Dynamic production planning model: a dynamic programming approach


Production planning is one of the most important issues in manufacturing. The nature of this problem is complex and therefore researchers have studied it under several and different assumptions. In this paper, applied production planning problem is studied in a general manner and it is assumed that there exists an optimal control problem that its production planning strategy is a digital controller and must be optimized. Since this is a random problem because of stochastic values of sales in future, it is modeled as a stochastic dynamic programming and then it is transformed to a linear programming model using successive approximations. Then, it is proved that these two models are equivalent. The main objective of the proposed model is achieving optimal decisions using forecasting sales which can be applied in master production schedule, manufacturing resource planning, capacity requirements planning, and job shop/shop floor scheduling.

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  1. 1.

    Zwicker E (1980) System dynamics in inventory and production planning. OR-Spektrum 1:143–168

    MATH  Article  Google Scholar 

  2. 2.

    Byrne MD, Bakir MA (1999) Production planning using a hybrid simulation-analytical approach. Int J Prod Econ 59:305–311

    Article  Google Scholar 

  3. 3.

    Elhafsi M (2002) A production planning model for an unreliable production facility: case of finite horizon and single demand. Eur J Oper Res 143:94–114

    MATH  Article  Google Scholar 

  4. 4.

    Yokoyama M, Lewis HW (2003) Optimization of the stochastic dynamic production cycling problem by a genetic algorithm. Comput Oper Res 30:1831–1849

    MathSciNet  MATH  Article  Google Scholar 

  5. 5.

    Wang RC, Liang TF (2005) Applying possibilistic linear programming to aggregate production planning. Int J Prod Econ 98:328–341

    Article  Google Scholar 

  6. 6.

    Rein-qian Z (2007) Research on capacity planning under stochastic production and uncertain demand. Syst Eng Theory Pract 27(1):51–59

    Article  Google Scholar 

  7. 7.

    Chazal M, Jouini E, Tahraoui R (2008) Production planning and inventories optimization: a backward approach in the convex storage cost case. Int J Math Econ 44:997–1023

    MathSciNet  MATH  Article  Google Scholar 

  8. 8.

    Jamalnia A, Soukhakian MA (2009) A hybrid fuzzy goal programming approach with different goal priorities to aggregate production planning. Comput Ind Eng 56:1474–1486

    Article  Google Scholar 

  9. 9.

    Pilar CM, Escudero LF, Monge JF (2009) On stochastic dynamic programming for solving large-scale planning problems under uncertainty. Comput Oper Res 36:2418–2428

    MathSciNet  MATH  Article  Google Scholar 

  10. 10.

    Huang K, Ahmed S (2010) A stochastic programming approach for planning horizons of infinite horizon capacity planning problems. Eur J Oper Res 200:74–84

    MathSciNet  MATH  Article  Google Scholar 

  11. 11.

    Sethi S, Thompson GL (2000) Optimal control theory: applications to management science and economics, 2nd ed. Springer, New York

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Correspondence to Mohammad Reisi-Nafchi.

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Khaledi, H., Reisi-Nafchi, M. Dynamic production planning model: a dynamic programming approach. Int J Adv Manuf Technol 67, 1675–1681 (2013). https://doi.org/10.1007/s00170-012-4600-7

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  • Production planning
  • Dynamic programming
  • Linear programming
  • Optimal control