Exact and approximate solution for optimal inventory control of two-stock with reworking and forecasting of demand

Original Paper
First Online:
Received:
Revised:
Accepted:

Abstract

The aim of this paper is to describe a new optimal control model for optimal inventory control along with reworking items and forecasting the demand. The proposed model contains two stocks, one for serviceable products and one for returned products. The dynamic of the proposed system includes forecasting the demand and also the production planning. The exact analytical solution of the proposed optimal control model is obtained. Also the ability of neural networks to approximate the exact solution is examined, when the analytical solution maybe difficult to calculate. Numerical simulations are provided to illustrate the treatment of proposed model.

Keywords

Inventory systems Production planning Forecasting Optimal control Pontryagin maximum principle Neural networks 

Mathematics Subject Classification

49J15 90B30 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

The authors would like to thanks the anonymous reviewers for their valuable remarks. This work was supported in part by: Research Deputy of Ferdowsi University of Mashhad, under Grant No. 39098 (dated Feb. 28, 2016).

References

  1. Effati S, Pakdaman M (2013) Optimal control problem via neural networks. Neural Comput Appl 23:2093–2100CrossRefGoogle Scholar
  2. Foul A, Tadj L (2006) Optimal control of a hybrid periodic-review production inventory system with disposal. Int J Oper Res 2(4):481–494CrossRefGoogle Scholar
  3. Foul A, Djemili S, Tadj L (2007) Optimal and self-tuning optimal control of a periodic-review hybrid production inventory system. Nonlinear Anal Hybrid Syst 1(1):68–80CrossRefGoogle Scholar
  4. Giri BC, Sharma S (2016) Optimal ordering policy for an inventory system with linearly increasing demand and allowable shortages under two levels trade credit financing. Oper Res 16:25–50Google Scholar
  5. Goyal SK, Giri BC (2001) Recent trends in modeling of deteriorating inventory. Eur J Oper Res 134:1–16CrossRefGoogle Scholar
  6. Hedjar R, Bounkhel M, Tadj L (2005) Receding horizon control of a hybrid production system with deteriorating items. Nonlinear Anal Spec Ser Hybrid Syst Appl 63:405–422CrossRefGoogle Scholar
  7. Hedjar R, Abid C, Tadj L (2011) Optimal control of a continuous-review integrated production—forecasting system with stock-dependent demand and deteriorating items. In: 4th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO), 2011Google Scholar
  8. Hedjar R, Tadj L, Abid C (2012) Optimal control of integrated production-forecasting system. In: Chiang J (ed) Decision support systems. In-Tech Series in Numerical Analysis and Scientific Computing, Rijeka, Croatia (ISBN: 978-953-51-0799-6)Google Scholar
  9. Levin RI, Mclaughlin CP, Lamone RP, Kottas JF (1972) Production/operations management: contemporary policy for managing operating systems. McGraw-Hill, New YorkGoogle Scholar
  10. Mezghiche A, Moulai M, Tadj L (2015) Model predictive control of a forecasting production system with deteriorating items. Int J Oper Res Inf Syst 6(4):19–37CrossRefGoogle Scholar
  11. Nahmias S (1982) Perishable inventory theory: a review. Oper Res 30:680–708CrossRefGoogle Scholar
  12. Pakdaman M, Effati S (2016) Approximating the solution of optimal control problems by Fuzzy systems. Neural Process Lett 43(3):667–686 CrossRefGoogle Scholar
  13. Pavlidis NG, Plagianakos VP, Tasoulis DK, Vrahatis MN (2006) Financial forecasting through unsupervised clustering and neural networks. Oper Res 6:103–127Google Scholar
  14. Raafat F (1991) Survey of literature on continuously deteriorating inventory models. J Oper Res Soc 42:27–37CrossRefGoogle Scholar
  15. Silver EA, Peterson R (1985) Decision systems for inventory management and production planning, 2nd edn. Wiley, New YorkGoogle Scholar
  16. Wang L, Zeng Y, Chen T (2015) Back propagation neural network with adaptive differential evolution algorithm for time series forecasting. Expert Syst Appl 42:855–863CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of ManagementFerdowsi University of MashhadMashhadIran
  2. 2.Department of Applied MathematicsFerdowsi University of MashhadMashhadIran
  3. 3.Department of Information Systems and Decision SciencesFairleigh Dickinson UniversityVancouverCanada

Personalised recommendations