Abstract
The design of configuration and the transportation planning are crucial issues to the effectiveness of multi-stage supply chain networks. The decision makers are interested in the determination the optimal locations of the hubs and the optimal transportation routes to minimize the total costs incurred in the whole system. One may formulate this problem as a 0-1 mixed integer non-linear program though commercial packages are not able to efficiently solve this problem due to its complexity. This study proposes a new spanning tree-based Genetic Algorithm (GA) using determinant encoding for solving this problem. Also, we employ an efficient heuristic that fixes illegal spanning trees existing in the chromosomes obtained from the evolutionary process of the proposed GA. Our numerical experiments demonstrate that the proposed GA outperforms the other previously published GA in the solution quality and convergence rate.
Similar content being viewed by others
References
Abuali FN, Wainwright RL, Schoenefeld DA (1995) Determinant factorization: A new encoding scheme for spanning trees applied to the probabilistic minimum spanning tree problem. In: Eshelman LJ (ed) Proceedings of the sixth international conference on genetic algorithms. Morgan Kaufmann, San Mateo, pp 155–192
Azevedo AL, Sousa JP (2000) Order planning for networked make-to-order enterprises: A case study. J Oper Res Soc 51:1116–1127
Bramel J, Simchi-Levi D (1997) The logic of logistics: Theory, algorithms and applications for logistics management. Springer, New York
Chou H, Premkumar G, Chu CH (2001) Genetic algorithm for communications network design—An empirical study for the factors that influence performance. IEEE Trans Evolut Comput 5(3):236–249
Delbem ACB, de Leon Ferreira de Carvalho A, Bretas NG (2005) Main chain representation for evolutionary algorithms applied to distribution system reconfiguration. IEEE Trans Power Syst 20:425–436
Gen M, Cheng R (1997) Genetic algorithms and engineering design. Wiley, New York
Gen M, Kumar A, Kim JR (2005) Recent network design techniques using evolutionary algorithms. Int J Prod Econ 98(2):251–261
Geoffrion A, van Roy TJ (1979) Caution: Common sense planning methods can be hazardous to your corporate health. Sloan Manag Rev 20:30–42
Jo JB, Li YZ, Gen M (2007) Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Comput Ind Eng 53:290–298
Marry JM, Vidyaranya BG (2005) Global supply chain design: A literature review and critique. Transp Res Part E 41:531–550
Narula SC, Ho CA (1980) Degree-constrained minimum spanning tree. Comput Oper Res 7(4):239–249
Pirkul H, Jayaraman V (1998) A multi-commodity, multi-plant, capacitated location allocation problem: Formulation and efficient heuristic solution. Comput Oper Res 25:869–878
Ro H, Tcha D (1984) A branch and bound algorithm for two level uncapacitated facility location problem with some side constraint. Eur J Oper Res 18:349–358
Russell RM, Krajewski LJ (1991) Optimal purchase and transportation cost lot sizing for a single item. Dec Sci 22:940–954
Siajadi HR, Ibrahim N, Lochert PB, Chan WM (2005) Joint replenishment policy in inventory-production systems. Prod Plan Control 16:255–262
Sim E, Jang Y, Park J (2000) Study on the supply chain network design considering multi-level, multi-product, capacitated facility. In: Proceedings of Korean supply chain management society
Simchi-Levi D, Kaminsky P, Simchi-Levi E (2003) Designing and managing the supply chain: Concepts, strategies, and case studies, 2nd edn. McGraw-Hill, New York
Syarif A, Yun YS, Gen M (2002) Study on multi-stage logistic chain network A spanning tree-based genetic algorithm approach. Comput Ind Eng 43:299–314
Tilanus B (1997) Introduction to information system in logistics and transportation. Elsevier, London
Tragantalerngsak S, Holt J, Ronnqvist M (1997) Lagrangian heuristics for the two-echelon, single-source, capacitate location problem. Eur J Oper Res 102:611–625
Yeh WC (2005) A hybrid heuristic algorithm for the multistage supply chain network problem. Int J Adv Manuf Technol 26(5–6):675–685
Yu H (1997) ILOG in the supply chain. ILOG Technical Report
Zhou G, Gen M (2003) A genetic algorithm approach on tree-like telecommunication network design problem. J Oper Res Soc 54(3):248–254
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yao, MJ., Hsu, HW. A new spanning tree-based genetic algorithm for the design of multi-stage supply chain networks with nonlinear transportation costs. Optim Eng 10, 219–237 (2009). https://doi.org/10.1007/s11081-008-9059-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11081-008-9059-x