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A possibilistic approach to the modeling and resolution of uncertain closed-loop logistics

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Abstract

Closed-loop logistics planning is an important tactic for the achievement of sustainable development. However, the correlation among the demand, recovery, and landfilling makes the estimation of their rates uncertain and difficult. Although the fuzzy numbers can present such kinds of overlapping phenomena, the conventional method of defuzzification using level-cut methods could result in the loss of information. To retain complete information, the possibilistic approach is adopted to obtain the possibilistic mean and mean square imprecision index (MSII) of the shortage and surplus for uncertain factors. By applying the possibilistic approach, a multi-objective, closed-loop logistics model considering shortage and surplus is formulated. The two objectives are to reduce both the total cost and the root MSII. Then, a non-dominated solution can be obtained to support decisions with lower perturbation and cost. Also, the information on prediction interval can be obtained from the possibilistic mean and root MSII to support the decisions in the uncertain environment. This problem is non-deterministic polynomial-time hard, so a new algorithm based on the spanning tree-based genetic algorithm has been developed. Numerical experiments have shown that the proposed algorithm can yield comparatively efficient and accurate results.

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References

  • Abuali, F. N., Wainwright, R. L., & Schoenefeld, D. A. (1995). Determinant factorization: A new encoding scheme for spanning trees applied to the probabilistic minimum spanning tree problem. In L. J. Eshelman (Ed.), Proceedings of the sixth international conference on genetic algorithms (pp. 470–477). San Mateo, CA: Morgan Kaufmann.

  • Arumugam M. S., Rao M. V. C., Palaniappan R. (2005) New hybrid genetic operators for real coded genetic algorithm to compute optimal control of a class of hybrid systems. Applied Soft Computing 6(1): 38–52

    Article  Google Scholar 

  • Baumgarten, H., Christian, B., Annerous, F., & Thomas, S.-D. (2003). Supply chain management and reverse logistics-integration of reverse logistics processes into supply chain management approaches. In International symposium on electronics and the environment (pp. 79–83).

  • Biehl M., Prater E., Realff M. J. (2007) Assessing performance and uncertainly in developing carpet reverse logistics systems. Computers & Operations Research 34(2): 443–463

    Article  MATH  Google Scholar 

  • Carlsson C., Fullér R. (2001) On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets and Systems 122(2): 315–326

    Article  MathSciNet  MATH  Google Scholar 

  • Chang W.-D. (2006) An improved real-coded genetic algorithm for parameters estimation of nonlinear systems. Mechanical Systems and Signal Processing 20(1): 236–246

    Article  Google Scholar 

  • Chou H., Premkumar G., Chu C. H. (2001) Genetic algorithm for communications network design—an empirical study for the factors that influence performance. IEEE Transactions on Evolutionary Computation 5(3): 236–249

    Article  Google Scholar 

  • De Groot M. H. (1970) Optimal statistical decisions. McGraw-Hill, New York, NY

    Google Scholar 

  • Deep K., Thakur M. (2007) A new mutation operator for real coded genetic algorithms. Applied Mathematics and Computation 193(1): 211–230

    Article  MathSciNet  MATH  Google Scholar 

  • Dubois D., Prade H. (1987) The mean value of a fuzzy number. Fuzzy Sets and Systems 24(3): 279–300

    Article  MathSciNet  MATH  Google Scholar 

  • Duenas A., Petrovic D. (2008) Multi-objective genetic algorithm for single machine scheduling problem under fuzziness. Fuzzy Optimization and Decision Making 7(1): 87–104

    Article  MathSciNet  MATH  Google Scholar 

  • Fleischmann M., Krikke H. R., Dekker R., Flapper S. D. P. (2000) A classification of logistics networks for product recovery. Omega 28(6): 653–666

    Article  Google Scholar 

  • Gen M., Cheng R. (1997) Genetic algorithms and engineering design. Wiley, New York, NY

    Google Scholar 

  • Goetschel R., Voxman W. (1986) Elementary fuzzy calculus. Fuzzy Sets and Systems 18(1): 31–43

    Article  MathSciNet  MATH  Google Scholar 

  • Hsu H.-W., Wang H.-F. (2009) Modeling of green supply logistics. In: Wang H.-F. (eds) Web-based green products life cycle management systems: Reverse supply chain utilization. IGI Global Publication, USA, pp 268–282

    Google Scholar 

  • Jo J.-B., Yinzhen L., Gen M. (2007) Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Computers & Industrial Engineering 53(2): 290–298

    Article  Google Scholar 

  • Ke H., Liu B. (2007) Project scheduling problem with mixed uncertainty of randomness and fuzziness. European Journal of Operational Research 183(1): 135–147

    Article  MATH  Google Scholar 

  • Kongar, E. (2004). Performance measurement for supply chain management and evaluation criteria determination for reverse supply chain management. In Proceedings of SPIE: Environmentally conscious manufacturing IV, 5583 (pp. 106–117).

  • Kumar S., Naresh R. (2007) Efficient real coded genetic algorithm to solve the non-convex hydrothermal scheduling problem. Electrical Power and Energy Systems 29(10): 738–747

    Article  Google Scholar 

  • Listes O. (2007) A genetic stochastic model for supply-and-return network design. Computers & Operations Research 34(2): 417–442

    Article  MATH  Google Scholar 

  • López-González E., Rodríguez-Fernández M. A., Mendaña-Cuervo C. (2000) The logistic decision making in management accounting with genetic algorithms and fuzzy sets. Mathware & Soft Computing 7: 229–241

    MATH  Google Scholar 

  • Lu, Q., Christina, V., Stuart, J. A., & Rich, T. (2000). A practical framework for the reverse supply chain. In International symposium on electronics and the environment (pp. 266–271).

  • Peng J., Liu B. (2004) Parallel machine scheduling models with fuzzy processing times. Information Sciences 166(1–4): 49–66

    Article  MathSciNet  MATH  Google Scholar 

  • Salema M. I. G., Barbosa-Povoa A. P., Novais A. Q. (2007) An optimization model for the design of a capacitated multi-product reverse logistics network with uncertainty. European Journal of Operational Research 179(3): 1063–1077

    Article  MATH  Google Scholar 

  • Schultmann F., Zumkeller M., Rentz O. (2006) Modeling reverse logistic tasks within closed-loop supply chains: An example from the automotive industry. European Journal of Operational Research 171(3): 1033–1050

    Article  MATH  Google Scholar 

  • Syarif A., Yun Y. S., Gen M. (2002) Study on multi-stage logistic chain network: A spanning tree-based genetic algorithm approach. Computers & Industrial Engineering 43(1–2): 299–314

    Article  Google Scholar 

  • Wang H.-F., Hsu H.-W. (2010a) A closed-loop logistic model with a spanning-tree based genetic algorithm. Computers & Operations Research 37(2): 376–389

    Article  Google Scholar 

  • Wang H.-F., Hsu H.-W. (2010b) Resolution of an uncertain closed-loop logistics model: An application to fuzzy linear programs with risk analysis. Journal of Environmental Management 91(11): 2148–2162

    Article  Google Scholar 

  • Wen M., Iwamura K. (2008) Fuzzy facility location-allocation problem under the Hurwicz criterion. European Journal of Operational Research 184(2): 627–635

    Article  MathSciNet  MATH  Google Scholar 

  • Yang L., Ji X., Gao Z., Li K. (2007) Logistics distribution centers location problem and algorithm under fuzzy environment. Journal of Computational and Applied Mathematics 208(2): 303–315

    Article  MathSciNet  MATH  Google Scholar 

  • Yao M.-J., Hsu H.-W. (2009) A new spanning tree-based genetic algorithm for the design of multi-stage supply chain network with nonlinear transportation costs. Optimization and Engineering 10(2): 219–237

    Article  MATH  Google Scholar 

  • Yeh W.-C. (2005) A hybrid heuristic algorithm for the multistage supply chain network problem. International Journal of Advanced Manufacturing Technology 26(5–6): 675–685

    Article  Google Scholar 

  • Zadeh L. (1975) The concept of a linguistic variable and its application to approximate reasoning. Information Sciences 8(3): 199–249

    Article  MathSciNet  MATH  Google Scholar 

  • Zheng Y., Liu B. (2006) Fuzzy vehicle routing model with credibility measure and its hybrid intelligent algorithm. Applied Mathematics and Computation 176(2): 673–683

    Article  MathSciNet  MATH  Google Scholar 

  • Zikopoulos C., Tagaras G. (2007) Impact of uncertainty in the quality of returns on the profitability of a single-period refurbishing operation. European Journal of Operational Research 182(1): 205–225

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu, Taiwan, ROC

    Hsiao-Fan Wang & Hsin-Wei Hsu

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  1. Hsiao-Fan Wang
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  2. Hsin-Wei Hsu
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Correspondence to Hsin-Wei Hsu.

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Wang, HF., Hsu, HW. A possibilistic approach to the modeling and resolution of uncertain closed-loop logistics. Fuzzy Optim Decis Making 11, 177–208 (2012). https://doi.org/10.1007/s10700-012-9120-2

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