Skip to main content
SpringerLink
Log in

Developing a multi-objective, multi-item inventory model and three algorithms for its solution

  • Published:
Journal of Zhejiang University SCIENCE C Aims and scope Submit manuscript

Abstract

We develop a multi-objective model in a multi-product inventory system. The proposed model is a joint replenishment problem (JRP) that has two objective functions. The first one is minimization of total ordering and inventory holding costs, which is the same objective function as the classic JRP. To increase the applicability of the proposed model, we suppose that transportation cost is independent of time, is not a part of holding cost, and is calculated based on the maximum of stored inventory, as is the case in many real inventory problems. Thus, the second objective function is minimization of total transportation cost. To solve this problem three efficient algorithms are proposed. First, the RAND algorithm, called the best heuristic algorithm for solving the JRP, is modified to be applicable for the proposed problem. A multi-objective genetic algorithm (MOGA) is developed as the second algorithm to solve the problem. Finally, the model is solved by a new algorithm that is a combination of the RAND algorithm and MOGA. The performances of these algorithms are then compared with those of the previous approaches and with each other, and the findings imply their ability in finding Pareto optimal solutions to 3200 randomly produced problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Chan, C.K., Li, L.Y., Ng, C.T., Cheung, B.K., Langevin, A., 2006. Scheduling of multi-buyer joint replenishments. Int. J. Prod. Econ., 102(1):132–142. [doi:10.1016/j.ijpe.2005.02.005]

    Article  Google Scholar 

  • Djeffal, F., Bendib, T., 2011. Multi-objective genetic algorithms based approach to optimize the electrical performances of the gate stack double gate (GSDG) MOSFET. Microelectron. J., 42(5):661–666. [doi:10.1016/j.mejo.2011.03.003]

    Article  Google Scholar 

  • Fonesca, C.M., Fleming, P.J., 1993. Multi Objective Genetic Algorithm. IEE Colloquium on Genetic Algorithms for Control System Engineering, Digest No. 1993/20.

  • Fung, K.Y., Kwong, C.K., Siu, K.W.M., Yu, K.M., 2012. A multi-objective genetic algorithm approach to rule mining for affective product design. Exp. Syst. Appl., 39(8):7411–7419. [doi:10.1016/j.eswa.2012.01.065]

    Article  Google Scholar 

  • Gardner, E.S., Dannenbring, D.G., 1979. Using optimal policy surfaces to analyze aggregate inventory trade offs. Manag. Sci., 25(8):709–720. [doi:10.1287/mnsc.25.8.709]

    Article  MATH  Google Scholar 

  • Hsu, S.L., 2009. Optimal joint replenishment decisions for a central factory with multiple satellite factories. Exp. Syst. Appl., 36(2):2494–2502. [doi:10.1016/j.eswa.2008.01.069]

    Article  Google Scholar 

  • Kang, H., Lee, A., 2010. Inventory replenishment model using fuzzy multiple objective programming: a study of a high-tech company in Taiwan. Appl. Soft Comput., 10(4): 1108–1118. [doi:10.1016/j.asoc.2009.11.035]

    Article  MathSciNet  Google Scholar 

  • Kaspi, M., Rosenblatt, M.J., 1983. An improvement of Silver’s algorithm for the joint replenishment problem. IIE Trans., 15(3):264–269. [doi:10.1080/05695558308974644]

    Article  Google Scholar 

  • Kaspi, M., Rosenblatt, M.J., 1991. On the economic ordering quantity for jointly replenished items. Int. J. Prod. Res., 29(1):107–114. [doi:10.1080/00207549108930051]

    Article  Google Scholar 

  • Khouja, M., Michalewicz, M., Satoskar, S., 2000. A comparison between genetic algorithms and the RAND method for solving the joint replenishment problem. Prod. Plan. Control, 11(6):556–564. [doi:10.1080/095372800414115]

    Article  Google Scholar 

  • Khouja, M., Park, S., Saydam, C., 2005. Joint replenishment problem under continuous unit cost change. Int. J. Prod. Res., 43(2):311–326. [doi:10.1080/0020754042000270368]

    Article  MATH  Google Scholar 

  • Konak, A., Coit, D.W., Smith, A.E., 2006. Multi-objective optimization using genetic algorithms: a tutorial. Rel. Eng. Syst. Safety, 91(9):992–1007. [doi:10.1016/j.ress.2005.11.018]

    Article  Google Scholar 

  • Li, Q., 2004. Solving the multi-buyer joint replenishment problem with the RAND method. Comput. Ind. Eng., 46(4):755–762. [doi:10.1016/j.cie.2004.05.008]

    Article  Google Scholar 

  • Moon, K., Cha, B.C., 2006. The joint replenishment problem with resource restriction. Eur. J. Oper. Res., 173(1):190–198. [doi:10.1016/j.ejor.2004.11.020]

    Article  MathSciNet  MATH  Google Scholar 

  • Olsen, A., 2008. Inventory replenishment with interdependent ordering: an evolutionary algorithm solution. Int. J. Prod. Econ., 113(1):359–369. [doi:10.1016/j.ijpe.2007.09.004]

    Article  Google Scholar 

  • Ozkaya, U., Gunes, F., 2012. A modified particle swarm optimization algorithm and its application to the multiobjective FET modeling problem. Turk. J. Electr. Eng. Comput. Sci., 20(2):263–271. [doi:10.3906/elk-1102-1032]

    Google Scholar 

  • Padmanabhan, G., Vrat, P., 1990. Analysis of multi-item inventory systems under resource constrains: a non-linear goal programming approach. Eng. Costs Prod. Econ., 20(2):121–127. [doi:10.1016/0167-188X(90)90096-Z]

    Article  Google Scholar 

  • Porras, E., Dekker, R., 2008. A solution method for the joint replenishment problem with correction factor. Int. J. Prod. Econ., 113(2):834–851. [doi:10.1016/j.ijpe.2007.11.008]

    Article  Google Scholar 

  • Qu, B.Y., Suganthan, P.N., 2010. Multi-objective differential evolution with diversity enhancement. J. Zhejiang Univ.-Sci. C (Comput. & Electron.), 11(7):538–543. [doi:10.1631/jzus.C0910481]

    Article  Google Scholar 

  • Sahoo, N.C., Ganguly, S., Das, D., 2012. Multi-objective planning of electrical distribution systems incorporating sectionalizing switches and tie-lines using particle swarm optimization. Swarm Evol. Comput., 3:15–32. [doi:10.1016/j.swevo.2011.11.002]

    Article  Google Scholar 

  • Siajadi, H., Ibrahim, R.N., Lochert, P.B., Chan, W.M., 2005. Joint replenishment policy in inventory production systems. Prod. Plan. Control, 16(3):255–262. [doi:10.1080/09537280500033213]

    Article  Google Scholar 

  • Singh, D.P., Khare, A., 2011. Different aspects of evolutionary algorithms, multi-objective optimization algorithms and application domain. Int. J. Adv. Network. Appl., 2(4):770–775.

    Google Scholar 

  • Sundar, D., Umadevi, B., Alagarsamy, K., 2010. Multi-objective genetic algorithm for the optimized resource usage and the prioritization of the constraints in the software project planning. Int. J. Comput. Appl., 3(3):1–4. [doi:10.5120/718-1010]

    Google Scholar 

  • Tsou, C., 2009. Evolutionary Pareto optimized for continuous review stochastic inventory system. Eur. J. Oper. Res., 195(2):364–371. [doi:10.1016/j.ejor.2008.02.039]

    Article  MathSciNet  MATH  Google Scholar 

  • Wang, L., He, J., Wu, D., Zeng, Y.R., 2012. A novel differential evolution algorithm for joint replenishment problem under interdependence and its application. Int. J. Prod. Econ., 135(1):190–198. [doi:10.1016/j.ijpe.2011.06.015]

    Article  Google Scholar 

  • Wang, Y.C., Cheng, W.T., 2008. A sensitivity analysis of solving joint replenishment problems using the RAND method under inaccurate holding cost estimates and demand forecasts. Comput. Ind. Eng., 55(1):243–252. [doi:10.1016/j.cie.2007.12.010]

    Article  Google Scholar 

  • Wee, H.M., Lo, C.C., Hsu, P.H., 2009. A multi-objective joint replenishment inventory model of deteriorated items in a fuzzy environment. Eur. J. Oper. Res., 197(2):620–631. [doi:10.1016/j.ejor.2006.08.067]

    Article  MathSciNet  MATH  Google Scholar 

  • Xu, J., Liu, Y., 2008. Multi-objective decision making model under fuzzy random environment and its application to inventory problems. Inf. Sci., 178(14):2899–2914. [doi:10.1016/j.ins.2008.03.003]

    Article  MATH  Google Scholar 

  • Xu, J., Zhao, L., 2010. A multi-objective decision-making model under fuzzy rough coefficient and its application to inventory problem. Inf. Sci., 180(5):679–696. [doi:10.1016/j.ins.2009.11.002]

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

    Ommolbanin Yousefi, Mirbahadorgholi Aryanezhad & Seyed Jafar Sadjadi

  2. Department of Management, University of Isfahan, Isfahan, Iran

    Arash Shahin

Authors
  1. Ommolbanin Yousefi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mirbahadorgholi Aryanezhad
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Seyed Jafar Sadjadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Arash Shahin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ommolbanin Yousefi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yousefi, O., Aryanezhad, M., Sadjadi, S.J. et al. Developing a multi-objective, multi-item inventory model and three algorithms for its solution. J. Zhejiang Univ. - Sci. C 13, 601–612 (2012). https://doi.org/10.1631/jzus.C1100384

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1631/jzus.C1100384

Key words

CLC number

Search

Navigation