Abstract
This paper deals with the Multiobjective Linear Transportation Problem that has fuzzy cost coefficients. In the solution procedure, many objectives may conflict with each other; therefore decision‐making process becomes complicated. And also due to the fuzziness in the costs, this problem has a nonlinear structure. In this paper, fuzziness in the objective functions is handled with a fuzzy programming technique in the sense of multiobjective approach. And then we present a compensatory approach to solve Multiobjective Linear Transportation Problem with fuzzy cost coefficients by using Werner′s μand operator. Our approach generates compromise solutions which are both compensatory and Pareto optimal. A numerical example has been provided to illustrate the problem.
Highlights
The classical transportation problem TP is a special type of linear programming problem, and it has wide practical applications in manpower planning, personnel allocation, inventory control, production planning, and so forth
We focus on the solution procedure of the multiobjective linear Transportation Problem MOLTP with fuzzy cost coefficients
A Single Objective Transportation Problem with Fuzzy Cost Coefficients In this paper, we studied MOLTP with crisp supply&demand parameters but fuzzy costs which are given as trapezoidal fuzzy numbers
Summary
The classical transportation problem TP is a special type of linear programming problem, and it has wide practical applications in manpower planning, personnel allocation, inventory control, production planning, and so forth. In real-life situations, it is required to take into account more than one objective to reflect the problem more realistically, and multiobjective transportation problem MOTP becomes more useful These objectives can be quantity of goods delivered, unfulfilled demand, average delivery time of the commodities, reliability of transportation, accessibility to the users, and product deterioration. Ahlatcioglu et al 3 proposed a model for solving the transportation problem whose supply and demand quantities are given as triangular fuzzy numbers bounded from below and above, respectively. Liu and Kao 4 developed a procedure to derive the fuzzy objective value of the fuzzy transportation problem where the cost coefficients, supply and demand quantities are fuzzy numbers. We focus on the solution procedure of the multiobjective linear Transportation Problem MOLTP with fuzzy cost coefficients.
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