A., Kumar, A., & Motwani, J. (1997). Flow shop scheduling/sequencing research: A statistical review of the literature, 1952–1994. IEEE Transactions on Engineering Management, 44, 316–329.

    Article  Google Scholar 

  • Rigby, F. D. (1971). Scheduling, sequencing and networks (No. Serial-T-243). George Washington University, Washington DC, Program in logistics.

  • Rigby, F. D. (1975). Private Communication.

  • Ruiz, R., & Maroto, C. (2005). A comprehensive review and evaluation of permutation flow shop heuristics. European Journal of Operational Research, 165(2), 479–494.

    Article  Google Scholar 

  • Ruiz, R., & Vazquez-Rodriguez, J. A. (2010). The hybrid flow shop scheduling problem. European Journal of Operational Research, 205, 1–18.

    Article  Google Scholar 

  • Smith, M. L., Panwalkar, S. S., & Dudek, R. A. (1975). Flow shop sequencing problem with ordered processing time matrices. Management Science, 21(5), 544–549.

    Article  Google Scholar 

  • Smith, M. L., Panwalkar, S. S., & Dudek, R. A. (1976). Flow shop sequencing problem with ordered processing time matrices: A general case. Naval Research Logistics, 23(3), 481–486.

    Article  Google Scholar 

  • Smutnicki, C. (1998). A two-machine permutation flow shop scheduling problem with buffers. Operations-Research-Spektrum, 20(4), 229–235.

    Article  Google Scholar 

  • Soylu, B., Kirca, Ö., & Azizoğlu, M. (2007). Flow shop-sequencing problem with synchronous transfers and makespan minimization. International Journal of Production Research, 45(15), 3311–3331.

    Article  Google Scholar 

  • Spencer, D. L. (1969). An investigation of the relationships between the sequencing and scheduling problems. Doctoral dissertation, Texas Tech University.

  • Spieksma, F. C., & Woeginger, G. J. (2005). The no-wait flow-shop paradox. Operations Research Letters, 33(6), 603–608.

    Article  Google Scholar 

  • Stern, H. I., & Vitner, G. (1990). Scheduling parts in a combined production-transportation work cell. Journal of the Operational Research Society, 41, 625–632.

    Article  Google Scholar 

  • Waldherr, S., & Knust, S. (2015). Complexity results for flow shop problems with synchronous movement. European Journal of Operational Research, 242(1), 34–44.

    Article  Google Scholar 

  • Weaver, P. (2006). A brief history of scheduling: Back to the future. In Proceedings of the 2006 myPrimavera06 conference, Canberra.

  • Wilson, J. M. (2003). Gantt charts: A centenary appreciation. European Journal of Operational Research, 149(2), 430–437.

    Article  Google Scholar 

  • Yenisey, M. M., & Yagmahan, B. (2014). Multi-objective permutation flow shop scheduling problem: Literature review, classification and current trends. Omega, 45, 119–135.

    Article  Google Scholar 

  • Ying, K. C., & Liao, C. J. (2004). An ant colony system for permutation flow-shop sequencing. Computers & Operations Research, 31(5), 791–801.

    Article  Google Scholar 

Download references

Acknowledgements

We would like to thank the Associate Editor and the referees for their valuable comments; these comments helped us improve an earlier version of this paper.

Author information

Authors and Affiliations

  1. Carey Business School, Johns Hopkins University, 100 International Drive, Baltimore, MD, 21202, USA

    S. S. Panwalkar

  2. Department of ISBA, College of Business, Florida International University, Miami, FL, 33199, USA

    Christos Koulamas

Authors
  1. S. S. Panwalkar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christos Koulamas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christos Koulamas.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Panwalkar, S.S., Koulamas, C. The evolution of schematic representations of flow shop scheduling problems. J Sched 22, 379–391 (2019). https://doi.org/10.1007/s10951-018-0594-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10951-018-0594-9

Keywords

Search

Navigation