Paradox in a non-linear capacitated transportation problem
DOI:
https://doi.org/10.2298/YJOR0602189DKeywords:
capacitated transportation problem, paradox, fixed chargeAbstract
This paper discusses a paradox in fixed charge capacitated transportation problem where the objective function is the sum of two linear fractional functions consisting of variables costs and fixed charges respectively. A paradox arises when the transportation problem admits of an objective function value which is lower than the optimal objective function value, by transporting larger quantities of goods over the same route. A sufficient condition for the existence of a paradox is established. Paradoxical range of flow is obtained for any given flow in which the corresponding objective function value is less than the optimum value of the given transportation problem. Numerical illustration is included in support of theory.References
Arora, S.R., Khurana, A. (2004) Three dimensional fixed charge bi-criterion indefinite quadratic transportation problem. Yugoslav Journal of Operations Research, vol. 14, br. 1, str. 83-97
Arora, S.R., Ahuja, A. (2000) A paradox in fixed charge transportation problem. Indian Journal of Pure and Applied Mathematics, 31(7) 809-822
Basu, M., Pal, B.B., Kundu, A. (1994) An algorithm for finding the optimum solution of solid fixed-charge transportation problem. Optimization, 31, 283-291
Bit, A.K., Biswal, M.P., Alam, S.S. (1993) Fuzzy programming technique for multi objective capacitated transportation problem. Journal of Fuzzy Mathematics, 1(2) 367-376
Dinkelbach, W. (1967) On nonlinear fractional programming. Management Science, 13(7) 492-498
Hirsch, W.M., Dantzig, G.B. (1954) Notes on linear programming: Part XIX, the fixed charge problem. u: Rand Research Memorandum, Santa Monica, California, br. 1383
Kassay, F. (1981) Operator method for transportation problem with bounded variables. Skoly Dopravy Spojov v v Ziline Se ria Matematicko-Fyzika lna, 4, 89-98
Murty, K.G. (1976) Linear and combinatorial programming. New York, itd: Wiley
Sandrock, K. (1988) A simple algorithm for solving small fixed-charge transportation problems. Journal of the Operational Research Society, 39, 467-475
Swarup, K. (1966) Transportation technique in linear fractional functions programming. Journal of Royal Naval Scientific Service, 21(5) 256-260
Szwarc, W. (1971) The transportation paradox. Naval Research Logistics Quarterly, 18(2) 185-202
Thirwani, D. (1998) A note on fixed charge bi-criterion transportation problem with enhanced flow. Indian Journal of Pure and Applied Mathematics, 29(5) 565-571
Verma, V., Puri, M.C. (1991) On a paradox in linear fractional transportation problem. u: S.Kumar [ur.] Recent Developments in Australian Society of Operational Research, Gordan and Breach Science Publishers, str. 413-424
Zheng, H.R., Xu, J.M., Hu, Z.M. (1994) Transportation problems with upper limit constraints on the variables and with parameters. Journal of Wuhan University Natural Science Edition, 5 1-5
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