Optimal Batch Production with Rework Process for Products with Time-Varying Demand Over Finite Planning Horizon

  • Lakdere Benkherouf
  • Konstantina SkouriEmail author
  • Ioannis Konstantaras
Part of the Springer Optimization and Its Applications book series (SOIA, volume 113)


In this paper a finite planning horizon, production–inventory model with rework, is considered. During the production process defective items are produced. These items, after the end of the production process, are repaired and converted into items of perfect quality. The demand for the item is assumed to be time varying. The objective is the determination of the production–reworking schedule that minimizes the total cost over the planning horizon. A procedure is proposed for the determination of such schedule.


Production Imperfect Rework Finite horizon Time-varying demand 

2010Mathematics Subject Classification:

90B05; 90B30 


  1. 1.
    F.W. Harris, How many parts to make at once. Fact. Mag. Manage. 10, 135–136, 152 (1913)Google Scholar
  2. 2.
    M.J. Rosenblatt, H.L. Lee, Economic production cycles with imperfect production processes. IIE Trans. 18, 48–55 (1986)CrossRefGoogle Scholar
  3. 3.
    M. Hariga, M. Ben-Daya, Note: the economic manufacturing lot-sizing problem with imperfect production processes: bounds and optimal solutions. Nav. Res. Log. 45, 423–433 (1998)CrossRefzbMATHGoogle Scholar
  4. 4.
    I. Moon, B.C. Giri, K. Choi, Economic lot scheduling problem with imperfect production processes and setup times. J. Oper. Res. Soc. 53, 620–629 (2002)CrossRefzbMATHGoogle Scholar
  5. 5.
    C.H. Wang, Integrated production and product inspection policy for a deteriorating production system. Int. J. Prod. Econ. 95, 123–134 (2005)CrossRefGoogle Scholar
  6. 6.
    S.S. Sana, S.K. Goyal, K. Chaudhuri, An imperfect production process in a volume flexible inventory model. Int. J. Prod. Econ. 105, 548–559 (2007)CrossRefGoogle Scholar
  7. 7.
    L.E. Cardenas-Barron, Economic production quantity with rework process at a single-stage manufacturing system with planned backorders. Comput. Ind. Eng. 57, 1105–1113 (2009)CrossRefGoogle Scholar
  8. 8.
    P.A. Hayek, M.K. Salameh, Production lot sizing with the reworking of imperfect quality item produced. Prod. Plan. Control. 12, 584–590 (2001)CrossRefGoogle Scholar
  9. 9.
    Y.P. Chiu, Determining the optimal lot size for the finite production model with random defective rate, the rework process, and backlogging, Eng. Optim. 35, 427–437 (2003)CrossRefGoogle Scholar
  10. 10.
    A.M.M. Jamal, B.R. Sarker, S. Mondal, Optimal manufacturing batch size with rework process at a single stage production system. Comput. Ind. Eng. 47, 77–89 (2004)CrossRefGoogle Scholar
  11. 11.
    L.E. Cardenas–Barron, Optimal manufacturing batch size with rework in a single–stage production system–a simple derivation. Comput. Ind. Eng. 55, 758–765 (2008)Google Scholar
  12. 12.
    P. Biswas, B. Sarker, Optimal batch quantity models for a lean production system with in-cycle rework and scrap. Int. J. Prod. Res. 46, 6585–6610 (2008)CrossRefGoogle Scholar
  13. 13.
    Y.S.P. Chiu, K.K. Chen, F.T. Cheng, M.F. Wu, Optimization of the finite production rate model with scrap, rework and stochastic machine breakdown. Comput. Math. Appl. 59, 919–932 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    C.J. Chung, G.A. Widyadana, H.M. Wee, Economic production quantity model for deteriorating inventory with random machine unavailability and shortage. Int. J. Prod. Res. 49, 883–902 (2011)CrossRefzbMATHGoogle Scholar
  15. 15.
    H.M. Wee, W.T. Wang, P.C. Yang, A production quantity model for imperfect quality items with shortage and screening constraint. Int. J. Prod. Res. 51, 1869–1884 (2013)CrossRefGoogle Scholar
  16. 16.
    A.H. Tai, Economic production quantity models for deteriorating/imperfect products and service with rework. Comput. Ind. Eng. 66, 879–888 (2013)CrossRefGoogle Scholar
  17. 17.
    B. Pal, S.S. Sana, K. Chaudhuri, Maximising profits for an EPQ model with unreliable machine and rework of random defective items. Int. J. Syst. Sci. 44, 582–594 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    B. Sarkar, L.E. Cardenas–Barron, M. Sarkar, M.L. Singgih, An economic production quantity model with random defective rate, rework process and backorders for a single stage production system. J. Manuf. Syst. 33, 423–435 (2014)Google Scholar
  19. 19.
    C.K. Sivashankari, S. Panayappan, Production inventory model with reworking of imperfect production, scrap and shortages. Int. J. Manag. Sci. Eng. Manag. 9, 9–20 (2014)Google Scholar
  20. 20.
    E.A. Silver, D.F. Pyke, R. Peterson, Inventory Management and Production Planning and Scheduling (Wiley, New York, 1998Google Scholar
  21. 21.
    Z.T. Balkhi, On a finite production lot size inventory model for deteriorating items: an optimal solution. Eur. J. Oper. Res. 132, 210–223 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    S. Sana, S.K. Goyal, K.S. Chaudhuri, Production–inventory model for a deteriorating item with trended demand and shortages. Eur. J. Oper. Res. 157, 357–371 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    A. Roy, S. Kar, M. Maiti, Volume flexible production-policy for randomly deteriorating item with trended demand and shortages. Int. J. Prod. Econ. 128, 188–199 (2010)CrossRefGoogle Scholar
  24. 24.
    H.-L. Yang, A partial backlogging production-inventory lot-size model for deteriorating items with time-varying production and demand rate over a finite time horizon. Int. J. Syst. Sci. 42, 1397–1407 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    L. Benkherouf, D. Boushehri, Optimal policies for a finite-horizon production inventory model. Adv. Oper. Res. Article ID 768929, 16 p. (2012). doi:10.1155/2012/768929Google Scholar
  26. 26.
    D. Das, M.B. Kar, A. Roy, S. Kar, Two-warehouse production inventory model for a deteriorating item with time-varying demand and shortages: a genetic algorithm with varying population size approach. Optim. Eng. 15, 889–907 (2014)MathSciNetCrossRefGoogle Scholar
  27. 27.
    L. Benkherouf, K. Skouri, I. Konstantaras, Optimal control of production remanufacturing and refurbishing activities in a finite planning horizon inventory system. J. Optim. Theory Appl. 168, 677–698 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    L. Benkherouf, M.A. Omar, Optimal manufacturing batch size with rework for a finite-horizon and time-varying demand rates inventory model. RAIRO Oper. Res. 51 (1), 173–187 (2017)CrossRefGoogle Scholar
  29. 29.
    T.M. Al-Khamis, L. Benkherouf, M.A. Omar, Optimal policies for a finite-horizon batching inventory model. Int. J. Syst. Sci 45, 2196–2202 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    S. Dharmadhikari, J.D. Kumar, Unimodality, convexity, and applications, in Probability and Mathematical Statistics (Academic, Boston, 1988)zbMATHGoogle Scholar
  31. 31.
    H. Rau, B.C. Ouyang, A general and optimal approach for three inventory models with a linear trend in demand. Comput. Ind. Eng. 52, 521–532 (2007)CrossRefGoogle Scholar
  32. 32.
    L. Benkherouf, B.H. Gilding, On a class of optimization problems for finite time horizon models. SIAM J. Control Optim. 48, 993–1030 (2009)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Lakdere Benkherouf
    • 1
  • Konstantina Skouri
    • 2
    Email author
  • Ioannis Konstantaras
    • 3
  1. 1.Faculty of Science, Department of Statistics and Operations ResearchKuwait UniversitySafatKuwait
  2. 2.Department of MathematicsUniversity of IoanninaIoanninaGreece
  3. 3.Department of Business AdministrationSchool of Business Administration, University of MacedoniaThessalonikiGreece

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