Abstract
In the present paper, a fuzzy programming model with quadratic membership functions has been developed for the solution of a Multi-Objective Transportation problem. In literature, several fuzzy programming approaches exist with various types of membership functions such as linear, exponential, hyperbolic etc. These membership functions are defined, by taking the lower and upper values of the objective functions into account. In some cases, these methods fail to obtain an integer compromise optimal solution. In the present method, two coefficients of the quadratic membership functions are determined by the lower and upper values of the objective functions. The other coefficient is taken as a variable in the fuzzy programming approach. This means that the membership curve is fixed at the two end points and set free in between. Application of the method on numerical examples proved that the approach could generate integer compromise optimal solutions.
Highlights
In the classical transportation problem, unit quantities of a homogeneous product are to be transported from m sources to n destinations in such a way that the total transportation cost is a minimum
A variable xij represents the unknown quantity to be transported from the ith source to the jth destination
Fuzzy programming techniques with hyperbolic and exponential membership functions to obtain optimal compromise solutions of the multi-objective transportation problem (MOTP) were introduced by Verma et al[11]
Summary
In the classical transportation problem, unit quantities of a homogeneous product are to be transported from m sources to n destinations in such a way that the total transportation cost is a minimum. There is a penalty cij associated with transporting a unit of the product from the ith source to the jth destination. In the real world situations, the transportation problem usually involves multiple, incommensurable and conflicting objectives. A. Satyanarayana Murthy solution for MOTP was obtained by Bit.et al[4] using fuzzy programming technique with linear membership functions. Bit.et al[6], have presented an additive fuzzy programming model that considers weights and priorities for all non-equivalent objectives for the MOTP problem. Fuzzy programming techniques with hyperbolic and exponential membership functions to obtain optimal compromise solutions of the MOTP were introduced by Verma et al[11]. A fuzzy programming approach with the linear membership functions to determine the optimal compromise solution of the MOTP was presented by Abd Elwahed [1]. An interactive fuzzy goal programming for multi-objective transportation problems was developed by Abd El-wahed and Lee[2]
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