Abstract
The objective of the paper is to deal with a kind of possibilistic linear programming (PLP) problem involving multiple objectives of conflicting nature. In particular, we have considered a multi objective linear programming (MOLP) problem whose objective is to simultaneously minimize cost and maximize profit in a supply chain where cost and profit coefficients, and related parameters such as available supply, forecast demand and budget are fuzzy with trapezoidal fuzzy numbers. An example is given to illustrate the strategy used to solve the aforesaid PLP problem.
Highlights
In a supply chain, a distribution planning decision (DPD) problem involves optimizing the distribution plan for transporting goods from a set of sources to a set of destinations
After the pioneering work on fuzzy linear programming by Zimmermann [3], several kinds of fuzzy linear programming problems have appeared in the literature and different methods have been proposed to solve such problems
We have considered an multi objective linear programming (MOLP) problem whose objective is to simultaneously minimize cost and maximize profit in a supply chain where cost and profit coefficients, and related parameters such as available supply, forecast demand and budget are fuzzy with trapezoidal fuzzy numbers
Summary
A distribution planning decision (DPD) problem involves optimizing the distribution plan for transporting goods from a set of sources to a set of destinations. Lai and Hwang [7] developed an auxiliary MOLP model for solving PLP problems with imprecise objective and/or constraint coefficients with triangular distributions. Tien-Fu Liang [8] integrated the available concepts to solve multi-objective DPD problems involving imprecise available supply, forecast demand and unit cost/time coefficients with triangular possibility distributions. We have considered an MOLP problem whose objective is to simultaneously minimize cost and maximize profit in a supply chain where cost and profit coefficients, and related parameters such as available supply, forecast demand and budget are fuzzy with trapezoidal fuzzy numbers. The proposed methodology can be applied to various real world multi objective problems such as assignment problems, transportation problems and many more such problems in which the information is given in the form of trapezoidal/triangular/interval possibility distributions
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