Simoltaneous Lot-sizing and Scheduling in Hybrid Flow Shop Production Environment with Resource Constraint

Document Type: Research Paper


1 Department of Economic and Management, Semnan University, Semnan, Iran

2 Department of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran


The aim of this Paper is to study a multi-product, multi-period production systems in a hybrid flow shop so that lot-sizing and scheduling will be detemined simultaneously. A new mixed-integer programming model is proposed to formulate the studied problem. The objective function in this investigation includes the total cost of production, inventory and external supply. In the case of not satisfying the demand of customers, this demand should be met by foreign suppliers with higher price. The simultaneous lot-sizing and scheduling problem are classified in strongly NP-hard class. Due to the high computational complexity of the studied problem, particle swarm optimization (PSO) and imperialist competitive algorithms (ICA) are implemented for solving the considered problem. The algorithms explore the solution space for both lot-sizing and scheduling and find a combination of production plan and sequence that is feasible and close to optimum. First, the implemented algorithms are used for solving randomly generated instances with different sizes. Then, these methods are used to solve the case of tile industry and the obtained results by two methods are compared with each other. Computational experiences show that the algorithms are able to achieve good-quality solutions for the problem in a reasonable time. Also, the results of ICA are better than PSO results for the mentioned case study.


Main Subjects

  1. Wagner, H. M. and Whithin, T. M. (1958). “Dynamic version of the economic lot size model”, Management Science, Vol. 5, No. 1, PP. 89– 96.
  2. Gupta, D. and Magnusson, T. (2005). “The capacitated lot-sizing and scheduling problem with sequence-dependent setup costs and setup times”, Computers & Operations Research, Vol. 32, No. 4, PP. 727– 747.
  3. Almada-Lobo, B., Klabjan, D., Carravilla, M. A. and Oliveira, J. (2007). “Single machine multiproduct capacitated lotsizing with sequence-dependent setups”, International Journal of Production Research, Vol. 45, No. 20, PP. 4873– 4894.
  4. James, R. J. W. and Almada-Lobo, B. (2011). “Single and parallel machine capacitated lotsizing and scheduling: New iterative MIP-based neighborhood search heuristics”, Computers & Operations Research, Vol. 38, No. 12, PP. 1816- 1825.
  5. Buschkühl, L., Sahling, F., Helber, S. and Tempelmeier, H. (2010). “Dynamic capacitated lot-sizing problems: A classification and review of solution approaches”, OR Spectrum, Vol. 32, No. 2, PP. 231– 261.
  6. Kimms, A. (1996). “Multi-level, single-machine lotsizing and scheduling (with initial inventory)”, European Journal of Operational Research, Vol. 89, No. 1, PP. 86– 99.
  7. Kimms, A. and Drexl, A. (1998). “Some insights into proportional lotsizing and scheduling”, Journal of the Operational Research, Vol. 49, No. 11, PP. 1196- 1205.
  8. Fandel, G. and Stammen-Hegene, C. (2006). “Simultaneous lot sizing and scheduling for multi-product multi-level production”, International Journal of Production Economics, Vol. 104, No. 2, PP. 308– 316.
  9. Mohammadi, M., Fatemi Ghomi, S. M. T., Karimi, B. and Torabi, S. A. (2010). “Rolling-horizon and fix-and-relax heuristics for the multi-product multi-level capacitated lotsizing problem with sequence-dependent setups”, Journal of Intelligent Manufacturing, Vol. 21, No. 4, PP. 501– 510.
  10. Mohammadi, M., Karimi, B., Fatemi Ghomi, S. M. T. and Torabi, S. A. (2010). “A new algorithmic approach for capacitated lot-sizing problem in flow shops with sequence-dependent setups”, International Journal of Advanced Manufacturing Technology, Vol. 49, No. 1, PP. 201– 211.
  11. Clark, A. R. and Clark, S. J. (2000). “Rolling-horizon lot-sizing when setup times are sequence-dependent”, International Journal of Production Research, Vol. 38, No. 10, PP. 2287– 2308.
  12. Mohammadi. M., Fatemi Ghomi. S. M. T. and Jafari, N. (2011). “A genetic algorithm for simultaneous lotsizing and sequencing of the permutation flow shops with sequence-dependent setups”, International Journal of Computer Integrated Manufacturing, Vol. 24, No. 1, PP. 87– 93.
  13. Ramezanian, R., Saidi-Mehrabad, M. and Fattahi, P. (2013). “Integrated lot-sizing and scheduling with overlapping for multi-level capacitated production system”, International Journal of Computer Integrated Manufacturing, Vol. 26, No. 7, PP. 681- 695.
  14. Ramezanian, R., Saidi-Mehrabad, M. and Fattahi, P. (2013). “MIP formulation and heuristics for multi-stage capacitated lot-sizing and scheduling problem with availability constraints”, Journal of Manufacturing Systems, Vol. 32, No. 2, PP. 392- 401.
  15. Ramezanian, R., Shafiei-Nikabadi, M. and Fallah, S. (2014). “Particle swarm optimization algorithm for integrated lot-sizing and scheduling in the flow shop production environment”, Journal of Industrial Engineering (University of Tehran), Vol. 48, No. 2, PP. 215- 228.
  16. Babaei, M. Affiliated withDepartment of Industrial Engineering, Faculty of Engineering, Kharazmi University, Mohammadi, M. and Fatemi Ghomi, S. M. T. (2013). “A genetic algorithm for the simultaneous lot sizing and scheduling problem in capacitated flow shop with complex setups and backlogging”, International Journal of Advanced Manufacturing Technology, Vol. 70, No. 1- 4, PP. 125- 134.
  17. Urrutia, E. D. G., Aggoune, R. and Dauzère-Pérès, S. (2014). “Solving the integrated lot-sizing and job-shop scheduling problem”, International Journal of Production Research, Vol. 52, No. 17, PP. 5236– 5254.
  18. Wolosewicz, C., Dauzère-Pérès, S. and Aggoune, R. (2015). “A lagrangian heuristic for an integrated lot-sizing and fixed scheduling problem”, European Journal of Operational Research, Vol. 244, No. 1, PP. 3–12.
  19. Glover, F. and Kochenberger, G. (2005). Handbook of metaheuristics, Kluwer Academic Publishers, Norwell.
  20. Eberhart, R. and Kennedy, J. (1995). “A New Optimizer Using Particles Swarm Theory”, Proc. Sixth International Symposium on Micro Machine and Human Science (Nagoya, Japan), IEEE Service Center, Piscataway, NJ, PP. 39- 43.
  21. Kennedy, J. and Eberhart, R. (1995). “Particle Swarm Optimization”, IEEE Conference on Neural Networks, (Perth, Australia), Piscataway, NJ, IV, PP. 1942- 1948.
  22. Shi, Y. and Eberhart, R. C. (1998). “A modified particle swarm optimizer”, In Proceedings of the IEEE Congress on Evolutionary Computation, PP. 69– 73.
  23. Pinedo, M. (2008). Scheduling: Theory, algorithms and systems, 3rd edition, Springer.
  24. Atashpaz-Gargari E. and Lucas, C. (2007). “Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition”, IEEE Congress on Evolutionary Computation Singapore, PP. 4661–4667.
  25. Riane, F. (1998). Scheduling hybrid flowshops: Algorithms and applications, PhD thesis, CREGI-FUCaM, Belgium.