Encyclopedia of Optimization

2001 Edition
| Editors: Christodoulos A. Floudas, Panos M. Pardalos

Minimum Concave Transportation Problems

MCTP
  • Bruce W. Lamar
Reference work entry
DOI: https://doi.org/10.1007/0-306-48332-7_282
How to cite
The minimum concave transportation problem MCTP concerns the least cost method of carrying flow on a bipartite network in which the marginal cost for an arc is a nonincreasing function of the flow on that arc. A bipartite network contains source nodes and sink nodes, but no transshipment (i.e., intermediate) nodes. The MCTP can be formulated as
90C26 90C35 90B06 90B10 
flows in networks global optimization nonconvex programming fixed charge transportation problem 
This is a preview of subscription content, log in to check access.

References

  1. [1]
    Balinski, M. L.: ‘Fixed-cost transportation problems’, Naval Res. Logist.8 (1961), 41–54.MATHGoogle Scholar
  2. [2]
    Barr, R. S., Glover, F., and Klingman, D.: ‘A new optimization method for large scale fixed charge transportation problems’, Oper. Res.29 (1981), 448–463.MathSciNetMATHGoogle Scholar
  3. [3]
    Bell, G. B., Lamar, B. W.: ‘Solution methods for nonconvex network problems’, in P. M. Pardalos D. W. Hearn and W. W. Hager (eds.): Network Optimization, 450 of Lecture Notes Economics and Math. Systems, Springer 1997, pp. 32–50.Google Scholar
  4. [4]
    Cabot, A. V., and Erenguc, S. S.: ‘Some branch-and-bound procedures for fixed-cost transportation problems’, Naval Res. Logist.31 (1984), 145–154.MathSciNetMATHGoogle Scholar
  5. [5]
    Diaby, M.: ‘Successive linear approximation procedure for generalized fixed-charge transportation problems’, J. Oper. Res. Soc.42 (1991), 991–1001.MATHGoogle Scholar
  6. [6]
    Florian, M., and Robilland, P.: ‘An implicit enumeration algorithm for the concave cost network flow problem’, Managem. Sci.18 (1971), 184–193.MATHGoogle Scholar
  7. [7]
    Floudas, C. A., and Pardalos, P. M.: A collection of test problems for constrained global optimization Algorithms, Vol. 455 of Lecture Notes Computer Sci., Springer 1990.Google Scholar
  8. [8]
    Gray, P.: ‘Exact solution of the fixed-charge transportation problem’, Oper. Res.19 (1971), 1529–1538.MATHGoogle Scholar
  9. [9]
    Guisewite, G. M., and Pardalos, P. M.: ‘Minimum concave-cost network flow problems: Applications, complexity, and algorithms’, Ann. Oper. Res.25 (1990), 75–100.MathSciNetMATHGoogle Scholar
  10. [10]
    Kendall, K. E., and Zoints, S.: ‘Solving integer programming problems by aggregating constraints’, Oper. Res.25 (1977), 346–351.MATHGoogle Scholar
  11. [11]
    Kennington, J.: ‘The fixed-charge transportation problem: A computational study with a branch-and-bound code’, AIIE Trans.8 (1976), 241–247.Google Scholar
  12. [12]
    Kennington, J., and Unger, V. E.: ‘A new branch-and-bound algorithm for the fixed charge transportation problem’, Managem. Sci.22 (1976), 1116–1126.MathSciNetMATHGoogle Scholar
  13. [13]
    Khang, D. B., and Fujiwara, O.: ‘Approximate solutions of capacitated fixed-charge minimum cost network flow problems’, Networks21 (1991), 689–704.MathSciNetMATHGoogle Scholar
  14. [14]
    Kim, D., and Pardalos, P. M.: ‘A solution approach to the fixed charge network flow problem using a dynamic slope scaling procedure’, Oper. Res. Lett.24 (1999), 195–203.MathSciNetMATHGoogle Scholar
  15. [15]
    Lamar, B. W.: ‘An improved branch and bound algorithm for minimum concave cost network flow problems’, J. Global Optim.3 (1993), 261–287.MathSciNetMATHGoogle Scholar
  16. [16]
    Lamar, B. W.: ‘A method for solving network flow problems with general nonlinear arc costs’, in D.-Z Du and P. M. Pardalos (eds.): Network Optimization Problems: Algorithms, Applications, and Complexity, World Sci. 1993, pp. 147–167.Google Scholar
  17. [17]
    Lamar, B. W., and Wallace, C. A.: ‘A comparison of conditional penalties for the fixed charge transportation problem’, Techn. Report Dept. Management Univ. Canterbury (1996).Google Scholar
  18. [18]
    Lamar, B. W., and Wallace, C. A.: ‘Revised-modified penalties for fixed charge transportation problems’, Managem. Sci.43 (1997), 1431–1436.Google Scholar
  19. [19]
    Lawler, E. L.: Combinatorial optimization: Networks and matroids, Holt, Rinehart and Winston 1976.Google Scholar
  20. [20]
    Palekar, U. S., Karwan, M. H., and Zionts, S.: ‘A branch-and-bound method for the fixed charge transportation problem’, Managem. Sci.36 (1990), 1092–1105.MathSciNetMATHGoogle Scholar
  21. [21]
    Rech, P., and Barton, L. G.: ‘A non-convex transportation algorithm’, in E. M.L. Beale (ed.): Applications of Mathematical Programming Techniques, English Univ. Press 1970.Google Scholar
  22. [22]
    Soland, R. M.: ‘Optimal facility location with concave costs’, Oper. Res.22 (1974), 373–382.MathSciNetMATHGoogle Scholar
  23. [23]
    Wagner, H. M.: ‘On a class of capacitated transportation problems’, Managem. Sci.5 (1959), 304–318.MATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Bruce W. Lamar
    • 1
  1. 1.Economic and Decision Analysis Center The MITRE Corp.BedfordUSA