Journal of Scheduling

, Volume 14, Issue 5, pp 483–500 | Cite as

A water-flow algorithm for flexible flow shop scheduling with intermediate buffers

  • Trung Hieu TranEmail author
  • Kien Ming Ng


We investigate the flexible flow shop scheduling problem with limited or unlimited intermediate buffers. A common objective of the problem is to find a production schedule that minimizes the completion time of jobs. Other objectives that we also consider are minimizing the total weighted flow time of jobs and minimizing the total weighted tardiness time of jobs. We propose a water-flow algorithm to solve this scheduling problem. The algorithm is inspired by the hydrological cycle in meteorology and the erosion phenomenon in nature. In the algorithm, we combine the amount of precipitation and its falling force to form a flexible erosion capability. This helps the erosion process of the algorithm to focus on exploiting promising regions strongly. To initiate the algorithm, we use a constructive procedure to obtain a seed permutation. We also use an improvement procedure for constructing a complete schedule from a permutation that represents the sequence of jobs in the first stage of the scheduling problem. To evaluate the proposed algorithm, we use benchmark instances taken from the literature and randomly generated instances of the scheduling problem. The computational results demonstrate the efficacy of the algorithm. We have also obtained several improved solutions for the benchmark instances using the proposed algorithm. We further illustrate the algorithm’s capability for solving problems in practical applications by applying it to a maltose syrup production problem.


Water-flow algorithm Metaheuristic Flexible flow shop scheduling Intermediate buffers 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Akturk, M. S., & Yildirim, M. B. (1998). A new lower bounding scheme for the total weighted tardiness problem. Computers and Operations Research, 25(4), 265–278. CrossRefGoogle Scholar
  2. Azizoglu, M., Cakmak, E., & Kondakci, S. (2001). A flexible flow shop problem with total flow time minimization. European Journal of Operational Research, 132(3), 528–538. CrossRefGoogle Scholar
  3. Goudie, A. (1993). The nature of the environment. Oxford: Blackwell Sci. Google Scholar
  4. Grabowski, J., & Pempera, J. (2000). Sequencing of jobs in some production system. European Journal of Operational Research, 125(3), 535–550. CrossRefGoogle Scholar
  5. Holy, M. (1982). Erosion and environment. Elmsford: Pergamon. Google Scholar
  6. Hull, P. (2010). Glucose syrups: Technology and applications. New York: Wiley–Blackwell. CrossRefGoogle Scholar
  7. Kim, I. K., Jung, D. W., & Park, R. H. (2002). Document image binarization based on topographic analysis using a water flow model. Pattern Recognition, 35(1), 265–277. CrossRefGoogle Scholar
  8. 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), 925–936. CrossRefGoogle Scholar
  9. Oh, H. H., Lim, K. T., & Chien, S. I. (2005). An improved binarization algorithm based on a water flow model for document image with inhomogeneous backgrounds. Pattern Recognition, 38(12), 2612–2625. CrossRefGoogle Scholar
  10. Pedersen, S., & Vang-Hendriksen, H. (2001). Method for production of maltose and/or enzymatically modified starch. World Intellectual Property Organization, International Publication Number: WO 01/16349 A1. Google Scholar
  11. Pinedo, M. (2005). Planning and scheduling in manufacturing and services. New York: Springer. Google Scholar
  12. Quadt, D., & Kuhn, H. (2007). A taxonomy of flexible flow line scheduling procedures. European Journal of Operational Research, 178(3), 686–698. CrossRefGoogle Scholar
  13. Ribas, I., Leisten, R., & Framinan, J. M. (2010). Review and classification of hybrid flow shop scheduling problems from a production system and a solutions procedure perspective. Computers and Operations Research, 37(8), 1439–1454. CrossRefGoogle Scholar
  14. Ruiz, R., & Vazquez-Rodriguez, J. A. (2010). The hybrid flow shop scheduling problem. European Journal of Operational Research, 205(1), 1–18. CrossRefGoogle Scholar
  15. Sawik, T. (2000). Mixed integer programming for scheduling flexible flow lines with limited intermediate buffers. Mathematical and Computer Modeling, 31(13), 39–52. CrossRefGoogle Scholar
  16. Sawik, T. (2001). Mixed integer programming for scheduling surface mount technology lines. International Journal of Production Research, 39(14), 3219–3235. CrossRefGoogle Scholar
  17. Shah-Hosseini, H. (2007). Problem solving by intelligent water drops. Proceedings IEEE Congress on Evolutionary Computation CEC, 2007, 3226–3231. CrossRefGoogle Scholar
  18. Shah-Hosseini, H. (2008). Intelligent water drops algorithm: A new optimization method for solving the multiple knapsack problem. International Journal of Intelligent Computing and Cybernetics, 1(2), 193–212. CrossRefGoogle Scholar
  19. Shah-Hosseini, H. (2009). The intelligent water drops algorithm: a nature-inspired swarm-based optimization algorithm. International Journal of Bio-Inspired Computation, 1(1–2), 71–79. CrossRefGoogle Scholar
  20. Sherali, H. D., Sarin, S. C., & Kodialam, M. S. (1990). Models and algorithms for a two-stage production process. Production Planning and Control, 1(1), 27–39. CrossRefGoogle Scholar
  21. Tang, L. X., & Xuan, H. (2006). Lagrangian relaxation algorithms for real-time hybrid flowshop scheduling with finite intermediate buffers. Journal of the Operational Research Society, 57(3), 316–324. CrossRefGoogle Scholar
  22. Tavakkoli-Moghaddam, R., Safaei, N., & Sassani, F. (2009). A memetic algorithm for the flexible flow line scheduling problem with processor blocking. Computers and Operations Research, 36(2), 402–414. CrossRefGoogle Scholar
  23. Wardono, B. (2001). Algorithms for the multi-stage parallel machine problem with buffer constraints. Ph.D. dissertation, North Carolina State University. Google Scholar
  24. Wardono, B., & Fathi, Y. (2004). A tabu search algorithm for the multi-stage parallel machine problem with limited buffer capacities. European Journal of Operational Research, 155(2), 380–401. CrossRefGoogle Scholar
  25. Wittrock, R. J. (1988). An adaptable scheduling algorithm for flexible flow lines. Operations Research, 36(3), 445–453. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Industrial and Systems EngineeringNational University of SingaporeSingaporeSingapore

Personalised recommendations