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A Heuristic Adjacent Extreme Point Algorithm for the Fixed Charge Problem

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  • Warren E. Walker

    (Chemical Bank)

Abstract

An algorithm with three variations is presented for the approximate solution of fixed charge problems. Computational experience shows it to be extremely fast and to yield very good solutions. The basic approach is (1) to obtain a local optimum by using the simplex method with a modification of the rule for selection of the variable to enter the basic solution, and (2) once at a local optimum, to search for a better extreme point by jumping over adjacent extreme points to resume iterating two or three extreme points away. This basic approach is the same as that used by Steinberg [Steinberg, D. I. 1970. The fixed charge problem. Naval Res. Log. Quart. 17 217-236.], Cooper [Cooper, L. 1975. The fixed charge problem--I: A new heuristic method. Comp. & Maths, with Appls. 1 89-95.], and Denzler [Denzler, D. R. 1969. An approximate algorithm for the fixed charge problem. Naval Res. Log. Quart. 16 411-416.] in their algorithms, but is an extension and improvement of all three. The algorithm is being used by the U.S Environmental Protection Agency's Office of Solid Waste Management Programs to decide on the number, type, size, and location of the disposal facilities to operate in a region, and how to allocate the region's wastes to these facilities.

Suggested Citation

  • Warren E. Walker, 1976. "A Heuristic Adjacent Extreme Point Algorithm for the Fixed Charge Problem," Management Science, INFORMS, vol. 22(5), pages 587-596, January.
    • Handle: RePEc:inm:ormnsc:v:22:y:1976:i:5:p:587-596
    DOI: 10.1287/mnsc.22.5.587
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    Cited by:

    1. Badri, Masood A., 1999. "Combining the analytic hierarchy process and goal programming for global facility location-allocation problem," International Journal of Production Economics, Elsevier, vol. 62(3), pages 237-248, September.
    2. F Altiparmak & I Karaoglan, 2008. "An adaptive tabu-simulated annealing for concave cost transportation problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(3), pages 331-341, March.
    3. 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.
    4. Adlakha, Veena & Kowalski, Krzysztof, 2003. "A simple heuristic for solving small fixed-charge transportation problems," Omega, Elsevier, vol. 31(3), pages 205-211, June.
    5. Erika Buson & Roberto Roberti & Paolo Toth, 2014. "A Reduced-Cost Iterated Local Search Heuristic for the Fixed-Charge Transportation Problem," Operations Research, INFORMS, vol. 62(5), pages 1095-1106, October.
    6. Roberto Roberti & Enrico Bartolini & Aristide Mingozzi, 2015. "The Fixed Charge Transportation Problem: An Exact Algorithm Based on a New Integer Programming Formulation," Management Science, INFORMS, vol. 61(6), pages 1275-1291, June.
    7. Aristide Mingozzi & Roberto Roberti, 2018. "An Exact Algorithm for the Fixed Charge Transportation Problem Based on Matching Source and Sink Patterns," Transportation Science, INFORMS, vol. 52(2), pages 229-238, March.
    8. Adlakha, Veena & Kowalski, Krzysztof & Wang, Simi & Lev, Benjamin & Shen, Wenjing, 2014. "On approximation of the fixed charge transportation problem," Omega, Elsevier, vol. 43(C), pages 64-70.
    9. Julian Yeomans, 2011. "Efficient generation of alternative perspectives in public environmental policy formulation: applying co-evolutionary simulation–optimization to municipal solid waste management," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(4), pages 391-413, December.
    10. Lev, Benjamin & Kowalski, Krzysztof, 2011. "Modeling fixed-charge problems with polynomials," Omega, Elsevier, vol. 39(6), pages 725-728, December.
    11. 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.
    12. Sagratella, Simone & Schmidt, Marcel & Sudermann-Merx, Nathan, 2020. "The noncooperative fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 284(1), pages 373-382.
    13. Seyma Gozuyilmaz & O. Erhun Kundakcioglu, 2021. "Mathematical optimization for time series decomposition," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 733-758, September.
    14. 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.
    15. V Adlakha & K Kowalski, 2004. "A simple algorithm for the source-induced fixed-charge transportation problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1275-1280, December.
    16. Jeffery L. Kennington & Charles D. Nicholson, 2010. "The Uncapacitated Time-Space Fixed-Charge Network Flow Problem: An Empirical Investigation of Procedures for Arc Capacity Assignment," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 326-337, May.
    17. Adlakha, Veena & Kowalski, Krzysztof & Lev, Benjamin, 2010. "A branching method for the fixed charge transportation problem," Omega, Elsevier, vol. 38(5), pages 393-397, October.
    18. Yeomans, Julian Scott, 2007. "Solid waste planning under uncertainty using evolutionary simulation-optimization," Socio-Economic Planning Sciences, Elsevier, vol. 41(1), pages 38-60, March.
    19. V. Adlakha & K. Kowalski, 2015. "Fractional Polynomial Bounds for the Fixed Charge Problem," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 1026-1038, March.

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