Three dimensional fixed charge bi-criterion indefinite quadratic transportation problem
DOI:
https://doi.org/10.2298/YJOR0401083AKeywords:
three dimensional quadratic transportation problem, cost-time trade-off pairs, fixed charge, bi-criterion indefinite quadratic transportation problemAbstract
The three-dimensional fixed charge transportation problem is an extension of the classical three-dimensional transportation problem in which a fixed cost is incurred for every origin. In the present paper three-dimensional fixed charge bi-criterion indefinite quadratic transportation problem, giving the same priority to cost as well as time, is studied. An algorithm to find the efficient cost-time trade off pairs in a three dimensional fixed charge bi-criterion indefinite quadratic transportation problem is developed. The algorithm is illustrated with the help of a numerical example.References
Ahuja, A., and Arora, S.R., “Multi-index fixed charge bi-criterion transportation problem”, Indian Journal of Pure and Applied Mathematics, 32(5) (2001) 739-746.
Basu, M., Pal, B.B., and Kundu, A., “An algorithm for optimum time-cost trade-off in fixed charge bi-criterion transportation problem”, Optimization, 30 (1994) 53-68.
Basu, M., Pal, B.B., and Kundu, A., “An algorithm for finding the optimum solution of solid fixed-charge transportation problem”, 31 (1994) 283-291.
Bhatia, H.L., Swaroop, K., and Puri, M.C., “Time-cost trade-off in a transportation problem”, Opsearch, 13 (1976) 129-142.
Bhatia, H.L., Swaroop, K., and Puri, M.C., “A procedure for time minimization transportation problem”, Indian Journal of Pure and Applied Mathematics, 8 (1977) 920- 929.
Haley, K.B, “The solid transportation problem”, Operations Research, (1962) 448-463.
Haley, K.B., “The multi-index problem”, Operations Research, (1963) 368-379.
Hammer, Peter, L., “Time-minimizing transportation problems”, Naval Research Logistics Quarterly, 16 (1969) 345- 357.
Hirsch, W.M., and Dantzig, G.B., “Notes on linear programming: Part XIX, The fixed charge problem”, Rand Research Memorandum No. 1383, Santa Monica, California, 1954.
Kuhn, H., and Baumol, W., "An approximate algorithm for the fixed-charge transportation problem", Naval Research Logistics Quarterly, 9 (1962) 1-15.
Murty, K. G., “Solving the fixed-charge problem by ranking the extreme points”, Operations Research, 16 (1968) 268-279.
Ramakrishnan, C.S, “A note on the time minimizing transportation problem”, Opsearch, 14 (1977) 207-209.
Sadagopan, S., and Ravindran, A., “A vertex ranking algorithm for the fixed-charge transportation problem”, Journal of Optimization Theory and Applications, 37 (1982) 221- 230.
Sandrock, K., “A simple algorithm for solving small fixed-charge transportation problems”, Journal of the Operational Research Society, 39 (1988) 467-475.
Steinberg, D.I., “The fixed-charge problem”, Naval Research Logistics Quarterly, 17 (1970) 217-236.
Szwarc, W., “Some remarks on the time transportation problem”, Naval Research Logistics Quarterly, 18 (1971) 473 - 485.
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