Abstract
This paper deals with a capacitated, multi-objective and solid transportation problem with imprecise nature of resources, demands, capacity of conveyance and cost. Here transportation cost is inversely varying with the quantity-to be transported from source to destinations in addition with a fixed per unit cost and a small vehicle cost. The transportation problem has been formulated as a constrained fuzzy non-linear programming problem. Next it is transformed into an equivalent crisp multi-objective problem using fuzzy interval approximation and then solved by Interactive Fuzzy Programming Technique (IFPT) and Generalized Reduced Gradient (GRG) method. An illustrative numerical example is demonstrated to find the optimal solution of the proposed model.
Highlights
The classical transportation problem (Hitchcock transportation problem) is one of the sub-classes of non-linear programming problem in which all the constraints are of equality type
The real life problems are modeled with multi-objective functions which are measured in different respects and they are non-commensurable and conflicting in nature
It is frequently difficult for the decision maker to combine the objective functions in one overall utility function
Summary
The classical transportation problem (Hitchcock transportation problem) is one of the sub-classes of non-linear programming problem in which all the constraints are of equality type. The real life problems are modeled with multi-objective functions which are measured in different respects and they are non-commensurable and conflicting in nature. A capacitated-multi-objective, solid transportation problem is formulated in fuzzy environment with non-linear varying transportation charge and an extra cost for transporting the amount to an interior place through small vehicles (like rickshaw, auto etc.). The fuzzy quantities and parameters are replaced by equivalent nearest interval numbers and a fuzzy multiobjective, capacitated and solid transportation problem is transformed to corresponding crisp multi-objective transportation problems. We find a closed interval Cd( A ) which is nearest to A with respect to metric d It can be done since each interval is a fuzzy number with constant α-cut for all α € [0, 1]. Following ($4) fuzzy numbers a i , b j , e k , C iPjk , and H ijk are approximated to
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