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Cost-time trade-off in three-axial sums' transportation problem

Published online by Cambridge University Press:  17 February 2009

Lakshmisree Bandopadhyaya
Lakshmisree Bandopadhyaya
Affiliation:
Deshbandhu College, University of Delhi.
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Abstract

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The bi-objective Cost-time Trade-off Three Axial Sums' Transportation Problem is shown to be equivalent to a single-objective standard Three Axial Sums' problem, which can be solved easily by the existing efficient methods. The equivalence is established for some specially defined solutions termed as Lexicographic optimal solutions with minimum pipe-line.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 35 , Issue 4 , April 1994 , pp. 498 - 505
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Bhatia, H. L., Swarup, K. and Puri, M. C., “Time-cost trade-off in a transportation problem”, Opsearch 13 (1976) 129–142.Google Scholar
[2]Bhatia, H. L., Swarup, K. and Puri, M. C., “A procedure for the time minimizing transportation problem”, Indian J. Pure Appl. Math. 8 (1977) 920–929.Google Scholar
[3]Charnes, A. and Cooper, W. W., Management models and industrial applications of linear programming, Vols 1 and 2 (Wiley, New York, 1961).Google Scholar
[4]Corban, Adrian, “A multi-dimensional transportation problem”, Rev. Roum. Math. Pure and Appl. 9 (8) (1964) 721–735.Google Scholar
[5]Garfinkel, R. S. and Rao, M. R., “The bottleneck transportation problem”, Nav. Res. Log. Quart. 18 (1971) 465–172.CrossRefGoogle Scholar
[6]Hammer, P. L., “Time minimizing transportation problems”, Nav. Res. Log. Quart. 16 (1969) 345–357.CrossRefGoogle Scholar
[7]Hammer, P. L., “Time minimizing transportation problems”, Nav. Res. Log. Quart. 18 (1971) 487–490.CrossRefGoogle Scholar
[8]Ignizio, J. P., “S-II Trajectory Study and Optimum Antenna Placement”, North American Aviation Report SID-63, Downey, California, 1963.Google Scholar
[9]Ignizio, J. P., Goal programming and extensions (Heath (Lexington Books), Lexington, Mass, 1976).Google Scholar
[10]Ignizio, J. P., “Goal programming: A tool for multi-objective analysis”, J. Oper. Res. Soc. 29 (2) (1978) 1109–1119.CrossRefGoogle Scholar
[11]Iziri, Y., Management goals and accounting for control (Rand Mcnally, Chicago, 1965).Google Scholar
[12]Prakash, S., “On minimizing the duration of transportation”, Proc. Ind. Acad. Sci. (Math. Sci) 91 (1982) 53–57.CrossRefGoogle Scholar
[13]Schell, E. D., “Distribution of a product by several properties”, in Proceedings of the 2nd Symposium in Linear programming, DCS/Comptroller H.Q.U.S.A.F., Washington D. C. (1955).Google Scholar
[14]Seshan, C. R. and Tikekar, V. G., “On Sharma-Swarup algorithm for time minimizing transportation problems”, Proc. Ind. Acad. Sci. (Math. Sci) 89 (1980) 101–102.CrossRefGoogle Scholar
[15]Sharma, J. K. and Swarup, K., “Time minimizing transportation problem”, Proc. Ind. Acad. Sci. (Math. Sci) 86 (1977) 513–518.CrossRefGoogle Scholar
[16]Szwarc, W., “Some remarks on the time minimizing transportation problem”, Nav. Res. Log. Quart. 18 (1971) 473–485.CrossRefGoogle Scholar