Optimization and Engineering

, Volume 15, Issue 3, pp 697–720 | Cite as

Development of a production inventory model with uncertainty and reliability considerations

  • Sanjoy Kumar Paul
  • Abdullahil Azeem
  • Ruhul Sarker
  • Daryl Essam


This paper addresses a problem of an imperfect production system under fuzzy demand and inventory holding cost. Production process reliability is considered because of the imperfect production process. In this problem, reliability of the system in regards to producing defective and non-defective items is considered as a decision variable. The objective is to maximize the graded mean integration value (GMIV) of the expected average profit while considering revenues as well as any other relevant costs. The developed model belongs to the class of a geometric programming. We have developed a simple mathematical methodology to solve the model. Genetic algorithm and simulated annealing algorithms are also applied to solve and validate the results. A numerical example has been presented to interpret the solutions.


Production inventory system Optimization Fuzzy random variable Signomial geometric programming Genetic algorithm Simulated annealing algorithm 


  1. Bag S, Chakraborty D, Roy AR (2009) A production inventory model with fuzzy random demand and with flexibility and reliability considerations. Comput Ind Eng 56(1):411–416 CrossRefGoogle Scholar
  2. Beightler CS, Phillips DT (1976) Applied geometric programming. Wiley, New York MATHGoogle Scholar
  3. Chang HC (2004) An application of fuzzy sets theory to the EOQ model with imperfect quality items. Comput Oper Res 31(12):2079–2092 MathSciNetCrossRefMATHGoogle Scholar
  4. Cheng TCE (1989) An economic production quantity model with flexibility and reliability consideration. Eur J Oper Res 39(2):174–179 CrossRefMATHGoogle Scholar
  5. Chen SH, Chang SM (2008) Optimization of fuzzy production inventory model with unrepairable defective products. Int J Prod Econ 113(2):887–894 CrossRefGoogle Scholar
  6. Chen SH, Hsieh CH (1999) Graded mean integration representation of generalized fuzzy numbers. J Chin Fuzzy Syst 5(2):1–7 Google Scholar
  7. Dubois D, Prade H (1980) Fuzzy sets and systems theory and applications. Academic Press, New York MATHGoogle Scholar
  8. Duffin RJ, Peterson EL, Zener C (1967) Geometric programming: theory and application. Wiley, New York MATHGoogle Scholar
  9. Dutta P, Chakraborty D, Roy AR (2007) Continuous review inventory model in mixed fuzzy and stochastic environment. Appl Math Comput 188(1):970–980 MathSciNetCrossRefMATHGoogle Scholar
  10. Dutta P, Chakraborty D, Roy AR (2005) A single-period inventory model with fuzzy random variable demand. Math Comput Model 41(8–9):915–922 MathSciNetCrossRefMATHGoogle Scholar
  11. Hsieh CH (2002) Optimization of fuzzy production inventory models. Inf Sci 146(1–4):29–40 CrossRefMATHGoogle Scholar
  12. Kao C, Hsu WK (2002) A single-period inventory model with fuzzy demand. Comput Math Appl 43(6–7):841–848 MathSciNetCrossRefMATHGoogle Scholar
  13. Lee HM, Yao JS (1998) Economic production quantity for fuzzy demand quantity, and fuzzy production quantity. Eur J Oper Res 109(1):203–211 CrossRefMATHGoogle Scholar
  14. Lin CS (1999) Integrated production-inventory models with imperfect production processes and a limited capacity for raw materials. Math Comput Model 29(2):81–89 CrossRefMATHGoogle Scholar
  15. Lin CS, Chen CH, Kroll DE (2003) Integrated production-inventory models for imperfect production processes under inspection schedules. Comput Ind Eng 44(4):633–650 CrossRefGoogle Scholar
  16. Mohebbi E, Hao D (2008) An inventory model with non-resuming randomly interruptible lead time. Int J Prod Econ 114(2):755–768 CrossRefGoogle Scholar
  17. Panda D, Maiti M (2009) Multi-item inventory models with price dependent demand under flexibility and reliability consideration and imprecise space constraint: a geometric programming approach. Math Comput Model 49(9–10):1733–1749 MathSciNetCrossRefMATHGoogle Scholar
  18. Sana SS, Goyal SK, Chaudhuri K (2007) An imperfect production process in a volume flexible inventory model. Int J Prod Econ 105(2):548–559 CrossRefGoogle Scholar
  19. Sarkar B, Moon I (2011) An EPQ model with inflation in an imperfect production system. Appl Math Comput 217(13):6159–6167 MathSciNetCrossRefMATHGoogle Scholar
  20. Sarkar B (2012) An inventory model with reliability in an imperfect production process. Appl Math Comput 218(9):4881–4891 MathSciNetCrossRefMATHGoogle Scholar
  21. Sana S (2010) A production–inventory model in an imperfect production process. Eur J Oper Res 200(2):451–464 MathSciNetCrossRefMATHGoogle Scholar
  22. Wang L, Fu QL, Zeng YR (2012) Continuous review inventory models with a mixture of backorders and lost sales under fuzzy demand and different decision situations. Expert Syst Appl 39(4):4181–4189 CrossRefGoogle Scholar
  23. Wang X (2011) Continuous review inventory model with variable lead time in a fuzzy random environment. Expert Syst Appl 38(9):11715–11721 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Sanjoy Kumar Paul
    • 1
    • 2
  • Abdullahil Azeem
    • 1
  • Ruhul Sarker
    • 2
  • Daryl Essam
    • 2
  1. 1.Department of Industrial and Production EngineeringBangladesh University of Engineering and TechnologyDhakaBangladesh
  2. 2.School of Engineering and Information TechnologyUniversity of New South WalesCanberraAustralia

Personalised recommendations