A stochastic production planning problem in hybrid manufacturing and remanufacturing systems with resource capacity planning

Abstract

Hybrid manufacturing and remanufacturing systems have become a topic of considerable interest in the advanced manufacturing industry due in part to the profit and cost saving by reusing remaufacturable parts in the end-of-use products. In this paper, we investigate a production planning problem in such a hybrid system with the integration of resource capacity planning that is shared by both manufacturing and remanufacturing processes. Due to the uncertain nature in practice, both new and remanufactured product demands are stochastic. Taking a scenario-based approach to express the stochastic demands according to the historical data, we formulate the stochastic aggregate production planning problem as a mixed integer linear programming (MILP) model. Based on the Lagrangian relaxation (LR) technique, the MILP model is decomposed into four sets of sub-problems. For these sub-problems, four heuristic procedures are developed, respectively. Then, a LR based heuristic for the main problem is proposed and further tested on a large set of problem instances. The results show that the algorithm generates solutions very close to optimums in an acceptable time. At last, the impact of demands uncertainty on the solution is analyzed by the sensitivity analysis on a number of scenarios.

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

Fig. 1
Fig. 2
Fig. 3

References

  1. 1.

    Akcali, E., Cetinkaya, S.: Quantitative models for inventory and production planning in closed-loop supply chains. Int. J. Prod. Res. 49(8), 2373–2407 (2011)

    Article  Google Scholar 

  2. 2.

    Bertsekas, D.P.: Constrained Optimization and Lagrangian Multiplier Methods. Academic Press, New York (1982)

    Google Scholar 

  3. 3.

    Chen, M., Abrishami, P.: A mathematical model for production planning in hybrid manufacturing–remanufacturing systems. Int. J. Adv. Manuf. Technol. 71(5–8), 1187–1196 (2014)

    Article  Google Scholar 

  4. 4.

    Chen, Z.L., Li, S.L., Tirupati, D.: A scenario-based stochastic programming approach for technology and capacity planning. Comput. Oper. Res. 29(7), 781–806 (2002)

    MathSciNet  Article  MATH  Google Scholar 

  5. 5.

    Fleischmann, M., BloemhofRuwaard, J.M., Dekker, R., et al.: Quantitative models for reverse logistics: a review. Eur. J. Oper. Res. 103(1), 1–17 (1997)

    Article  MATH  Google Scholar 

  6. 6.

    Han, S.H., Dong, M.Y., Lu, S.X., et al.: Production planning for hybrid remanufacturing and manufacturing system with component recovery. J. Oper. Res. Soc. 64(10), 1447–1460 (2013)

    Article  Google Scholar 

  7. 7.

    Hsu, C.I., Li, H.C.: An integrated plant capacity and production planning model for high-tech manufacturing firms with economies of scale. Int. J. Prod. Econ. 118(2), 486–500 (2009)

    Article  Google Scholar 

  8. 8.

    Kaya, O., Bagci, F., Turkay, M.: Planning of capacity, production and inventory decisions in a generic reverse supply chain under uncertain demand and returns. Int. J. Prod. Res. 52(1), 270–282 (2014)

    Article  Google Scholar 

  9. 9.

    Kenne, J.P., Dejax, P., Gharbi, A.: Production planning of a hybrid manufacturing–remanufacturing system under uncertainty within a closed-loop supply chain. Int. J. Prod. Econ. 135(1), 81–93 (2012)

    Article  Google Scholar 

  10. 10.

    Lage, M., Godinho, M.: Production planning and control for remanufacturing: literature review and analysis. Prod. Plan. Control 23(6), 419–435 (2012)

    Article  Google Scholar 

  11. 11.

    Li, C.B., Liu, F., Cao, H.J., Wang, Q.L.: A stochastic dynamic programming based model for uncertain production planning of re-manufacturing system. Int. J. Prod. Res. 47(13), 3657–3668 (2009)

    Article  MATH  Google Scholar 

  12. 12.

    Li, J., Gonzales, M., Zhu, Y.: A hybrid simulation optimization method for production planning of dedicated remanufacturing. Int. J. Prod. Econ. 117(2), 286–301 (2009)

    Article  Google Scholar 

  13. 13.

    Li, Y.J., Chen, J., Cai, X.Q.: Heuristic genetic algorithm for capacitated production planning problems with batch processing and remanufacturing. Int. J. Prod. Econ. 105(2), 301–317 (2007)

    Article  Google Scholar 

  14. 14.

    Liu, S.S., Papageorgiou, L.G.: Multiobjective optimisation of production, distribution and capacity planning of global supply chains in the process industry. Omega 41(2), 369–382 (2013)

    Article  Google Scholar 

  15. 15.

    Lusa, A., Matinez-costa, C., Mas-Machura, M.: An integral planning model that includes production, selling price, cash flow management and flexible capacity. Int. J. Prod. Res. 50(6), 1568–1581 (2012)

    Article  Google Scholar 

  16. 16.

    Merzifonluoglu, Y., Geunes, J., Romeijn, H.E.: Integrated capacity, demand, and production planning with subcontracting and overtime options. Nav. Res. Logist. 54(4), 433–447 (2007)

    MathSciNet  Article  MATH  Google Scholar 

  17. 17.

    Naeem, M.A., Dias, D.J., Tibrewal, R., et al.: Production planning optimization for manufacturing and remanufacturing system in stochastic environment. J. Intell. Manuf. 24(4), 717–728 (2013)

    Article  Google Scholar 

  18. 18.

    Pan, Z.D., Tang, J.F., Liu, O.: Capacitated dynamic lot sizing problems in closed-loop supply chain. Eur. J. Oper. Res. 198(3), 810–821 (2009)

    MathSciNet  Article  MATH  Google Scholar 

  19. 19.

    Rockafellar, R.T.: Augmented Lagrangians and application of the proximal point algorithm in convex programming. Math. Oper. Res. 1(2), 97–116 (1976)

    MathSciNet  Article  MATH  Google Scholar 

  20. 20.

    Rockafellar, R.T., Wets, R.J.B.: Scenarios and policy aggregation in optimization under uncertainty. Math. Oper. Res. 16(1), 119–147 (1991)

    MathSciNet  Article  MATH  Google Scholar 

  21. 21.

    Shi, J.M., Zhang, G.Q., Sha, J.C.: Optimal production planning for a multi-product closed loop system with uncertain demand and return. Comput. Oper. Res. 38(3), 641–650 (2011)

    MathSciNet  Article  MATH  Google Scholar 

  22. 22.

    Tang, L.X., Che, P., Liu, J.Y.: A stochastic production planning problem with nonlinear cost. Comput. Oper. Res. 39(9), 1977–1987 (2012)

    MathSciNet  Article  MATH  Google Scholar 

  23. 23.

    Tempelmeier, H., Derstroff, M.: A Lagrangean-based heuristic for dynamic multilevel multiitem constrained lotsizing with setup times. Manage. Sci. 42(5), 738–757 (1996)

    Article  MATH  Google Scholar 

  24. 24.

    vanderLaan, E., Salomon, M.: Production planning and inventory control with remanufacturing and disposal. Eur. J. Oper. Res. 102(2), 264–278 (1997)

    Article  MATH  Google Scholar 

  25. 25.

    Zanjani, M.K., Nourelfath, M., Ait-Kadi, D.: A scenario decomposition approach for stochastic production planning in sawmills. J. Oper. Res. Soc. 64(1), 48–59 (2013)

    Article  Google Scholar 

  26. 26.

    Zhang, J., Liu, X., Tu, Y.L.: A capacitated production planning problem for closed-loop supply chain with remanufacturing. Int. J. Adv. Manuf. Technol. 54(5–8), 757–766 (2011)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the Social Sciences Foundation of Anhui Province (No. AHSKQ2016D28), the First Major Project in Anhui Normal University (FRZD201302), the Public Projects of Zhejiang Province (No. 2017C31069), the Natural Science Foundation of Anhui Province (No. 1608085QG167, 1608085MG152), the National Natural Science Foundation of China (No. 71601065, 71231004, 71501058) and the Humanities and Social Sciences Foundation of the Chinese Ministry of Education (No. 15YJC630097). Panos M. Pardalos is partially supported by the project of “Distinguished International Professor by the Chinese Ministry of Education” (MS2014HFGY026).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Chao Zuo.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Fang, C., Liu, X., Pardalos, P.M. et al. A stochastic production planning problem in hybrid manufacturing and remanufacturing systems with resource capacity planning. J Glob Optim 68, 851–878 (2017). https://doi.org/10.1007/s10898-017-0500-6

Download citation

Keywords

  • Stochastic production planning
  • Hybrid manufacturing and remanufacturing system
  • Scenario based approach
  • Resource capacity planning
  • Lagrangian relaxation
  • MILP