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Solving fixed charge transportation problem with truck load constraint using metaheuristics

Author

Listed:
  • A. N. Balaji

    (K.L.N. College of Engineering)

  • J. Mukund Nilakantan

    (Aalborg University)

  • Izabela Nielsen

    (Aalborg University)

  • N. Jawahar

    (Thiagarajar College of Engineering)

  • S. G. Ponnambalam

    (Monash University Malaysia)

Abstract

Fixed charge transportation (FCT) problems addressed in literature assumed shipment between a source and a destination is fulfilled in a single lot. However, in reality the lot size may exceed the capacity of the carrier and hence the shipment needs to be executed by conducting more than one trip. This gives an increased fixed charge which is proportional to the number of trips performed. This paper proposes a special case of the FCT problem were the truck load constraint is considered and is referred as the fixed charge transportation problem with truck load constraints (FCT-TLC) problem. The objective considered in this problem is to minimize the total cost of transportation without violating the supply and demand constraints. The general FCT problem is classified as NP-hard and to solve this proposed problem with additional constraints, two metaheuristic algorithms are used. A Genetic Algorithm (GA) and a Simulated Annealing Algorithm (SAA) are proposed to solve the FCT-TLC problem and the performance of the algorithms is tested on twenty randomly generated problem instances. Detailed comparative study on the computational results obtained using GA and SAA are presented. Both metaheuristics show good results for solving the proposed problem. However, SAA outperformed GA for many problems with different truck load capacities. To test the performance of the proposed algorithms, comparison with approximate and lower bound solutions for the problem with a relaxed truck capacity constraint is also presented.

Suggested Citation

  • A. N. Balaji & J. Mukund Nilakantan & Izabela Nielsen & N. Jawahar & S. G. Ponnambalam, 2019. "Solving fixed charge transportation problem with truck load constraint using metaheuristics," Annals of Operations Research, Springer, vol. 273(1), pages 207-236, February.
    • Handle: RePEc:spr:annopr:v:273:y:2019:i:1:d:10.1007_s10479-017-2692-z
    DOI: 10.1007/s10479-017-2692-z
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    1. Sun, Minghe & Aronson, Jay E. & McKeown, Patrick G. & Drinka, Dennis, 1998. "A tabu search heuristic procedure for the fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 441-456, April.
    2. Gen, Mitsuo & Kumar, Anup & Ryul Kim, Jong, 2005. "Recent network design techniques using evolutionary algorithms," International Journal of Production Economics, Elsevier, vol. 98(2), pages 251-261, November.
    3. Hak-Jin Kim & John Hooker, 2002. "Solving Fixed-Charge Network Flow Problems with a Hybrid Optimization and Constraint Programming Approach," Annals of Operations Research, Springer, vol. 115(1), pages 95-124, September.
    4. Katta G. Murty, 1968. "Solving the Fixed Charge Problem by Ranking the Extreme Points," Operations Research, INFORMS, vol. 16(2), pages 268-279, April.
    5. Kowalski, Krzysztof & Lev, Benjamin & Shen, Wenjing & Tu, Yan, 2014. "A fast and simple branching algorithm for solving small scale fixed-charge transportation problem," Operations Research Perspectives, Elsevier, vol. 1(1), pages 1-5.
    6. Adlakha, Veena & Kowalski, Krzysztof, 2003. "A simple heuristic for solving small fixed-charge transportation problems," Omega, Elsevier, vol. 31(3), pages 205-211, June.
    7. John Fisk & Patrick McKeown, 1979. "The pure fixed charge transportation problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(4), pages 631-641, December.
    8. Y. T. Herer & M. J. Rosenblatt & I. Hefter, 1996. "Fast Algorithms for Single-Sink Fixed Charge Transportation Problems with Applications to Manufacturing and Transportation," Transportation Science, INFORMS, vol. 30(4), pages 276-290, November.
    9. Szeto, W.Y. & Wu, Yongzhong & Ho, Sin C., 2011. "An artificial bee colony algorithm for the capacitated vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 215(1), pages 126-135, November.
    10. Jesús Sáez Aguado, 2009. "Fixed Charge Transportation Problems: a new heuristic approach based on Lagrangean relaxation and the solving of core problems," Annals of Operations Research, Springer, vol. 172(1), pages 45-69, November.
    11. Baldacci, Roberto & Mingozzi, Aristide & Roberti, Roberto, 2012. "Recent exact algorithms for solving the vehicle routing problem under capacity and time window constraints," European Journal of Operational Research, Elsevier, vol. 218(1), pages 1-6.
    12. Michel Gendreau & Alain Hertz & Gilbert Laporte, 1994. "A Tabu Search Heuristic for the Vehicle Routing Problem," Management Science, INFORMS, vol. 40(10), pages 1276-1290, October.
    13. Dullaert, Wout & Sevaux, Marc & Sorensen, Kenneth & Springael, Johan, 2007. "Applications of metaheuristics," European Journal of Operational Research, Elsevier, vol. 179(3), pages 601-604, June.
    14. A.N. Balaji & N. Jawahar, 2010. "A Simulated Annealing Algorithm for a two-stage fixed charge distribution problem of a Supply Chain," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 7(2), pages 192-215.
    15. Adlakha, Veena & Kowalski, Krzysztof & Vemuganti, R.R. & Lev, Benjamin, 2007. "More-for-less algorithm for fixed-charge transportation problems," Omega, Elsevier, vol. 35(1), pages 116-127, February.
    16. Patrick G. McKeown, 1981. "A branch‐and‐bound algorithm for solving fixed charge problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(4), pages 607-617, December.
    17. Schaffer, Joanne R. & O'Leary, Daniel E., 1989. "Use of penalties in a branch and bound procedure for the fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 43(3), pages 305-312, December.
    18. Jawahar, N. & Balaji, A.N., 2009. "A genetic algorithm for the two-stage supply chain distribution problem associated with a fixed charge," European Journal of Operational Research, Elsevier, vol. 194(2), pages 496-537, April.
    19. Jeff Kennington & Ed Unger, 1976. "A New Branch-and-Bound Algorithm for the Fixed-Charge Transportation Problem," Management Science, INFORMS, vol. 22(10), pages 1116-1126, June.
    20. Yu, Bin & Yang, Zhong-Zhen & Yao, Baozhen, 2009. "An improved ant colony optimization for vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 196(1), pages 171-176, July.
    21. Jayaraman, Vaidyanathan & Pirkul, Hasan, 2001. "Planning and coordination of production and distribution facilities for multiple commodities," European Journal of Operational Research, Elsevier, vol. 133(2), pages 394-408, January.
    22. Udatta S. Palekar & Mark H. Karwan & Stanley Zionts, 1990. "A Branch-and-Bound Method for the Fixed Charge Transportation Problem," Management Science, INFORMS, vol. 36(9), pages 1092-1105, September.
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