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. | Yugoslav Journal of Operations Research 16 (2006), Number 2, 189-210 PARADOX IN A NON-LINEAR CAPACITATED TRANSPORTATION PROBLEM Kalpana DAHIYA, Vanita VERMA Department of Mathematics, Panjab University, Chandigarh, India e-mail: kalpana_math@ e-mail: v_verma1@ Received: February 2005 / Accepted: April 2006 Abstract: 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. Keywords: Capacitated transportation problem, paradox, fixed charge. 1. INTRODUCTION The fixed charge transportation problem is an extension of the classical transportation problem in which a fixed cost is incurred for every origin. The fixed charge transportation problem (FCTP) was originally formulated by Hirsch and Dantzig [6]. Sandrock [9] gave a simplex algorithm for solving a FCTP. Basu .[3] gave an algorithm for finding optimal solution of solid-fixed charge transportation problem. Fixed charge transportation problems have been studied by Arora .[2], Thirwani [12] and many others. Many distribution problems in practice can only be modelled as FCTPs. For example, rails, roads and trucks have invariably used freight rates which consists of a fixed cost and a variable cost. The fixed cost may represent the cost of renting a vehicle, landing fees at an airport, set up costs for machines in .
