Multi-Objective Inventory Planning under Stochastic Availability of Complement in Fuzzy Environment

  • Muhammad Nazim
  • Zhimiao Tao
  • Muhammad Hashim
  • Abid Hussain Nadeem
  • Jamil Ahmad
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 241)


Effective inventory planing is instrumental in reducing costs and leadtime. In this paper, a multi-objective inventory planing model is proposed with imprecise demand, lead time and inventory costs. An inventory policy is proposed to minimize the costs using man–machine interaction. The fuzzy parameters of leadtime, inventory costs and demand are expressed through linear non-linear membership functions. The fuzzy parameters are first transformed into corresponding interval numbers and then following the interval mathematics, objective function of average cost is changed into respective multi-objective functions. An interactive fuzzy decision making method is used to minimize these functions and solve for Paretooptimum solutions. The proposed model is illustrated numerically and the results are presented in tabular forms.


Multi-objective optimization Fuzzy lead-time Fuzzy inventory cost parameters Inventory planing Interactive fuzzy decision making method 


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  1. 1.
    Das C (1975) Effect of lead time on inventory: A static analysis. Operations Research 26(2):273–282Google Scholar
  2. 2.
    Foote B, Kebriaci N, Kumin H (1988) Heuristic policies for inventory ordering problems with long and random varying leadt imes. Journal of Operations and Management 7(3):115–124Google Scholar
  3. 3.
    Maiti A, Maiti M, Maiti M (2009) Inventory model with stochastic lead-time and price dependent demand in corporating advance payment. Applied Mathematical Modelling 33(5):2433– 2443Google Scholar
  4. 4.
    Hayya J, Harrison T, He X (2011) The impact of stochastic lead time reduction on inventory cos tunder order crossover. European Journal of Operational Research 211(2):274–281Google Scholar
  5. 5.
    Yu M, Tang Y, Fu Y et al (2012) A deteriorating repairable system with stochastic lead time and replaceable repair facility. Computers and Industrial Engineering 62(2):609–615Google Scholar
  6. 6.
    Abginehchi S, Farahani R (2010) Modeling and analysis for determining optimal suppliers under stochastic lead times. Applied Mathematical Modelling 34(5):1311–1328Google Scholar
  7. 7.
    Maiti M, Maiti M (2007) Two-storage inventory model with lot-size dependent fuzzy leadtime under possibility constraints via genetic algorithm. European Journal of Operational Research 179(2):352–371Google Scholar
  8. 8.
    Rong M, Mahapatra N, Maiti M (2008) A two warehouse inventory model for a deteriorating item with partially/fully back logged shortage and fuzzy lead time. European Journal of Operational Research 189(1):59–75Google Scholar
  9. 9.
    Hayya J, Bagchi U, Kim J et al (2008) On static schastic order crossover. International Journal of Production Economics 114(1):404–413Google Scholar
  10. 10.
    Zadeh L (1965) Fuzzy sets. Information and Control 8(3):338–353Google Scholar
  11. 11.
    Petrovic D, Sweeney E (1994) Inventory models involving lead time as decision variable. Journal of the Operational Research Societ 45:579–582Google Scholar
  12. 12.
    Vujosevic M, Petrovic D, Petrovic R (1996) EOQ formula when inventory cost is fuzzy. International Journal of Production Economics 45(1):499–504Google Scholar
  13. 13.
    Chen S, Wang C (1996) Backorder fuzzy inventory model under functional principle. Information Sciences 95(1-2):71–79Google Scholar
  14. 14.
    Roy T, Maiti M (1997) A fuzzy EOQ model with demand-dependent unit cost under limited storage capacity. European Journal of Operational Research 99(2):425–432Google Scholar
  15. 15.
    Gen M, Tsujimura Y, Zheng P (1997) An application of fuzzy set theory to inventory control models. Computers and Industrial Engineering 33(3):553–556Google Scholar
  16. 16.
    Chang S, Yao J, Lee H (1998) Economic reorder point for fuzzy backorder quantity. European Journal of Operational Research 109(1):183–202Google Scholar
  17. 17.
    Lee H, Yao J (1998) Economic production quantity for fuzzy demand quantity and fuzzy production quantity. European Journal of Operational Research 109(1):203–211Google Scholar
  18. 18.
    Lin T, Yao J (2000) Fuzzy economic production for production inventory. Fuzzy Sets and Systems 111(3):465–495Google Scholar
  19. 19.
    Ouyang L, Yao J (2002) A minimax distribution free procedure for mixed inventory model involving variable lead time with fuzzy demand. Computers and Operations Research 29(5):471–487Google Scholar
  20. 20.
    Padmanabhan G, Vrat P (1990) Analysis of multi-item inventory systems under resource constraints: A non-linear goal programming approach. Engineering Cost and Production Economics 20(2):121–127Google Scholar
  21. 21.
    Agrell P (1995) A multicriteria framework for inventory control. International Journal of Production Economics 41(1):59–70Google Scholar
  22. 22.
    Roy T, Maiti M (1998) Multi-objective inventory models of deteriorating items with some constraints in a fuzzy environment. Computers and Operations Research 25(12):1085–1095Google Scholar
  23. 23.
    Mahapatra N, Maiti M (2005) Multi-objective inventory models of multi-items with quality and stock-dependent demand and stochas-tic deterioration. AMO-Advanced Modeling and Optimization 7(1):69–84Google Scholar
  24. 24.
    Grzegorzewski P (2002) Nearest interval approximation of a fuzzy number. Fuzzy Sets and Systems 130(3):321–330Google Scholar
  25. 25.
    Bellman R, Zadeh L (1970) Decision-making in fuzzy environment. Management Science 17(4):B141–B164Google Scholar
  26. 26.
    Zimmermann H (1978) Fuzzy linear programing with several objective functions. Fuzzy Sets and Systems 1(1):46–55Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Muhammad Nazim
    • 1
  • Zhimiao Tao
    • 1
  • Muhammad Hashim
    • 1
  • Abid Hussain Nadeem
    • 1
  • Jamil Ahmad
    • 1
  1. 1.Uncertainty Decision-Making LaboratorySichuan UniversityChengduPeople’s Republic of China

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