Abstract

In this study, a mathematical model for the integration of lot sizing and flow shop scheduling with lot streaming was proposed. A mixed-integer linear model for multi-product lot sizing and lot streaming problem was developed. Mixed-integer programming formulation is proposed which will enable user to identify optimal production quantities, inventory levels, sub lot sizes and sequences simultaneously. Two situations where considered: 1) all machines are available and 2) all machines need preventive maintenance tasks. For both situations a new mixed-integer formulation is developed. To demonstrate the practicality of the proposed model, numerical example was used. It is shown that, the best makespan can be achieved through consistent sublots with intermingling cases as compared to non-intermingling cases.

Keywords:

Flow shop scheduling, lot sizing, lot streaming, mixed integer programming, preventive maintenance,

References

1. Biskup, D. and M. Feldmann, 2005. Lot streaming with variable sublots: An integer programming formulation. J. Oper. Res. Soc., 57(3): 296-303.
   CrossRef    
2. Chang, J.H. and H.N. Chiu, 2005. A comprehensive review of lot streaming. Int. J. Prod. Res., 43(8): 1515-1536.
   CrossRef    
3. Chiu, H., J. Chang and C. Lee, 2004. Lot streaming models with a limited number of capacitated transporters in multistage batch production systems. Comput. Oper. Res., 31(12): 2003-2020.
   CrossRef    
4. Feldmann, M. and D. Biskup, 2008. Lot streaming in a multiple product permutation flow shop with intermingling. Int. J. Prod. Res., 46(1): 197-216.
   CrossRef    
5. Glass, C.A. and E. Possani, 2011. Lot streaming multiple jobs in a flow shop. Int. J. Prod. Res., 49(9): 2669-2681.
   CrossRef    
6. Johnson, S.M., 1954. Optimal two-and three-stage production schedules with setup times included. Naval Res. Logist. Q., 1(1): 61-68.
   CrossRef    
7. Kalir, A.A. and S.C. Sarin, 2000. Evaluation of the potential benefits of lot streaming in flow-shop systems. Int. J. Prod. Econ., 66(2): 131-142.
   CrossRef    
8. Kalir, A.A. and S.C. Sarin, 2003. Constructing near optimal schedules for the flow-shop lot streaming problem with sublot-attached setups. J. Comb. Optim., 7(1): 23-44.
   CrossRef    
9. Li, Z. and M.G. Ierapetritou, 2010. Production planning and scheduling integration through augmented lagrangian optimization. Comput. Chem. Eng., 34(6): 996-1006.
   CrossRef    
10. Palaniappan, P.K. and N. Jawahar, 2011. A genetic algorithm for simultaneous optimisation of lot sizing and scheduling in a flow line assembly. Int. J. Prod. Res., 49(2): 375-400.
    CrossRef    
11. Ramezanian, R., M. Saidi-Mehrabad and P. Fattahi, 2013. MIP formulation and heuristics for multi-stage capacitated lot-sizing and scheduling problem with availability constraints. J. Manuf. Syst., 32(2): 392-401.
    CrossRef    
12. Sarin, S.C. and P. Jaiprakash, 2007. Flow Shop Lot Streaming Problems. Springer, New York.
    CrossRef    
13. Trietsch, D. and K.R. Baker, 1993. Basic techniques for lot streaming. Oper. Res., 41(6): 1065-1076.
    CrossRef    
14. Yan, H. and X. Zhang, 2007. A case study on integrated production planning and scheduling in a three-stage manufacturing system. IEEE T. Autom. Sci. Eng., 4(1): 86-92.
    CrossRef    
15. Yan, H., Q. Xia, M. Zhu, X. Liu and Z. Guo, 2003. Integrated production planning and scheduling on automobile assembly lines. Iie Trans., 35(8): 711-725.
    CrossRef    
16. Zhang, W., C. Yin, J. Liu and R.J. Linn, 2005. Multi-job lot streaming to minimize the mean completion time in m-1 hybrid flowshops. Int. J. Prod. Econ., 96(2): 189-200.
    CrossRef    

Competing interests

The authors have no competing interests.

Open Access Policy

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Copyright

The authors have no competing interests.