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Three dimensional fixed charge bi criterion indefinite quadratic transportation problem

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. | Yugoslav Journal of Operations Research 14 (2004), Number 1, 83-97 THREE DIMENSIONAL FIXED CHARGE BI-CRITERION INDEFINITE QUADRATIC TRANSPORTATION PROBLEM* S.R. ARORA Department of Mathematics, Hans Raj College, University of Delhi Delhi-110007, India. srarora@yahoo.com Archana KHURANA Department of Mathematics, University of Delhi, Delhi-110007, India archana2106@rediffmail.com, archana@du.ac.in Received: October 2002 / Accepted: August 2003 Abstract: 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. Keywords: Three dimensional quadratic transportation problem, cost-time trade-off pairs, fixed charge, bi-criterion indefinite quadratic transportation problem 1. INTRODUCTION In the classical transportation problem the cost of transportation is directly proportional to the number of units of the commodity transported. But in real world situations when a commodity is transported, a fixed cost is incurred in the objective function. The fixed cost may represent the cost of renting a vehicle, landing fees in an airport, set up costs for machines in a manufacturing environment etc. * 1991 Mathematics Subject Classification: Primary: 90B06; Secondary: 90C08 84 S.R. Arora, A. Khurana / Three Dimensional Fixed Charge The fixed charge transportation problem was originally formulated by G.B.Dantzig and W. Hirsch [9] in 1954. Then in 1968 K.G.Murty [11] solved the fixed charge problem by ranking the extreme points. After that several .